diff --git a/Parameters.md b/Parameters.md index f1f5be8..716566e 100644 --- a/Parameters.md +++ b/Parameters.md @@ -9,7 +9,463 @@ function animation. Some simulations use variants of the published code. The lis updated gradually. -### 28 May 22 - How to make a rocket with Lennard-Jones particles ### +### 25 June 22 - Potential landscape view of the 2D hydrogen atom with zero angular momentum ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(-0.7, 0.0, 3.5, 0.0, 0.15, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 480 /* number of grid points on x axis */ +#define NY 240 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 2 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 15 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000002 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1150 /* number of frames of movie */ +#define NVID 850 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +/* Plot type - color scheme */ + +#define CPLOT 30 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +// #define ZPLOT 30 /* z coordinate in 3D plot */ +// #define ZPLOT_B 32 /* z coordinate in second 3D plot */ +#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 0.5 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 7.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 15.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.075 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.2 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 24 June 22 - Rotating view of waves escaping the Mandelbrot set ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1800 /* number of grid points on x axis */ +#define NY 900 /* number of grid points on y axis */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define XMIN -2.2 +#define XMAX 1.8 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 24 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 1 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 3 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.025 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2100 /* number of frames of movie */ +#define NVID 6 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 103 /* color scheme */ + +#define ZPLOT_B 109 +#define CPLOT_B 109 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.02 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 540.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 2.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 0.2 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 7.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 1000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ +#define LOG_SHIFT -0.5 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 50.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.05 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 23 June 22 - Convection of Lennard-Jones particles ### **Program:** `lennardjones.c` @@ -17,11 +473,10 @@ updated gradually. #define MOVIE 1 /* set to 1 to generate movie */ #define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ -#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ /* so far incompatible with double movie */ #define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ - /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ @@ -32,15 +487,15 @@ updated gradually. #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ -#define INITXMIN -0.7 -#define INITXMAX 0.7 /* x interval for initial condition */ -#define INITYMIN -0.5 -#define INITYMAX 0.5 /* y interval for initial condition */ +#define INITXMIN -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.05 +#define INITYMAX 1.05 /* y interval for initial condition */ #define BCXMIN -2.0 -#define BCXMAX 5.0 /* x interval for boundary condition */ -#define BCYMIN -1.6 -#define BCYMAX 1.6 /* y interval for boundary condition */ +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.125 /* y interval for boundary condition */ #define OBSXMIN -2.0 #define OBSXMAX 2.0 /* x interval for motion of obstacle */ @@ -48,10 +503,10 @@ updated gradually. #define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ #define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 5 /* pattern of repelling segments, see list in global_ljones.c */ +#define ADD_FIXED_SEGMENTS 0 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 9 /* pattern of repelling segments, see list in global_ljones.c */ #define TWO_TYPES 0 /* set to 1 to have two types of particles */ #define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ @@ -67,14 +522,14 @@ updated gradually. #define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ #define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 3.33 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_DISTANCE 4.0 /* minimal distance in Poisson disc process, controls density of particles */ #define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ -#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */ +#define LAMBDA 0.2 /* parameter controlling the dimensions of domain */ #define MU 0.012 /* parameter controlling radius of particles */ -#define MU_B 0.018 /* parameter controlling radius of particles of second type */ -#define NPOLY 18 /* number of sides of polygon */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 20 /* number of sides of polygon */ #define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ @@ -93,10 +548,10 @@ updated gradually. /* Parameters for length and speed of simulation */ -#define NSTEPS 2000 /* number of frames of movie */ -#define NVID 500 /* number of iterations between images displayed on screen */ -#define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 50 /* time after which to start saving frames */ +#define NSTEPS 3000 /* number of frames of movie */ +#define NVID 80 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 100 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 1 /* width of particle boundary */ #define LINK_WIDTH 2 /* width of links between particles */ #define CONTAINER_WIDTH 4 /* width of container boundary */ @@ -110,14 +565,16 @@ updated gradually. /* Boundary conditions, see list in global_ljones.c */ -#define BOUNDARY_COND 3 +#define BOUNDARY_COND 0 /* Plot type, see list in global_ljones.c */ #define PLOT 0 #define PLOT_B 8 /* plot type for second movie */ +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ #define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ /* Color schemes */ @@ -145,38 +602,38 @@ updated gradually. #define PARTICLE_HUE_MIN 359.0 /* color of original particle */ #define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ #define PARTICLE_EMAX 1.0e3 /* energy of particle with hottest color */ -#define HUE_TYPE0 45.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 300.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 300.0 /* hue of particles of type 2 */ -#define HUE_TYPE3 300.0 /* hue of particles of type 3 */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 180.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ #define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ #define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ #define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ #define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 1.0e-1 /* damping coefficient of particles */ -#define PARTICLE_MASS 4.0 /* mass of particle of radius MU */ +#define DAMPING 25.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ #define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ #define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ #define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 10.0 /* initial velocity range */ +#define V_INITIAL 0.0 /* initial velocity range */ #define OMEGA_INITIAL 10.0 /* initial angular velocity range */ #define THERMOSTAT 1 /* set to 1 to switch on thermostat */ #define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ #define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.02 /* initial inverse temperature */ +#define BETA 0.1 /* initial inverse temperature */ #define MU_XI 0.01 /* friction constant in thermostat */ #define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ #define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ -#define GRAVITY 0.0 /* gravity acting on all particles */ +#define NBH_DIST_FACTOR 6.0 /* radius in which to count neighbours */ +#define GRAVITY 1000.0 /* gravity acting on all particles */ #define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ +#define GRAVITY_FACTOR 50.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ #define ROTATION 0 /* set to 1 to include rotation of particles */ #define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ @@ -192,10 +649,10 @@ updated gradually. #define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ #define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 0.025 /* factor by which to change BETA during simulation */ +#define BETA_FACTOR 0.02 /* factor by which to change BETA during simulation */ #define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ #define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ -#define FINAL_CONSTANT_PHASE 1000 /* final phase in which temperature is constant */ +#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ #define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ #define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ @@ -217,8 +674,10 @@ updated gradually. #define N_T_AVERAGE 50 /* size of temperature averaging window */ #define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ #define PARTIAL_THERMO_COUPLING 1 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ -#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_REGION 2 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ #define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ #define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ @@ -228,8 +687,8 @@ updated gradually. #define NPART_BOTTOM 100 /* number of particles at the bottom */ #define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 500 /* time at which to add first particle */ -#define ADD_PERIOD 250 /* time interval between adding further particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ #define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ #define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ @@ -241,16 +700,20 @@ updated gradually. #define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ #define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ -#define PERIOD_ROTATE_BOUNDARY 500 /* period of rotating boundary */ -#define ROTATE_INITIAL_TIME 100 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 365 /* final time without rotation */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ #define PRINT_OMEGA 0 /* set to 1 to print angular speed */ #define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ -#define MOVE_BOUNDARY 1 /* set to 1 to move repelling segments, due to force from particles */ -#define SEGMENTS_MASS 100.0 /* mass of collection of segments */ -#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 5.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 0 /* set to 1 to deactivate last segment after a certain time */ #define SEGMENT_DEACTIVATION_TIME 1000 /* time at which to deactivate last segment */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 -0.75 /* initial position of segments */ #define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ #define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ @@ -258,7 +721,7 @@ updated gradually. #define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ #define RD_TYPES 3 /* number of types in reaction-diffusion equation */ -#define REACTION_PROB 0.03 /* probability controlling reaction term */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ #define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ #define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ @@ -278,8 +741,8 @@ updated gradually. #define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ #define PMAX 1000.0 /* maximal force */ -#define HASHX 100 /* size of hashgrid in x direction */ -#define HASHY 40 /* size of hashgrid in y direction */ +#define HASHX 60 /* size of hashgrid in x direction */ +#define HASHY 30 /* size of hashgrid in y direction */ #define HASHMAX 100 /* maximal number of particles per hashgrid cell */ #define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ @@ -290,2859 +753,11 @@ updated gradually. ``` -### 27 May 22 - Waves radiating from the Mandelbrot set: Index of refraction increasiing with decreasing escape time ### - -**Program:** `wave_3d.c` - -**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 1800 /* number of grid points on x axis */ -#define NY 900 /* number of grid points on y axis */ -#define YMIN -1.041666667 -#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - -#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ - -#define XMIN -2.5 -#define XMAX 1.5 /* x interval */ - -#define JULIA_SCALE 0.8 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 24 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ - -#define VARIABLE_IOR 1 /* set to 1 for a variable index of refraction */ -#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ -#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependece of IoR on Mandelbrot escape speed */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ -#define MU 0.5 /* parameter controlling the dimensions of domain */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 3 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 36 /* number of grid point for grid of disks */ -#define NGRIDY 6 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -2.9 -#define ISO_XSHIFT_RIGHT 1.4 -#define ISO_YSHIFT_LEFT -0.15 -#define ISO_YSHIFT_RIGHT -0.15 -#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ - - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard below */ - -/* Physical parameters of wave equation */ - -#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ -#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ - -#define OMEGA 0.017 /* frequency of periodic excitation */ -#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.025 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-6 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ -#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ -/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ -/* The physical damping coefficient is given by GAMMA/(DT)^2 */ -/* Increasing COURANT speeds up the simulation, but decreases accuracy */ -/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ - -#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ -#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 2 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 2000 /* number of frames of movie */ -#define NVID 6 /* number of iterations between images displayed on screen */ -#define NSEG 1000 /* number of segments of boundary */ -#define INITIAL_TIME 0 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -/* Parameters of initial condition */ - -#define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define ZPLOT 108 /* wave height */ -#define CPLOT 108 /* color scheme */ - -#define ZPLOT_B 109 -#define CPLOT_B 109 /* plot type for second movie */ - - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define FLOOR_ZCOORD 1 /* set to 1 to draw only facets with z not too negative */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ -#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ -#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ - -#define PLOT_SCALE_ENERGY 0.02 /* vertical scaling in energy plot */ -#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - - -/* Color schemes */ - -#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 2.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define VSCALE_ENERGY 7.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 1000.0 /* scaling factor for energy representation */ -#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ -#define LOG_SHIFT -0.5 /* shift of colors on log scale */ -#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ -#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ - -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 15.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 50.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ - -/* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -/* Parameters controlling 3D projection */ - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.05 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D -0.1 /* overall y shift for REP_PROJ_3D representation */ - -``` - -### 26 May 22 - An almost coherent state of the 2D quantum harmonic oscillator ### +### 22 June 22 - Potential landscape view of the 2D hydrogen atom ### **Program:** `rde.c` -**Initial condition in function `animation()`:** `init_coherent_state(-0.75, 0.0, 5.0, -7.0, 0.2, phi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 480 /* number of grid points on x axis */ -#define NY 250 /* number of grid points on y axis */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.041666667 -#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - -/* Choice of simulated equation */ - -#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ -#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ -#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ - -#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ -#define POTENTIAL 1 /* type of potential, see list in global_3d.c */ - -#define JULIA_SCALE 0.5 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ -#define MU 0.1 /* parameter controlling the dimensions of domain */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 5 /* depth of computation of Menger gasket */ -#define MRATIO 5 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 15 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -1.65 -#define ISO_XSHIFT_RIGHT 0.4 -#define ISO_YSHIFT_LEFT -0.05 -#define ISO_YSHIFT_RIGHT -0.05 -#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard in sub_wave.c */ - -/* Physical patameters of wave equation */ - -#define DT 0.00000001 - -#define VISCOSITY 1.0 - -#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ -#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ - -#define EPSILON 0.8 /* time scale separation */ -#define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define K_HARMONIC 1.5 /* spring constant of harmonic potential */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ - -#define T_OUT 2.0 /* outside temperature */ -#define T_IN 0.0 /* inside temperature */ -#define SPEED 0.0 /* speed of drift to the right */ - -#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ - -#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ -#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ -#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ -#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, - for numerical stability */ - -#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ -#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ -#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ -#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ - - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 1 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 1500 /* number of frames of movie */ -#define NVID 1200 /* number of iterations between images displayed on screen */ -#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ -#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ -#define MAX_DT 0.024 /* maximal value of integration step */ -#define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 2 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define INITIAL_TIME 0 /* initial still time */ -#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 50 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ - -/* Plot type - color scheme */ - -#define CPLOT 30 -#define CPLOT_B 31 - -/* Plot type - height of 3D plot */ - -#define ZPLOT 30 /* z coordinate in 3D plot */ -#define ZPLOT_B 30 /* z coordinate in second 3D plot */ - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ -#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ -#define DRAW_OUTSIDE_GRAY 1 /* experimental - draw outside of billiard in gray */ - -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ - -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ -#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ - -#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ -#define FIELD_LINE_WIDTH 1 /* width of field lines */ -#define N_FIELD_LINES 120 /* number of field lines */ -#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ -#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - -/* Color schemes, see list in global_pdes.c */ - -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* black background */ - -#define COLOR_SCHEME 3 /* choice of color scheme */ - -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ -#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define E_SCALE 100.0 /* scaling factor for energy representation */ -#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT 0.0 - -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 5.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -/* only for compatibility with wave_common.c */ -#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OMEGA 0.005 /* frequency of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.03 /* Courant number in medium B */ -#define INITIAL_AMP 0.5 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ -#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -/* end of constants added only for compatibility with wave_common.c */ - - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.5 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ - - -/* For debugging purposes only */ -#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -``` - -### 25 May 22 - A faster-rotating hourglass with Lennard-Jones particles ### - -**Program:** `lennardjones.c` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ - /* so far incompatible with double movie */ -#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ - - -/* General geometrical parameters */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.125 -#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ - -#define INITXMIN -0.7 -#define INITXMAX 0.7 /* x interval for initial condition */ -#define INITYMIN 0.1 -#define INITYMAX 0.6 /* y interval for initial condition */ - -#define BCXMIN -0.7 -#define BCXMAX 0.7 /* x interval for boundary condition */ -#define BCYMIN -0.85 -#define BCYMAX 0.85 /* y interval for boundary condition */ - -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ - -#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ - -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ - -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 2 /* pattern of repelling segments, see list in global_ljones.c */ - -#define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ -#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ -#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ -#define CENTER_PY 0 /* set to 1 to center vertical momentum */ -#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ - -#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ -#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ -#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ -#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 2.75 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ -#define MU 0.013 /* parameter controlling radius of particles */ -#define MU_B 0.018 /* parameter controlling radius of particles of second type */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 4 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 46 /* number of grid point for grid of disks */ -#define NGRIDY 24 /* number of grid point for grid of disks */ -#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ -#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 1915 /* number of frames of movie */ -#define NVID 3250 /* number of iterations between images displayed on screen */ -#define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 0 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of particle boundary */ -#define LINK_WIDTH 2 /* width of links between particles */ -#define CONTAINER_WIDTH 4 /* width of container boundary */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -/* Boundary conditions, see list in global_ljones.c */ - -#define BOUNDARY_COND 0 - -/* Plot type, see list in global_ljones.c */ - -#define PLOT 0 -#define PLOT_B 8 /* plot type for second movie */ - -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ -#define HUE_TYPE0 45.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 300.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 300.0 /* hue of particles of type 2 */ -#define HUE_TYPE3 300.0 /* hue of particles of type 3 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 5.0e-7 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 1.0e2 /* damping coefficient of particles */ -#define PARTICLE_MASS 5.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 10.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ -#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.01 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ -#define GRAVITY 50000.0 /* gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 100.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 0.02 /* factor by which to change BETA during simulation */ -#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ -#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ -#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 500 /* time at which to add first particle */ -#define ADD_PERIOD 250 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define ROTATE_BOUNDARY 1 /* set to 1 to rotate the repelling segments */ -#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ -#define PERIOD_ROTATE_BOUNDARY 500 /* period of rotating boundary */ -#define ROTATE_INITIAL_TIME 50 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 365 /* final time without rotation */ -#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ -#define PRINT_PARTICLE_SPEEDS 1 /* set to 1 to print average speeds/momenta of particles */ - -#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ -#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ -#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ -#define REACTION_PROB 0.03 /* probability controlling reaction term */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ - -#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ - -#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ -#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ -#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_VMAX 100.0 /* max speed of wall */ -#define WALL_TIME 500 /* time during which to keep wall */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e12 /* maximal force */ -#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 40 /* size of hashgrid in x direction */ -#define HASHY 20 /* size of hashgrid in y direction */ -#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -``` - -### 24 May 22 - Waves radiating from the Mandelbrot set: Index of refraction decreasing with escape time ### - -**Program:** `wave_3d.c` - -**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 1800 /* number of grid points on x axis */ -#define NY 900 /* number of grid points on y axis */ - -#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ - -#define XMIN -2.5 -#define XMAX 1.5 /* x interval */ -#define YMIN -1.125 -#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ - -#define JULIA_SCALE 0.8 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 24 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ - -#define VARIABLE_IOR 1 /* set to 1 for a variable index of refraction */ -#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ -#define MANDEL_IOR_SCALE 0.02 /* parameter controlling dependece of IoR on Mandelbrot escape speed */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ -#define MU 0.5 /* parameter controlling the dimensions of domain */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 3 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 36 /* number of grid point for grid of disks */ -#define NGRIDY 6 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -2.9 -#define ISO_XSHIFT_RIGHT 1.4 -#define ISO_YSHIFT_LEFT -0.15 -#define ISO_YSHIFT_RIGHT -0.15 -#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ - - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard below */ - -/* Physical parameters of wave equation */ - -#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ -#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ - -#define OMEGA 0.017 /* frequency of periodic excitation */ -#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.025 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-6 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ -#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ -/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ -/* The physical damping coefficient is given by GAMMA/(DT)^2 */ -/* Increasing COURANT speeds up the simulation, but decreases accuracy */ -/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ - -#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ -#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 2 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 1600 /* number of frames of movie */ -#define NVID 6 /* number of iterations between images displayed on screen */ -#define NSEG 1000 /* number of segments of boundary */ -#define INITIAL_TIME 0 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -/* Parameters of initial condition */ - -#define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define ZPLOT 108 /* wave height */ -#define CPLOT 108 /* color scheme */ - -#define ZPLOT_B 109 -#define CPLOT_B 109 /* plot type for second movie */ - - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define FLOOR_ZCOORD 1 /* set to 1 to draw only facets with z not too negative */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ -#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ -#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ - -#define PLOT_SCALE_ENERGY 0.02 /* vertical scaling in energy plot */ -#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - -/* Color schemes */ - -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 12 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 2.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define VSCALE_ENERGY 10.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 1000.0 /* scaling factor for energy representation */ -#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ -#define LOG_SHIFT -0.5 /* shift of colors on log scale */ -#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ -#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ - -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 15.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 50.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ - -/* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -/* Parameters controlling 3D projection */ - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.07 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D -0.1 /* overall y shift for REP_PROJ_3D representation */ - -``` - -### 23 May 22 - A quantum Ehrenfest model, in 3D ### - -**Program:** `rde.c` - -**Initial condition in function `animation()`:** `init_coherent_state(-1.0, 0.0, 20.0, -5.0, 0.15, phi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 600 /* number of grid points on x axis */ -#define NY 300 /* number of grid points on y axis */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.041666667 -#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - -/* Choice of simulated equation */ - -#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ -#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ -#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ - -#define JULIA_SCALE 0.5 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 11 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ -#define MU 0.1 /* parameter controlling the dimensions of domain */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 5 /* depth of computation of Menger gasket */ -#define MRATIO 5 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 15 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -1.65 -#define ISO_XSHIFT_RIGHT 0.4 -#define ISO_YSHIFT_LEFT -0.05 -#define ISO_YSHIFT_RIGHT -0.05 -#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard in sub_wave.c */ - -/* Physical patameters of wave equation */ - -#define DT 0.00000002 - -#define VISCOSITY 1.0 - -#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ -#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ - -#define EPSILON 0.8 /* time scale separation */ -#define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ - -#define T_OUT 2.0 /* outside temperature */ -#define T_IN 0.0 /* inside temperature */ -#define SPEED 0.0 /* speed of drift to the right */ - -#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ - -#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ -#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ -#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ -#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, - for numerical stability */ - -#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ -#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ -#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ -#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ - - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 1 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 2500 /* number of frames of movie */ -#define NVID 500 /* number of iterations between images displayed on screen */ -#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ -#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ -#define MAX_DT 0.024 /* maximal value of integration step */ -#define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 2 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define INITIAL_TIME 0 /* initial still time */ -#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 50 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ - -/* Plot type - color scheme */ - -#define CPLOT 30 -#define CPLOT_B 31 - -/* Plot type - height of 3D plot */ - -#define ZPLOT 30 /* z coordinate in 3D plot */ -#define ZPLOT_B 30 /* z coordinate in second 3D plot */ - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ -#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ -#define DRAW_OUTSIDE_GRAY 1 /* experimental - draw outside of billiard in gray */ - -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ - -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ -#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ - -#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ -#define FIELD_LINE_WIDTH 1 /* width of field lines */ -#define N_FIELD_LINES 120 /* number of field lines */ -#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ -#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - -/* Color schemes, see list in global_pdes.c */ - -#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* black background */ - -#define COLOR_SCHEME 3 /* choice of color scheme */ - -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 35.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ -#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define E_SCALE 100.0 /* scaling factor for energy representation */ -#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT 0.0 - -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -/* only for compatibility with wave_common.c */ -#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OMEGA 0.005 /* frequency of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.03 /* Courant number in medium B */ -#define INITIAL_AMP 0.5 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ -#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -/* end of constants added only for compatibility with wave_common.c */ - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 1.0 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ - -/* For debugging purposes only */ -#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -``` - -### 22 May 22 - A centrifuge without thermostat, and without gravity ### - -**Program:** `lennardjones.c` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ - /* so far incompatible with double movie */ -#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ - - -/* General geometrical parameters */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.125 -#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ - -#define INITXMIN -0.65 -#define INITXMAX 0.65 /* x interval for initial condition */ -#define INITYMIN -0.65 -#define INITYMAX 0.65 /* y interval for initial condition */ - -#define BCXMIN -2.0 -#define BCXMAX 2.0 /* x interval for boundary condition */ -#define BCYMIN -1.125 -#define BCYMAX 1.125 /* y interval for boundary condition */ - -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ - -#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ - -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ - -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 4 /* pattern of repelling segments, see list in global_ljones.c */ - -#define TWO_TYPES 1 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ -#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ -#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ -#define CENTER_PY 0 /* set to 1 to center vertical momentum */ -#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ - -#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ -#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ -#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ -#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 3.75 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 0.05 /* parameter controlling the dimensions of domain */ -#define MU 0.012 /* parameter controlling radius of particles */ -#define MU_B 0.018 /* parameter controlling radius of particles of second type */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 4 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 46 /* number of grid point for grid of disks */ -#define NGRIDY 24 /* number of grid point for grid of disks */ -#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ -#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 3850 /* number of frames of movie */ -#define NVID 300 /* number of iterations between images displayed on screen */ -#define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 100 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of particle boundary */ -#define LINK_WIDTH 2 /* width of links between particles */ -#define CONTAINER_WIDTH 4 /* width of container boundary */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -/* Boundary conditions, see list in global_ljones.c */ - -#define BOUNDARY_COND 3 - -/* Plot type, see list in global_ljones.c */ - -#define PLOT 5 -#define PLOT_B 8 /* plot type for second movie */ - -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ -#define HUE_TYPE0 45.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 300.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 300.0 /* hue of particles of type 2 */ -#define HUE_TYPE3 300.0 /* hue of particles of type 3 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 1.0e-6 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 1.0e2 /* damping coefficient of particles */ -#define PARTICLE_MASS 5.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 10.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ -#define VARY_THERMOSTAT 1 /* set to 1 for time-dependent thermostat schedule */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.1 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ -#define GRAVITY 0.0 /* gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 100.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 0.02 /* factor by which to change BETA during simulation */ -#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ -#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ -#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 500 /* time at which to add first particle */ -#define ADD_PERIOD 250 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define ROTATE_BOUNDARY 1 /* set to 1 to rotate the repelling segments */ -#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ -#define PERIOD_ROTATE_BOUNDARY 3350 /* period of rotating boundary */ -#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 500 /* final time without rotation */ -#define PRINT_OMEGA 1 /* set to 1 to print angular speed */ - -#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ -#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ -#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ -#define REACTION_PROB 0.03 /* probability controlling reaction term */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ - -#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ - -#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ -#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ -#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_VMAX 100.0 /* max speed of wall */ -#define WALL_TIME 500 /* time during which to keep wall */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e12 /* maximal force */ -#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 40 /* size of hashgrid in x direction */ -#define HASHY 20 /* size of hashgrid in y direction */ -#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -``` - -### 21 May 22 - Transition from 3-branched to 5-branched spirals in the Rock-Paper-Scissors-Lizard-Spock equation ### - -**Program:** `rde.c` - -**Initial condition in function `animation()`:** `init_random(0.5, 0.4, phi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 1920 /* number of grid points on x axis */ -#define NY 1000 /* number of grid points on y axis */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.041666667 -#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - -/* Choice of simulated equation */ - -#define RDE_EQUATION 41 /* choice of reaction term, see list in global_3d.c */ -#define NFIELDS 5 /* number of fields in reaction-diffusion equation */ -#define NLAPLACIANS 5 /* number of fields for which to compute Laplacian */ - -#define JULIA_SCALE 0.5 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ -#define MU 0.06 /* parameter controlling the dimensions of domain */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 5 /* depth of computation of Menger gasket */ -#define MRATIO 5 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 15 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -1.65 -#define ISO_XSHIFT_RIGHT 0.4 -#define ISO_YSHIFT_LEFT -0.05 -#define ISO_YSHIFT_RIGHT -0.05 -#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard in sub_wave.c */ - -/* Physical patameters of wave equation */ - -#define DT 0.0000005 -#define VISCOSITY 1.0 - -#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ -#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ - -#define EPSILON 0.8 /* time scale separation */ -#define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ - -#define T_OUT 2.0 /* outside temperature */ -#define T_IN 0.0 /* inside temperature */ -#define SPEED 0.0 /* speed of drift to the right */ - -#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ - -#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ -#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ -#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ -#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, - for numerical stability */ - -#define CHANGE_RPSLZB 1 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ -#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ -#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ -#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ - - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 1 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 2500 /* number of frames of movie */ -#define NVID 12 /* number of iterations between images displayed on screen */ -#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ -#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ -#define MAX_DT 0.024 /* maximal value of integration step */ -#define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 2 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define INITIAL_TIME 0 /* initial still time */ -#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -#define PLOT_3D 0 /* controls whether plot is 2D or 3D */ - -/* Plot type - color scheme */ - -#define CPLOT 40 -#define CPLOT_B 42 - -/* Plot type - height of 3D plot */ - -#define ZPLOT 42 /* z coordinate in 3D plot */ -#define ZPLOT_B 42 /* z coordinate in second 3D plot */ - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ -#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ - -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ - -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ -#define PRINT_RPSLZB 1 /* set to 1 to print rpslzb parameter */ - -#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ -#define FIELD_LINE_WIDTH 1 /* width of field lines */ -#define N_FIELD_LINES 120 /* number of field lines */ -#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ -#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - -/* Color schemes, see list in global_pdes.c */ - -#define COLOR_PALETTE 0 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 18 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* black background */ - -#define COLOR_SCHEME 3 /* choice of color scheme */ - -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ -#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define E_SCALE 100.0 /* scaling factor for energy representation */ -#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT 0.0 - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 0.55 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -/* only for compatibility with wave_common.c */ -#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OMEGA 0.005 /* frequency of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.03 /* Courant number in medium B */ -#define INITIAL_AMP 0.5 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ -#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -/* end of constants added only for compatibility with wave_common.c */ - - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.001 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.05 /* overall y shift for REP_PROJ_3D representation */ - - -/* For debugging purposes only */ -#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -``` - -### 20 May 22 - Quantum Sinai billiard: Wave function of a particle colliding with a circular obstacle ### - -**Program:** `rde.c` - -**Initial condition in function `animation()`:** `init_coherent_state(-0.7, 0.0, 15.0, 0.0, 0.15, phi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1000 /* window width */ -#define WINHEIGHT 1000 /* window height */ - -#define NX 650 /* number of grid points on x axis */ -#define NY 650 /* number of grid points on y axis */ - -#define XMIN -1.125 -#define XMAX 1.125 /* x interval */ -#define YMIN -1.125 -#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ - -/* Choice of simulated equation */ - -#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ -#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ -#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ - -#define JULIA_SCALE 0.5 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 3 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 0.15 /* parameter controlling the dimensions of domain */ -#define MU 0.06 /* parameter controlling the dimensions of domain */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 5 /* depth of computation of Menger gasket */ -#define MRATIO 5 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 15 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -1.65 -#define ISO_XSHIFT_RIGHT 0.4 -#define ISO_YSHIFT_LEFT -0.05 -#define ISO_YSHIFT_RIGHT -0.05 -#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard in sub_wave.c */ - -/* Physical patameters of wave equation */ - -#define DT 0.00000001 - -#define VISCOSITY 1.0 - -#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ -#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ - -#define EPSILON 0.8 /* time scale separation */ -#define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ - -#define T_OUT 2.0 /* outside temperature */ -#define T_IN 0.0 /* inside temperature */ -#define SPEED 0.0 /* speed of drift to the right */ - -#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ - -#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ -#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ -#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ -#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, - for numerical stability */ - -#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ -#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ -#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ -#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ - - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 1 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 600 /* number of frames of movie */ -#define NVID 550 /* number of iterations between images displayed on screen */ -#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ -#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ -#define MAX_DT 0.024 /* maximal value of integration step */ -#define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 2 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define INITIAL_TIME 0 /* initial still time */ -#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 50 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ - -/* Plot type - color scheme */ - -#define CPLOT 30 -#define CPLOT_B 31 - -/* Plot type - height of 3D plot */ - -#define ZPLOT 30 /* z coordinate in 3D plot */ -#define ZPLOT_B 30 /* z coordinate in second 3D plot */ - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ -#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ -#define DRAW_OUTSIDE_GRAY 1 /* experimental - draw outside of billiard in gray */ - -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ - -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ -#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ - -#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ -#define FIELD_LINE_WIDTH 1 /* width of field lines */ -#define N_FIELD_LINES 120 /* number of field lines */ -#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ -#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - -/* Color schemes, see list in global_pdes.c */ - -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 18 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* black background */ - -#define COLOR_SCHEME 3 /* choice of color scheme */ - -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 15.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ -#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define E_SCALE 100.0 /* scaling factor for energy representation */ -#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT 0.0 - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 0.55 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -/* only for compatibility with wave_common.c */ -#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OMEGA 0.005 /* frequency of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.03 /* Courant number in medium B */ -#define INITIAL_AMP 0.5 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ -#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -/* end of constants added only for compatibility with wave_common.c */ - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 1.0 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ - -/* For debugging purposes only */ -#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -``` - -### 19 May 22 - A centrifuge ### - -**Program:** `lennardjones.c` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ - /* so far incompatible with double movie */ -#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ - - -/* General geometrical parameters */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.125 -#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ - -#define INITXMIN -0.65 -#define INITXMAX 0.65 /* x interval for initial condition */ -#define INITYMIN -0.65 -#define INITYMAX 0.65 /* y interval for initial condition */ - -#define BCXMIN -2.0 -#define BCXMAX 2.0 /* x interval for boundary condition */ -#define BCYMIN -1.125 -#define BCYMAX 1.125 /* y interval for boundary condition */ - -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ - -#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ - -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ - -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 4 /* pattern of repelling segments, see list in global_ljones.c */ - -#define TWO_TYPES 1 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ -#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ -#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ -#define CENTER_PY 0 /* set to 1 to center vertical momentum */ -#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ - -#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ -#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ -#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ -#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 3.75 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 0.05 /* parameter controlling the dimensions of domain */ -#define MU 0.012 /* parameter controlling radius of particles */ -#define MU_B 0.018 /* parameter controlling radius of particles of second type */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 4 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 46 /* number of grid point for grid of disks */ -#define NGRIDY 24 /* number of grid point for grid of disks */ -#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ -#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 4100 /* number of frames of movie */ -#define NVID 300 /* number of iterations between images displayed on screen */ -#define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 100 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of particle boundary */ -#define LINK_WIDTH 2 /* width of links between particles */ -#define CONTAINER_WIDTH 4 /* width of container boundary */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -/* Boundary conditions, see list in global_ljones.c */ - -#define BOUNDARY_COND 3 - -/* Plot type, see list in global_ljones.c */ - -#define PLOT 5 -#define PLOT_B 8 /* plot type for second movie */ - -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ -#define HUE_TYPE0 60.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 260.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 220.0 /* hue of particles of type 2 */ -#define HUE_TYPE3 220.0 /* hue of particles of type 3 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 1.0e-6 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 0.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 5.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 10.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.1 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ -#define GRAVITY 5000.0 /* gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 100.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 0.02 /* factor by which to change BETA during simulation */ -#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ -#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ -#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 500 /* time at which to add first particle */ -#define ADD_PERIOD 250 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define ROTATE_BOUNDARY 1 /* set to 1 to rotate the repelling segments */ -#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ -#define PERIOD_ROTATE_BOUNDARY 3600 /* period of rotating boundary */ -#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 500 /* final time without rotation */ -#define PRINT_OMEGA 1 /* set to 1 to print angular speed */ - -#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ -#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ -#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ -#define REACTION_PROB 0.03 /* probability controlling reaction term */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ - -#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ - -#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ -#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ -#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_VMAX 100.0 /* max speed of wall */ -#define WALL_TIME 500 /* time during which to keep wall */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e12 /* maximal force */ -#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 40 /* size of hashgrid in x direction */ -#define HASHY 20 /* size of hashgrid in y direction */ -#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -``` - -### 18 May 22 - A Rock-Paper-Scissors-Lizard-Spock reaction-diffusion equation ### - -**Program:** `rde.c` - -**Initial condition in function `animation()`:** `init_random(0.5, 0.4, phi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 1920 /* number of grid points on x axis */ -#define NY 1000 /* number of grid points on y axis */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.041666667 -#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - -/* Choice of simulated equation */ - -#define RDE_EQUATION 41 /* choice of reaction term, see list in global_3d.c */ -#define NFIELDS 5 /* number of fields in reaction-diffusion equation */ -#define NLAPLACIANS 5 /* number of fields for which to compute Laplacian */ - -#define JULIA_SCALE 0.5 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ -#define MU 0.06 /* parameter controlling the dimensions of domain */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 5 /* depth of computation of Menger gasket */ -#define MRATIO 5 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 15 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -1.65 -#define ISO_XSHIFT_RIGHT 0.4 -#define ISO_YSHIFT_LEFT -0.05 -#define ISO_YSHIFT_RIGHT -0.05 -#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard in sub_wave.c */ - -/* Physical patameters of wave equation */ - -#define DT 0.0000005 -#define VISCOSITY 0.05 - -#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ -#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ - -#define EPSILON 0.8 /* time scale separation */ -#define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ - -#define T_OUT 2.0 /* outside temperature */ -#define T_IN 0.0 /* inside temperature */ -#define SPEED 0.0 /* speed of drift to the right */ - -#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ - -#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 1 /* set to 1 to decrease integration step when viscosity increases */ -#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ -#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ -#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, - for numerical stability */ - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 1 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 2000 /* number of frames of movie */ -#define NVID 12 /* number of iterations between images displayed on screen */ -#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ -#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ -#define MAX_DT 0.024 /* maximal value of integration step */ -#define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 2 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define INITIAL_TIME 0 /* initial still time */ -#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -#define PLOT_3D 0 /* controls whether plot is 2D or 3D */ - -/* Plot type - color scheme */ - -#define CPLOT 40 -#define CPLOT_B 42 - -/* Plot type - height of 3D plot */ - -#define ZPLOT 41 /* z coordinate in 3D plot */ -#define ZPLOT_B 42 /* z coordinate in second 3D plot */ - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ -#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ - -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ - -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ - -#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ -#define FIELD_LINE_WIDTH 1 /* width of field lines */ -#define N_FIELD_LINES 120 /* number of field lines */ -#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ -#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - -/* Color schemes, see list in global_pdes.c */ - -#define COLOR_PALETTE 0 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 18 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* black background */ - -#define COLOR_SCHEME 3 /* choice of color scheme */ - -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ -#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define E_SCALE 100.0 /* scaling factor for energy representation */ -#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT 0.0 - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 0.55 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -/* only for compatibility with wave_common.c */ -#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OMEGA 0.005 /* frequency of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.03 /* Courant number in medium B */ -#define INITIAL_AMP 0.5 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ -#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -/* end of constants added only for compatibility with wave_common.c */ - - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.05 /* overall y shift for REP_PROJ_3D representation */ - - -/* For debugging purposes only */ -#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -``` - -### 17 May 22 - Average energy of waves radiating from a von Koch snowflake ### - -**Program:** `wave_3d.c` - -**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 1200 /* number of grid points on x axis */ -#define NY 1200 /* number of grid points on y axis */ - -#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ - -#define XMIN -1.5 -#define XMAX 1.5 /* x interval */ -#define YMIN -1.5 -#define YMAX 1.5 /* y interval for 9/16 aspect ratio */ - -#define JULIA_SCALE 0.8 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 41 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ -#define MU 0.5 /* parameter controlling the dimensions of domain */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 7 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 36 /* number of grid point for grid of disks */ -#define NGRIDY 6 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -2.9 -#define ISO_XSHIFT_RIGHT 1.4 -#define ISO_YSHIFT_LEFT -0.15 -#define ISO_YSHIFT_RIGHT -0.15 -#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ - - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard below */ - -/* Physical parameters of wave equation */ - -#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ -#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ - -#define OMEGA 0.017 /* frequency of periodic excitation */ -#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ -#define COURANT 0.1 /* Courant number */ -#define COURANTB 0.025 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 2.0e-4 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ -#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ -/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ -/* The physical damping coefficient is given by GAMMA/(DT)^2 */ -/* Increasing COURANT speeds up the simulation, but decreases accuracy */ -/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ - -#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ -#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 2 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 1500 /* number of frames of movie */ -#define NVID 6 /* number of iterations between images displayed on screen */ -#define NSEG 1000 /* number of segments of boundary */ -#define INITIAL_TIME 0 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -/* Parameters of initial condition */ - -#define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define ZPLOT 108 /* wave height */ -#define CPLOT 108 /* color scheme */ - -#define ZPLOT_B 109 -#define CPLOT_B 109 /* plot type for second movie */ - - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define FLOOR_ZCOORD 1 /* set to 1 to draw only facets with z not too negative */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ -#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ - -#define PLOT_SCALE_ENERGY 0.02 /* vertical scaling in energy plot */ -#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - - -/* Color schemes */ - -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 12 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define VSCALE_ENERGY 10.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 1000.0 /* scaling factor for energy representation */ -#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ -#define LOG_SHIFT -0.0 /* shift of colors on log scale */ -#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ -#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ - -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 30.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 150.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ - -/* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -/* Parameters controlling 3D projection */ - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.07 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.5 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ - -``` - -### 16 May 22 - Lennard-Jones particles of increasing temperature approximating the Rock-Paper-Scissors system ### - -**Program:** `lennardjones.c` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ - /* so far incompatible with double movie */ -#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ - - -/* General geometrical parameters */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.125 -#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ - -#define INITXMIN -1.95 -#define INITXMAX 1.95 /* x interval for initial condition */ -#define INITYMIN -1.075 -#define INITYMAX 1.075 /* y interval for initial condition */ - -#define BCXMIN -2.0 -#define BCXMAX 2.0 /* x interval for boundary condition */ -#define BCYMIN -1.125 -#define BCYMAX 1.125 /* y interval for boundary condition */ - -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ - -#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ - -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ - -#define ADD_FIXED_SEGMENTS 0 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 2 /* pattern of repelling segments, see list in global_ljones.c */ - -#define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ -#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ -#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ -#define CENTER_PY 0 /* set to 1 to center vertical momentum */ -#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ - -#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ -#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ -#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ -#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ -#define MU 0.012 /* parameter controlling radius of particles */ -#define MU_B 0.0254 /* parameter controlling radius of particles of second type */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 4 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 46 /* number of grid point for grid of disks */ -#define NGRIDY 24 /* number of grid point for grid of disks */ -#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ -#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 1600 /* number of frames of movie */ -#define NVID 300 /* number of iterations between images displayed on screen */ -#define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 0 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of particle boundary */ -#define LINK_WIDTH 2 /* width of links between particles */ -#define CONTAINER_WIDTH 4 /* width of container boundary */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -/* Boundary conditions, see list in global_ljones.c */ - -#define BOUNDARY_COND 3 - -/* Plot type, see list in global_ljones.c */ - -#define PLOT 5 -#define PLOT_B 9 /* plot type for second movie */ - -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ -#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 180.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ -#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 1.0e-6 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 0.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 10.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 10.0 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 5.0e9 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 5.0e9 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ -#define GRAVITY 0.0 /* gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 100.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 0.02 /* factor by which to change BETA during simulation */ -#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ -#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ -#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 500 /* time at which to add first particle */ -#define ADD_PERIOD 250 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ -#define PERIOD_ROTATE_BOUNDARY 2500 /* period of rotating boundary */ -#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 500 /* final time without rotation */ - -#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ -#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define REACTION_DIFFUSION 1 /* set to 1 to simulate a chemical reaction (particles may change type) */ -#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ -#define REACTION_PROB 0.03 /* probability controlling reaction term */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ - -#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ - -#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ -#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ -#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_VMAX 100.0 /* max speed of wall */ -#define WALL_TIME 500 /* time during which to keep wall */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e9 /* maximal force */ -#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 100 /* size of hashgrid in x direction */ -#define HASHY 50 /* size of hashgrid in y direction */ -#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -``` - -### 15 May 22 - A scarred solution of Schrödinger’s equation in a stadium, rendered in 3D ### - -**Program:** `rde.c` - -**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 0.0, 15.0, 0.4, phi, xy_in);` +**Initial condition in function `animation()`:** `init_coherent_state(-0.7, 0.0, 0.0, -5.0, 0.15, phi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ @@ -3166,11 +781,14 @@ double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define NFIELDS 2 /* number of fields in reaction-diffusion equation */ #define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 2 /* type of potential, see list in global_3d.c */ + #define JULIA_SCALE 0.5 /* scaling for Julia sets */ /* Choice of the billiard table */ -#define B_DOMAIN 2 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ @@ -3178,11 +796,11 @@ double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ -#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ -#define MU 0.06 /* parameter controlling the dimensions of domain */ +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ #define NPOLY 6 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define APOLY 0.333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ #define MRATIO 5 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ @@ -3208,30 +826,42 @@ double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define DT 0.00000002 -#define VISCOSITY 0.1 +#define VISCOSITY 2.0 #define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ #define EPSILON 0.8 /* time scale separation */ #define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ #define T_OUT 2.0 /* outside temperature */ #define T_IN 0.0 /* inside temperature */ #define SPEED 0.0 /* speed of drift to the right */ #define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ #define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 1 /* set to 1 to decrease integration step when viscosity increases */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ #define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ #define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ #define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + /* Boundary conditions, see list in global_pdes.c */ @@ -3239,13 +869,13 @@ double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Parameters for length and speed of simulation */ -#define NSTEPS 3000 /* number of frames of movie */ -#define NVID 1000 /* number of iterations between images displayed on screen */ +#define NSTEPS 1250 /* number of frames of movie */ +#define NVID 850 /* number of iterations between images displayed on screen */ #define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ #define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ #define MAX_DT 0.024 /* maximal value of integration step */ #define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ +#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ #define PAUSE 100 /* number of frames after which to pause */ #define PSLEEP 2 /* sleep time during pause */ @@ -3253,7 +883,7 @@ double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define SLEEP2 1 /* final sleeping time */ #define INITIAL_TIME 0 /* initial still time */ #define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ #define FADE 1 /* set to 1 to fade at end of movie */ #define PLOT_3D 1 /* controls whether plot is 2D or 3D */ @@ -3265,7 +895,7 @@ double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Plot type - height of 3D plot */ -#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT 30 /* z coordinate in 3D plot */ #define ZPLOT_B 30 /* z coordinate in second 3D plot */ #define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ @@ -3273,11 +903,17 @@ double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ #define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ #define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 0.5 /* constant in front of added potential */ #define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ #define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ #define FIELD_LINE_WIDTH 1 /* width of field lines */ @@ -3296,22 +932,23 @@ double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Color schemes, see list in global_pdes.c */ -#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 0 /* Color palette, see list in global_pdes.c */ #define BLACK 1 /* black background */ #define COLOR_SCHEME 3 /* choice of color scheme */ -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 7.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define CURL_SCALE 0.000015 /* scaling factor for curl representation */ #define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ -#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define SLOPE_SCHROD_LUM 100.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.075 /* minimal luminosity in color scheme Z_ARGUMENT*/ #define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ #define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ @@ -3323,9 +960,9 @@ double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define LOG_SCALE 1.0 /* scaling factor for energy log representation */ #define LOG_SHIFT 0.0 -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 0.55 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ #define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ /* only for compatibility with wave_common.c */ @@ -3346,22 +983,2048 @@ double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_ double v_3d[2] = {-0.75, -0.45}; double w_3d[2] = {0.0, 0.015}; double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ -#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ #define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.05 /* overall y shift for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.2 /* overall y shift for REP_PROJ_3D representation */ /* For debugging purposes only */ #define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ +#define VMAX 2.0 /* max value of wave amplitude */ ``` -### 14 May 22 - Average energy of a wave in an anechoic chamber (3D representation) ### +### 21 June 22 - Flying around Olympus Mons: Rotating view of waves escaping a sunflower ring of obstacles ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1400 /* number of grid points on x axis */ +#define NY 1400 /* number of grid points on y axis */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define XMIN -1.5 +#define XMAX 1.5 /* x interval */ +#define YMIN -1.5 +#define YMAX 1.5 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 100 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.03 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 3 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 12 /* number of grid point for grid of disks */ +#define NGRIDY 15 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.0075 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.1 /* Courant number */ +#define COURANTB 0.04 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-1 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 8 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.05 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 108 /* wave height */ +#define CPLOT 108 /* color scheme */ + +#define ZPLOT_B 109 +#define CPLOT_B 109 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 3.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 540.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.25 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 100.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 500.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 50.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 50.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 15.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.05 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 20 June 22 - Lennard-Jones particles with Rock-Paper-Scissors dynamics, with time lapse ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.05 +#define INITYMAX 1.05 /* y interval for initial condition */ + +#define BCXMIN -2.0 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.125 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 0 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 9 /* pattern of repelling segments, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.2 /* parameter controlling the dimensions of domain */ +#define MU 0.01 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 20 /* number of sides of polygon */ +#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3000 /* number of frames of movie */ +#define NVID 80 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 100 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 3 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 5 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 1 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 180.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 20.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 10.0 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 6.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_FACTOR 50.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.002 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 5.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 0 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 1000 /* time at which to deactivate last segment */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 -0.75 /* initial position of segments */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 1 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 100 /* size of hashgrid in x direction */ +#define HASHY 50 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 19 June 22 - A quantum particle in a periodic egg carton potential ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(-0.5, 0.0, 1.5, 0.0, 0.1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 640 /* number of grid points on x axis */ +#define NY 360 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 3 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 15 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000001 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1100 /* number of frames of movie */ +#define NVID 1250 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +/* Plot type - color scheme */ + +#define CPLOT 32 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 32 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 1.0 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 0 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 5.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 25.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 18 June 22 - A randomized square grid wave protection, 3D plot ### + +**Program:** `waves_3d.c` + +**Initial condition in function `animation()`:** `init_wave_flat_mod(phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1800 /* number of grid points on x axis */ +#define NY 900 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 2 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 100 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependece of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */ +#define MU 0.028 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 3 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 12 /* number of grid point for grid of disks */ +#define NGRIDY 15 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.0075 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.06 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 2.0e-3 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1500 /* number of frames of movie */ +#define NVID 7 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.01 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 103 /* color scheme */ + +#define ZPLOT_B 108 +#define CPLOT_B 108 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + + +/* Color schemes */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.5 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 150.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 2000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ +#define LOG_SHIFT -0.5 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 30.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.1 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 1.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 17 June 22 - A rotating beam in Tokarsky's paper windmill room ### + +**Program:** `particle_trajectory.c` + +**Initial condition in function `animation()`:** +``` + time = (double)i/(double)(NSTEPS-1); + x = 0.0; + y = 0.0; + alpha = time*DPI; + period = compute_trajectories_xy(x, y, alpha, alpha + DPI, configs, trajectory, traj_length); +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -1.3 +#define XMAX 2.7 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ + +/* Choice of the billiard table, see global_particles.c */ + +#define B_DOMAIN 30 /* choice of domain shape */ + +#define CIRCLE_PATTERN 6 /* pattern of circles */ +#define POLYLINE_PATTERN 8 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 10000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 10000 /* total number of sides of polygonal line */ +#define NCX 9 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 4 /* Sierpinski gastket depth */ + +#define LAMBDA 0.8 /* parameter controlling shape of domain */ +#define MU 0.01 /* second parameter controlling shape of billiard */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NPOLY 7 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ +#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ + +#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ +#define DEBUG 0 /* draw trajectories, for debugging purposes */ + +/* Simulation parameters */ + +#define NPART 1 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define TRAJ_LENGTH 256 /* length of trajectory */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 1 /* set to 1 to show zoom on specific area */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ +#define PRINT_TRAJECTORY_LENGTH 1 /* set to 1 to print length of trajectory 0 */ +#define PRINT_TRAJECTORY_PERIOD 0 /* set to 1 to print period of trajectory 0 */ +#define DRAW_LENGTHS_PLOT 1 /* set to 1 to plot trajectory lengths */ + +#define NSTEPS 7200 /* number of frames of movie */ +#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.00001 /* integration step */ +#define NVID 150 /* number of iterations between images displayed on screen */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 64 /* number of colors */ +#define COLORSHIFT 0 /* hue of initial color */ +#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ +#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ +#define NSEG 100 /* number of segments of boundary */ +#define LENGTH 0.03 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 2 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define END_FRAMES 100 /* number of frames at end of movie */ + +``` + +### 16 June 22 - Quantum snowflake: Schrödinger’s equation in a von Koch fractal ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 5.0, 0.0, 0.15, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 640 /* number of grid points on x axis */ +#define NY 360 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 2 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 41 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 15 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.000000013 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.5 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1700 /* number of frames of movie */ +#define NVID 1400 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +/* Plot type - color scheme */ + +#define CPLOT 32 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 32 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 0 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 3.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 25.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {4.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D -0.1 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 15 June 22 - A triangular grid wave protection, 3D plot ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_wave_flat_mod(phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1800 /* number of grid points on x axis */ +#define NY 900 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 1 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 100 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependece of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */ +#define MU 0.028 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 3 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 12 /* number of grid point for grid of disks */ +#define NGRIDY 15 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.0075 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.06 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 2.0e-3 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1600 /* number of frames of movie */ +#define NVID 7 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.01 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 103 /* color scheme */ + +#define ZPLOT_B 108 +#define CPLOT_B 108 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + + +/* Color schemes */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.5 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 100.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 2000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ +#define LOG_SHIFT -0.5 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 30.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.1 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 1.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 14 June 22 - Archimedes’ principle ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.9 +#define INITXMAX 1.9 /* x interval for initial condition */ +#define INITYMIN -1.0 +#define INITYMAX 0.95 /* y interval for initial condition */ + +#define BCXMIN -2.0 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.125 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 9 /* pattern of repelling segments, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.75 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.2 /* parameter controlling the dimensions of domain */ +#define MU 0.012 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 20 /* number of sides of polygon */ +#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1800 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 100 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 20.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.01 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 6.0 /* radius in which to count neighbours */ +#define GRAVITY 500.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 1 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_FACTOR 50.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.002 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ + +#define MOVE_BOUNDARY 1 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 5.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 0 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 1000 /* time at which to deactivate last segment */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 -0.75 /* initial position of segments */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 80 /* size of hashgrid in x direction */ +#define HASHY 40 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 13 June 22 - Schrödinger’s equation in a hexagon (3D rendering) ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 5.0, 0.0, 0.15, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 640 /* number of grid points on x axis */ +#define NY 360 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 2 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 8 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 15 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000002 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.5 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1500 /* number of frames of movie */ +#define NVID 900 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +/* Plot type - color scheme */ + +#define CPLOT 32 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 32 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 5.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 25.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {4.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D -0.1 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +#### 12 June 22 - Waves in a quadratic resonance diffuser, rendered in 3D ### **Program:** `wave_3d.c` @@ -3389,10 +3052,14 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Choice of the billiard table */ -#define B_DOMAIN 44 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 46 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 100 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependece of IoR on Mandelbrot escape speed */ + #define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ #define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ @@ -3426,16 +3093,16 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Physical parameters of wave equation */ -#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.017 /* frequency of periodic excitation */ -#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ -#define COURANT 0.1 /* Courant number */ -#define COURANTB 0.05 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 2.0e-5 /* damping factor in wave equation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.06 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 2.0e-2 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ #define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ @@ -3455,8 +3122,8 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Parameters for length and speed of simulation */ -#define NSTEPS 1500 /* number of frames of movie */ -#define NVID 8 /* number of iterations between images displayed on screen */ +#define NSTEPS 2100 /* number of frames of movie */ +#define NVID 10 /* number of iterations between images displayed on screen */ #define NSEG 1000 /* number of segments of boundary */ #define INITIAL_TIME 0 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 1 /* width of billiard boundary */ @@ -3472,28 +3139,28 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Parameters of initial condition */ #define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ +#define INITIAL_VARIANCE 0.01 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ /* Plot type, see list in global_pdes.c */ -#define ZPLOT 108 /* wave height */ -#define CPLOT 108 /* color scheme */ - -#define ZPLOT_B 109 -#define CPLOT_B 109 /* plot type for second movie */ +#define ZPLOT 103 /* wave height */ +#define CPLOT 103 /* color scheme */ +#define ZPLOT_B 108 +#define CPLOT_B 108 /* plot type for second movie */ #define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ #define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ #define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define FLOOR_ZCOORD 1 /* set to 1 to draw only facets with z not too negative */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ #define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ #define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ #define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ #define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ -#define PLOT_SCALE_ENERGY 0.02 /* vertical scaling in energy plot */ +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ #define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ /* 3D representation */ @@ -3505,23 +3172,23 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Color schemes */ -#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 14 /* Color palette, see list in global_pdes.c */ #define BLACK 1 /* background */ #define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define SLOPE 0.15 /* sensitivity of color on wave amplitude */ #define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ #define VSCALE_ENERGY 10.0 /* additional scaling factor for color scheme P_3D_ENERGY */ #define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ #define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 1000.0 /* scaling factor for energy representation */ -#define LOG_SCALE 0.25 /* scaling factor for energy log representation */ -#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 500.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ +#define LOG_SHIFT -0.5 /* shift of colors on log scale */ #define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ #define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ #define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ @@ -3531,12 +3198,12 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ #define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ #define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 20.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 100.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 15.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 80.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ #define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ @@ -3550,17 +3217,17 @@ double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_ double v_3d[2] = {-0.75, -0.45}; double w_3d[2] = {0.0, 0.015}; double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ +double observer[3] = {6.0, 8.0, 7.0}; /* location of observer for REP_PROJ_3D representation */ -#define Z_SCALING_FACTOR 0.05 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.15 /* overall y shift for REP_PROJ_3D representation */ +#define Z_SCALING_FACTOR 0.01 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 1.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ ``` -### 13 May 22 - An approximation with Lennard-Jones particles of the Rock-Paper-Scissors reaction-diffusion equation ### +### 11 June 22 - A leaky centrifuge – Or a spinning washing machine ### **Program:** `lennardjones.c` @@ -3572,6 +3239,7 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D /* so far incompatible with double movie */ #define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ @@ -3582,10 +3250,10 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ -#define INITXMIN -1.95 -#define INITXMAX 1.95 /* x interval for initial condition */ -#define INITYMIN -1.05 -#define INITYMAX 1.05 /* y interval for initial condition */ +#define INITXMIN -0.75 +#define INITXMAX 0.75 /* x interval for initial condition */ +#define INITYMIN -0.75 +#define INITYMAX 0.75 /* y interval for initial condition */ #define BCXMIN -2.0 #define BCXMAX 2.0 /* x interval for boundary condition */ @@ -3598,13 +3266,13 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ #define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ -#define ADD_FIXED_SEGMENTS 0 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 2 /* pattern of repelling segments, see list in global_ljones.c */ +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 8 /* pattern of repelling segments, see list in global_ljones.c */ -#define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ +#define TWO_TYPES 1 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ #define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ #define CENTER_PX 0 /* set to 1 to center horizontal momentum */ #define CENTER_PY 0 /* set to 1 to center vertical momentum */ @@ -3617,14 +3285,14 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ #define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_DISTANCE 3.75 /* minimal distance in Poisson disc process, controls density of particles */ #define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define LAMBDA 0.1 /* parameter controlling the dimensions of domain */ #define MU 0.012 /* parameter controlling radius of particles */ -#define MU_B 0.0254 /* parameter controlling radius of particles of second type */ -#define NPOLY 3 /* number of sides of polygon */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 6 /* number of sides of polygon */ #define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ @@ -3643,10 +3311,10 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D /* Parameters for length and speed of simulation */ -#define NSTEPS 1400 /* number of frames of movie */ +#define NSTEPS 1500 /* number of frames of movie */ #define NVID 300 /* number of iterations between images displayed on screen */ #define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define INITIAL_TIME 20 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 1 /* width of particle boundary */ #define LINK_WIDTH 2 /* width of links between particles */ #define CONTAINER_WIDTH 4 /* width of container boundary */ @@ -3660,14 +3328,16 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D /* Boundary conditions, see list in global_ljones.c */ -#define BOUNDARY_COND 3 +#define BOUNDARY_COND 20 /* Plot type, see list in global_ljones.c */ #define PLOT 5 -#define PLOT_B 9 /* plot type for second movie */ +#define PLOT_B 8 /* plot type for second movie */ +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ #define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ /* Color schemes */ @@ -3690,37 +3360,38 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D /* particle properties */ -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ #define PARTICLE_HUE_MIN 359.0 /* color of original particle */ #define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define PARTICLE_EMAX 1.0e3 /* energy of particle with hottest color */ #define HUE_TYPE0 280.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 180.0 /* hue of particles of type 1 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ #define HUE_TYPE2 70.0 /* hue of particles of type 2 */ #define HUE_TYPE3 210.0 /* hue of particles of type 3 */ #define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ #define DT_PARTICLE 1.0e-6 /* time step for particle displacement */ #define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ #define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 0.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define DAMPING 20.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 2.0 /* mass of particle of radius MU */ #define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ #define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ #define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 10.0 /* initial velocity range */ +#define V_INITIAL 0.0 /* initial velocity range */ #define OMEGA_INITIAL 10.0 /* initial angular velocity range */ #define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 1 /* set to 1 for time-dependent thermostat schedule */ #define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.05 /* initial inverse temperature */ +#define BETA 0.1 /* initial inverse temperature */ #define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 5.0e9 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 5.0e9 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 6.0 /* radius in which to count neighbours */ #define GRAVITY 0.0 /* gravity acting on all particles */ #define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ #define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ @@ -3730,7 +3401,7 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define ROTATION 0 /* set to 1 to include rotation of particles */ #define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ #define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 50.0 /* force constant in angular dynamics */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ #define KTORQUE_B 10.0 /* force constant in angular dynamics */ #define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ #define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ @@ -3741,10 +3412,10 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ #define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 20.0 /* factor by which to change BETA during simulation */ +#define BETA_FACTOR 0.002 /* factor by which to change BETA during simulation */ #define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ #define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ -#define FINAL_CONSTANT_PHASE 2000 /* final phase in which temperature is constant */ +#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ #define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ #define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ @@ -3766,6 +3437,7 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define N_T_AVERAGE 50 /* size of temperature averaging window */ #define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ #define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ #define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ #define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ @@ -3776,8 +3448,8 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define NPART_BOTTOM 100 /* number of particles at the bottom */ #define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 500 /* time at which to add first particle */ -#define ADD_PERIOD 250 /* time interval between adding further particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ #define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ #define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ @@ -3787,20 +3459,31 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ #define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ -#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ -#define PERIOD_ROTATE_BOUNDARY 2500 /* period of rotating boundary */ +#define ROTATE_BOUNDARY 1 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ #define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 500 /* final time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 1 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 100.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 0 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 1000 /* time at which to deactivate last segment */ #define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ #define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ #define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ -#define REACTION_DIFFUSION 1 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ #define RD_TYPES 3 /* number of types in reaction-diffusion equation */ -#define REACTION_PROB 0.03 /* probability controlling reaction term */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ #define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ #define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ @@ -3813,12 +3496,12 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define WALL_TIME 500 /* time during which to keep wall */ #define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e9 /* maximal force */ +#define FMAX 1.0e12 /* maximal force */ #define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ #define PMAX 1000.0 /* maximal force */ -#define HASHX 100 /* size of hashgrid in x direction */ -#define HASHY 50 /* size of hashgrid in y direction */ +#define HASHX 80 /* size of hashgrid in x direction */ +#define HASHY 40 /* size of hashgrid in y direction */ #define HASHMAX 100 /* maximal number of particles per hashgrid cell */ #define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ @@ -3829,11 +3512,11 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D ``` -### 12 May 22 - Young’s double-slit experiment for a quantum particle, in 3D ### +### 10 June 22 - The 2D quantum hydrogen atom, with zero angular momentum ### **Program:** `rde.c` -**Initial condition in function `animation()`:** `init_coherent_state(-0.75, 0.0, 15.0, 0.0, 0.4, phi, xy_in);` +**Initial condition in function `animation()`:** `init_coherent_state(-0.7, 0.0, 5.0, 0.0, 0.15, phi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ @@ -3843,8 +3526,8 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define WINWIDTH 1920 /* window width */ #define WINHEIGHT 1000 /* window height */ -#define NX 600 /* number of grid points on x axis */ -#define NY 300 /* number of grid points on y axis */ +#define NX 480 /* number of grid points on x axis */ +#define NY 240 /* number of grid points on y axis */ #define XMIN -2.0 #define XMAX 2.0 /* x interval */ @@ -3857,11 +3540,14 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define NFIELDS 2 /* number of fields in reaction-diffusion equation */ #define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 2 /* type of potential, see list in global_3d.c */ + #define JULIA_SCALE 0.5 /* scaling for Julia sets */ /* Choice of the billiard table */ -#define B_DOMAIN 9 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ @@ -3869,8 +3555,8 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ -#define LAMBDA 0.4 /* parameter controlling the dimensions of domain */ -#define MU 0.06 /* parameter controlling the dimensions of domain */ +#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* parameter controlling the dimensions of domain */ #define NPOLY 6 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 5 /* depth of computation of Menger gasket */ @@ -3886,7 +3572,7 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define X_TARGET 0.4 #define Y_TARGET 0.7 /* shooter and target positions in laser fight */ -#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_LEFT -1.65 #define ISO_XSHIFT_RIGHT 0.4 #define ISO_YSHIFT_LEFT -0.05 #define ISO_YSHIFT_RIGHT -0.05 @@ -3897,32 +3583,44 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D /* Physical patameters of wave equation */ -#define DT 0.00000001 +#define DT 0.00000002 -#define VISCOSITY 0.1 +#define VISCOSITY 2.0 #define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ #define EPSILON 0.8 /* time scale separation */ #define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.5 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ #define T_OUT 2.0 /* outside temperature */ #define T_IN 0.0 /* inside temperature */ #define SPEED 0.0 /* speed of drift to the right */ #define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ #define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 1 /* set to 1 to decrease integration step when viscosity increases */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ #define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ #define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ #define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + /* Boundary conditions, see list in global_pdes.c */ @@ -3930,13 +3628,13 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D /* Parameters for length and speed of simulation */ -#define NSTEPS 1500 /* number of frames of movie */ -#define NVID 900 /* number of iterations between images displayed on screen */ +#define NSTEPS 1300 /* number of frames of movie */ +#define NVID 1000 /* number of iterations between images displayed on screen */ #define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ #define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ #define MAX_DT 0.024 /* maximal value of integration step */ #define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ #define PAUSE 100 /* number of frames after which to pause */ #define PSLEEP 2 /* sleep time during pause */ @@ -3944,7 +3642,7 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define SLEEP2 1 /* final sleeping time */ #define INITIAL_TIME 0 /* initial still time */ #define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ #define FADE 1 /* set to 1 to fade at end of movie */ #define PLOT_3D 1 /* controls whether plot is 2D or 3D */ @@ -3956,7 +3654,7 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D /* Plot type - height of 3D plot */ -#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT 30 /* z coordinate in 3D plot */ #define ZPLOT_B 30 /* z coordinate in second 3D plot */ #define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ @@ -3964,17 +3662,22 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ #define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ #define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ #define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ #define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ #define FIELD_LINE_WIDTH 1 /* width of field lines */ #define N_FIELD_LINES 120 /* number of field lines */ #define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ #define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ #define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ /* 3D representation */ @@ -3986,707 +3689,22 @@ double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D /* Color schemes, see list in global_pdes.c */ -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 12 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ #define BLACK 1 /* black background */ #define COLOR_SCHEME 3 /* choice of color scheme */ -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 20.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ -#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define E_SCALE 100.0 /* scaling factor for energy representation */ -#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT 0.0 - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 0.55 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -/* only for compatibility with wave_common.c */ -#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OMEGA 0.005 /* frequency of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.03 /* Courant number in medium B */ -#define INITIAL_AMP 0.5 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ -#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -/* end of constants added only for compatibility with wave_common.c */ - - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.05 /* overall y shift for REP_PROJ_3D representation */ - -/* For debugging purposes only */ -#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -``` - -### 11 May 22 - Average energy in a Tokarsky room, in 3D ### - -**Program:** `wave_3d.c` - -**Initial condition in function `animation()`:** `init_circular_wave_mod(polyline[85].x, polyline[85].y, phi, psi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 1800 /* number of grid points on x axis */ -#define NY 900 /* number of grid points on y axis */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.041666667 -#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - -#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ - -#define JULIA_SCALE 0.8 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 36 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ -#define MU 0.2 /* parameter controlling the dimensions of domain */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 3 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 36 /* number of grid point for grid of disks */ -#define NGRIDY 6 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -2.9 -#define ISO_XSHIFT_RIGHT 1.4 -#define ISO_YSHIFT_LEFT -0.15 -#define ISO_YSHIFT_RIGHT -0.15 -#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ - - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard below */ - -/* Physical parameters of wave equation */ - -#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ -#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ - -#define OMEGA 0.017 /* frequency of periodic excitation */ -#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ -#define COURANT 0.1 /* Courant number */ -#define COURANTB 0.06 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 0.0 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ -#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ -/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ -/* The physical damping coefficient is given by GAMMA/(DT)^2 */ -/* Increasing COURANT speeds up the simulation, but decreases accuracy */ -/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ - -#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ -#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 3 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 2400 /* number of frames of movie */ -#define NVID 8 /* number of iterations between images displayed on screen */ -#define NSEG 1000 /* number of segments of boundary */ -#define INITIAL_TIME 0 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -/* Parameters of initial condition */ - -#define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define ZPLOT 108 /* wave height */ -#define CPLOT 108 /* color scheme */ - -#define ZPLOT_B 109 -#define CPLOT_B 109 /* plot type for second movie */ - - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 1 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define FLOOR_ZCOORD 1 /* set to 1 to draw only facets with z not too negative */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw front of boundary after drawing wave */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ -#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ - -#define PLOT_SCALE_ENERGY 0.02 /* vertical scaling in energy plot */ -#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - - -/* Color schemes */ - -#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 11 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.4 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define VSCALE_ENERGY 150.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 1000.0 /* scaling factor for energy representation */ -#define LOG_SCALE 3.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT -2.0 /* shift of colors on log scale */ -#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ -#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ - -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 50.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 50.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 1 /* set to 1 to draw color scheme horizontally */ - -#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ - -/* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -/* Parameters controlling 3D projection */ - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {2.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.04 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.35 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.1 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.05 /* overall y shift for REP_PROJ_3D representation */ - -``` - -### 10 May 22 - What the hourglass icon should really look like: Rotating version with Lennard-Jones particles ### - -**Program:** `lennardjones.c` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ - /* so far incompatible with double movie */ -#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ - - -/* General geometrical parameters */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.125 -#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ - -#define INITXMIN -0.7 -#define INITXMAX 0.7 /* x interval for initial condition */ -#define INITYMIN 0.1 -#define INITYMAX 0.6 /* y interval for initial condition */ - -#define BCXMIN -0.7 -#define BCXMAX 0.7 /* x interval for boundary condition */ -#define BCYMIN -0.85 -#define BCYMAX 0.85 /* y interval for boundary condition */ - -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ - -#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ - -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ - -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 2 /* pattern of repelling segments, see list in global_ljones.c */ - -#define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ -#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ -#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ -#define CENTER_PY 0 /* set to 1 to center vertical momentum */ -#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ - -#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ -#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ -#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ -#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 2.75 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ -#define MU 0.013 /* parameter controlling radius of particles */ -#define MU_B 0.0254 /* parameter controlling radius of particles of second type */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 4 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 46 /* number of grid point for grid of disks */ -#define NGRIDY 24 /* number of grid point for grid of disks */ -#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ -#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 5500 /* number of frames of movie */ -#define NVID 650 /* number of iterations between images displayed on screen */ -#define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 10 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of particle boundary */ -#define LINK_WIDTH 2 /* width of links between particles */ -#define CONTAINER_WIDTH 4 /* width of container boundary */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -/* Boundary conditions, see list in global_ljones.c */ - -#define BOUNDARY_COND 0 - -/* Plot type, see list in global_ljones.c */ - -#define PLOT 0 -#define PLOT_B 8 /* plot type for second movie */ - -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ -#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 135.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 70.0 /* hue of particles of type 1 */ -#define HUE_TYPE3 210.0 /* hue of particles of type 1 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 5.0e-7 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 0.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 10.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.01 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 5.0e9 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 5.0e9 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ -#define GRAVITY 10000.0 /* gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 50.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 20.0 /* factor by which to change BETA during simulation */ -#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ -#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ -#define FINAL_CONSTANT_PHASE 2000 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 500 /* time at which to add first particle */ -#define ADD_PERIOD 250 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define ROTATE_BOUNDARY 1 /* set to 1 to rotate the repelling segments */ -#define PERIOD_ROTATE_BOUNDARY 2500 /* period of rotating boundary */ -#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 500 /* final time without rotation */ - -#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ -#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ - -#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ - -#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ -#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ -#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_VMAX 100.0 /* max speed of wall */ -#define WALL_TIME 500 /* time during which to keep wall */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e9 /* maximal force */ -#define FLOOR_OMEGA 1 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 40 /* size of hashgrid in x direction */ -#define HASHY 20 /* size of hashgrid in y direction */ -#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -``` - -### 9 May 22 - Colliding spirals in the Rock-Paper-Scissors equation 6: norm and direction of gradient in 3D ### - -**Program:** `rde.c` - -**Initial condition in function `animation()`:** `init_random(0.5, 0.4, phi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 1920 /* number of grid points on x axis */ -#define NY 1000 /* number of grid points on y axis */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.041666667 -#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - -/* Choice of simulated equation */ - -#define RDE_EQUATION 4 /* choice of reaction term, see list in global_3d.c */ -#define NFIELDS 3 /* number of fields in reaction-diffusion equation */ -#define NLAPLACIANS 3 /* number of fields for which to compute Laplacian */ - -#define JULIA_SCALE 0.5 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ -#define MU 0.8 /* parameter controlling the dimensions of domain */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 5 /* depth of computation of Menger gasket */ -#define MRATIO 5 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 15 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -1.65 -#define ISO_XSHIFT_RIGHT 0.4 -#define ISO_YSHIFT_LEFT -0.05 -#define ISO_YSHIFT_RIGHT -0.05 -#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard in sub_wave.c */ - -/* Physical patameters of wave equation */ - -#define DT 0.0000005 - -#define VISCOSITY 0.1 - -#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ - -#define EPSILON 0.8 /* time scale separation */ -#define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ - -#define T_OUT 2.0 /* outside temperature */ -#define T_IN 0.0 /* inside temperature */ -#define SPEED 0.0 /* speed of drift to the right */ - -#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ - -#define CHANGE_VISCOSITY 1 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 1 /* set to 1 to decrease integration step when viscosity increases */ -#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ -#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ -#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, - for numerical stability */ - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 1 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 2500 /* number of frames of movie */ -#define NVID 5 /* number of iterations between images displayed on screen */ -#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ -#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ -#define MAX_DT 0.024 /* maximal value of integration step */ -#define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 2 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define INITIAL_TIME 0 /* initial still time */ -#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ - -/* Plot type - color scheme */ - -#define CPLOT 231 -// #define CPLOT 22 -#define CPLOT_B 231 - -/* Plot type - height of 3D plot */ - -#define ZPLOT 23 /* z coordinate in 3D plot */ -#define ZPLOT_B 23 /* z coordinate in second 3D plot */ - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ -#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ - -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ - -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 1 /* set to 1 to print viscosity */ - -#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ -#define FIELD_LINE_WIDTH 1 /* width of field lines */ -#define N_FIELD_LINES 120 /* number of field lines */ -#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - -/* Color schemes, see list in global_pdes.c */ - -#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 0 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* black background */ - -#define COLOR_SCHEME 4 /* choice of color scheme */ - -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 1.75 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define CURL_SCALE 0.000015 /* scaling factor for curl representation */ #define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 25.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ #define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ #define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ @@ -4698,9 +3716,9 @@ double observer[3] = {2.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D #define LOG_SCALE 1.0 /* scaling factor for energy log representation */ #define LOG_SHIFT 0.0 -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 0.55 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 0.75 /* scale of color scheme bar for 2nd part */ #define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ /* only for compatibility with wave_common.c */ @@ -4721,703 +3739,121 @@ double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_ double v_3d[2] = {-0.75, -0.45}; double w_3d[2] = {0.0, 0.015}; double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D representation */ +double observer[3] = {4.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ -#define Z_SCALING_FACTOR 0.07 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 1.7 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ #define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.05 /* overall y shift for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D -0.1 /* overall y shift for REP_PROJ_3D representation */ /* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ ``` -### 8 May 22 - A circular lens, wave height and cumulative energy in 3D ### +## 9 June 22 - A room with a non-self-illuminable point, by George Tokarsky ### -**Program:** `wave_3d.c` +**Program:** `particle_billiard.c` -**Initial condition in function `animation()`:** `init_wave_flat_mod(phi, psi, xy_in);` +**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, 0.0, DPI, configs); ` ``` #define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 1800 /* number of grid points on x axis */ -#define NY 900 /* number of grid points on y axis */ - -#define XMIN -0.7 -#define XMAX 3.3 /* x interval */ -#define YMIN -1.041666667 -#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - -#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ - -#define JULIA_SCALE 0.8 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 47 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA -1.2 /* parameter controlling the dimensions of domain */ -#define MU 0.2 /* parameter controlling the dimensions of domain */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 3 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 36 /* number of grid point for grid of disks */ -#define NGRIDY 6 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -2.9 -#define ISO_XSHIFT_RIGHT 1.4 -#define ISO_YSHIFT_LEFT -0.15 -#define ISO_YSHIFT_RIGHT -0.15 -#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ - - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard below */ - -/* Physical parameters of wave equation */ - -#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ -#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ - -#define OMEGA 0.017 /* frequency of periodic excitation */ -#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ -#define COURANT 0.1 /* Courant number */ -#define COURANTB 0.06 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 0.0 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ -#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ -/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ -/* The physical damping coefficient is given by GAMMA/(DT)^2 */ -/* Increasing COURANT speeds up the simulation, but decreases accuracy */ -/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ - -#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ -#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 3 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 1600 /* number of frames of movie */ -#define NVID 8 /* number of iterations between images displayed on screen */ -#define NSEG 1000 /* number of segments of boundary */ -#define INITIAL_TIME 50 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 3 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -/* Parameters of initial condition */ - -#define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define ZPLOT 103 /* wave height */ -#define CPLOT 103 /* color scheme */ - -#define ZPLOT_B 107 -#define CPLOT_B 107 /* plot type for second movie */ - - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ -#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ - -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ -#define PLOT_SCALE_LOG_ENERGY 0.7 /* vertical scaling in log energy plot */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - - -/* Color schemes */ - -#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.2 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 1000.0 /* scaling factor for energy representation */ -#define LOG_SCALE 3.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT -2.0 /* shift of colors on log scale */ -#define LOG_ENERGY_FLOOR -8.0 /* floor value for log of (total) energy */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ - -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 14.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 35.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ - -/* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ - -/* Parameters controlling 3D projection */ - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.075 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.2 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.5 /* overall y shift for REP_PROJ_3D representation */ - -``` - -### 7 May 22 - Phonons in a Lennard-Jones crystal with defects ### - -**Program:** `lennardjones.c` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ - /* so far incompatible with double movie */ -#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ - - -/* General geometrical parameters */ - -#define WINWIDTH 1280 /* window width */ +#define WINWIDTH 720 /* window width */ #define WINHEIGHT 720 /* window height */ -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ +#define XMIN -1.125 +#define XMAX 1.125 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ -#define INITXMIN -1.48 -#define INITXMAX 1.48 /* x interval for initial condition */ -#define INITYMIN -0.77 -#define INITYMAX 0.77 /* y interval for initial condition */ +#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ -#define BCXMIN -1.5 -#define BCXMAX 1.5 /* x interval for boundary condition */ -#define BCYMIN -0.8 -#define BCYMAX 0.8 /* y interval for boundary condition */ +/* Choice of the billiard table, see global_particles.c */ -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ +#define B_DOMAIN 30 /* choice of domain shape */ -#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ +#define CIRCLE_PATTERN 1 /* pattern of circles */ +#define POLYLINE_PATTERN 8 /* pattern of polyline */ -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 3 /* pattern of repelling segments, see list in global_ljones.c */ +#define NMAXCIRCLES 100000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 100000 /* total number of sides of polygonal line */ +#define NCX 30 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 1 /* Sierpinski gastket depth */ -#define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ -#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ -#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ -#define CENTER_PY 0 /* set to 1 to center vertical momentum */ -#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ - -#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ -#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ -#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ -#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ -#define MU 0.016 /* parameter controlling radius of particles */ -#define MU_B 0.0254 /* parameter controlling radius of particles of second type */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 4 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 46 /* number of grid point for grid of disks */ -#define NGRIDY 24 /* number of grid point for grid of disks */ -#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ -#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 2500 /* number of frames of movie */ -#define NVID 550 /* number of iterations between images displayed on screen */ -#define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 10 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of particle boundary */ -#define LINK_WIDTH 2 /* width of links between particles */ -#define CONTAINER_WIDTH 4 /* width of container boundary */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -/* Boundary conditions, see list in global_ljones.c */ - -#define BOUNDARY_COND 0 - -/* Plot type, see list in global_ljones.c */ - -#define PLOT 8 -#define PLOT_B 3 /* plot type for second movie */ - -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 5.0e1 /* energy of particle with hottest color */ -#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 135.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 70.0 /* hue of particles of type 1 */ -#define HUE_TYPE3 210.0 /* hue of particles of type 1 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 1.0e-6 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 0.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 0.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.1 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 5.0e6 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 5.0e6 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ -#define GRAVITY 0.0 /* gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 50.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 20.0 /* factor by which to change BETA during simulation */ -#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ -#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ -#define FINAL_CONSTANT_PHASE 2000 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 1 /* set to 1 to add particles */ -#define ADD_TIME 500 /* time at which to add first particle */ -#define ADD_PERIOD 250 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ -#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ - -#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ - -#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ -#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ -#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_VMAX 100.0 /* max speed of wall */ -#define WALL_TIME 500 /* time during which to keep wall */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e9 /* maximal force */ -#define FLOOR_OMEGA 1 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 40 /* size of hashgrid in x direction */ -#define HASHY 20 /* size of hashgrid in y direction */ -#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -``` - -### 6 May 22 - Colliding spirals in the Rock-Paper-Scissors equation 5: norm of the change of phase ### - -**Program:** `rde.c` - -**Initial condition in function `animation()`:** `init_random(0.5, 0.4, phi, xy_in);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ - -/* General geometrical parameters */ - -#define WINWIDTH 1920 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 1920 /* number of grid points on x axis */ -#define NY 1000 /* number of grid points on y axis */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.041666667 -#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - -/* Choice of simulated equation */ - -#define RDE_EQUATION 4 /* choice of reaction term, see list in global_3d.c */ -#define NFIELDS 3 /* number of fields in reaction-diffusion equation */ -#define NLAPLACIANS 3 /* number of fields for which to compute Laplacian */ - -#define JULIA_SCALE 0.5 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ -#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define LAMBDA 1.5 /* parameter controlling shape of domain */ +#define MU 0.01 /* second parameter controlling shape of billiard */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NPOLY 6 /* number of sides of polygon */ -#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 5 /* depth of computation of Menger gasket */ -#define MRATIO 5 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 15 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ +#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ +#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ +#define DEBUG 0 /* draw trajectories, for debugging purposes */ -#define ISO_XSHIFT_LEFT -1.65 -#define ISO_XSHIFT_RIGHT 0.4 -#define ISO_YSHIFT_LEFT -0.05 -#define ISO_YSHIFT_RIGHT -0.05 -#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ +/* Simulation parameters */ -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard in sub_wave.c */ +#define NPART 5000 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 1 /* set to 1 to show zoom on specific area */ +#define PRINT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles */ +#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ -/* Physical patameters of wave equation */ +#define NSTEPS 1000 /* number of frames of movie */ +#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.00001 /* integration step */ +#define NVID 100 /* number of iterations between images displayed on screen */ -#define DT 0.0000005 +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ -#define VISCOSITY 0.05 - -#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ - -#define EPSILON 0.8 /* time scale separation */ -#define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ - -#define T_OUT 2.0 /* outside temperature */ -#define T_IN 0.0 /* inside temperature */ -#define SPEED 0.0 /* speed of drift to the right */ - -#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ - -#define CHANGE_VISCOSITY 1 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 1 /* set to 1 to decrease integration step when viscosity increases */ -#define VISCOSITY_INITIAL_TIME 25 /* initial time during which viscosity remains constant */ -#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ -#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, - for numerical stability */ - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 1 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 3200 /* number of frames of movie */ -#define NVID 5 /* number of iterations between images displayed on screen */ -#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ -#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ -#define MAX_DT 0.024 /* maximal value of integration step */ - -#define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 2 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define INITIAL_TIME 0 /* initial still time */ -#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -#define PLOT_3D 0 /* controls whether plot is 2D or 3D */ - -/* Plot type - color scheme */ - -#define CPLOT 22 -#define CPLOT_B 231 - -/* Plot type - height of 3D plot */ - -#define ZPLOT 22 /* z coordinate in 3D plot */ -#define ZPLOT_B 25 /* z coordinate in second 3D plot */ - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ -#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ - -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ - - - -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 1 /* set to 1 to print viscosity */ - -#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ -#define FIELD_LINE_WIDTH 1 /* width of field lines */ -#define N_FIELD_LINES 120 /* number of field lines */ -#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - -/* Color schemes, see list in global_pdes.c */ +/* Colors and other graphical parameters */ #define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 17 /* Color palette, see list in global_pdes.c */ -#define BLACK 1 /* black background */ +#define NCOLORS 64 /* number of colors */ +#define COLORSHIFT 0 /* hue of initial color */ +#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */ +#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ +#define NSEG 100 /* number of segments of boundary */ +#define LENGTH 0.03 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 3 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ -#define COLOR_SCHEME 4 /* choice of color scheme */ +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 1.75 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define E_SCALE 100.0 /* scaling factor for energy representation */ -#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT 0.0 - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 0.55 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -/* only for compatibility with wave_common.c */ -#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OMEGA 0.005 /* frequency of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.03 /* Courant number in medium B */ -#define INITIAL_AMP 0.5 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ -#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ -#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ -#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -/* end of constants added only for compatibility with wave_common.c */ - - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D representation */ - -#define Z_SCALING_FACTOR 0.035 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 1.7 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.05 /* overall y shift for REP_PROJ_3D representation */ - - -/* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ ``` -### 5 May 22 - Waves radiating from the Mandelbrot set, in 3D ### +### 8 June 22 - Waves radiating from the Mandelbrot set: Index of refraction equal to the escape time ### **Program:** `wave_3d.c` @@ -5445,16 +3881,20 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D /* Choice of the billiard table */ -#define B_DOMAIN 24 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 24 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ +#define VARIABLE_IOR 1 /* set to 1 for a variable index of refraction */ +#define IOR 100 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependece of IoR on Mandelbrot escape speed */ + #define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ #define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ -#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ -#define MU 0.037 /* parameter controlling the dimensions of domain */ +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 3 /* depth of computation of Menger gasket */ @@ -5486,12 +3926,12 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ -#define OMEGA 0.005 /* frequency of periodic excitation */ -#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ -#define COURANT 0.04 /* Courant number */ -#define COURANTB 0.08 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 0.0 /* damping factor in wave equation */ +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.06 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 2.0e-2 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ #define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ @@ -5511,11 +3951,11 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D /* Parameters for length and speed of simulation */ -#define NSTEPS 1750 /* number of frames of movie */ -#define NVID 8 /* number of iterations between images displayed on screen */ +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 10 /* number of iterations between images displayed on screen */ #define NSEG 1000 /* number of segments of boundary */ #define INITIAL_TIME 0 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 3 /* width of billiard boundary */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ #define PAUSE 100 /* number of frames after which to pause */ #define PSLEEP 2 /* sleep time during pause */ @@ -5533,22 +3973,24 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D /* Plot type, see list in global_pdes.c */ -#define ZPLOT 103 /* wave height */ -#define CPLOT 103 /* color scheme */ - -#define ZPLOT_B 107 -#define CPLOT_B 107 /* plot type for second movie */ +#define ZPLOT 108 /* wave height */ +#define CPLOT 108 /* color scheme */ +#define ZPLOT_B 109 +#define CPLOT_B 109 /* plot type for second movie */ #define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ #define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ #define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 1 /* set to 1 to draw only facets with z not too negative */ #define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ #define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ #define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ -#define PLOT_SCALE_LOG_ENERGY 0.7 /* vertical scaling in log energy plot */ +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ /* 3D representation */ @@ -5557,27 +3999,27 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D #define REP_AXO_3D 0 /* linear projection (axonometry) */ #define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - /* Color schemes */ -#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 14 /* Color palette, see list in global_pdes.c */ #define BLACK 1 /* background */ #define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.2 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 5.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define VSCALE_ENERGY 100.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 10.0 /* additional scaling factor for color scheme P_3D_ENERGY */ #define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ #define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 1000.0 /* scaling factor for energy representation */ -#define LOG_SCALE 1.5 /* scaling factor for energy log representation */ -#define LOG_SHIFT -2.0 /* shift of colors on log scale */ -#define LOG_ENERGY_FLOOR -8.0 /* floor value for log of (total) energy */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 500.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ +#define LOG_SHIFT -0.5 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ #define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ #define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ @@ -5585,12 +4027,12 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D #define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ #define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ #define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ #define COLORBAR_RANGE 10.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 80.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ +#define COLORBAR_RANGE_B 60.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ #define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ @@ -5604,282 +4046,21 @@ double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_ double v_3d[2] = {-0.75, -0.45}; double w_3d[2] = {0.0, 0.015}; double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +double observer[3] = {6.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ -#define Z_SCALING_FACTOR 0.075 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.25 /* overall x shift for REP_PROJ_3D representation */ +#define Z_SCALING_FACTOR 0.035 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ #define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ ``` -### 4 May 22 - Phonons induced by bombarding a Lennard-Jones crystal with atoms ### - -**Program:** `lennardjones.c` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ - -#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ - /* so far incompatible with double movie */ -#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ - - -/* General geometrical parameters */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -2.0 -#define XMAX 2.0 /* x interval */ -#define YMIN -1.125 -#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ - -#define INITXMIN -1.48 -#define INITXMAX 1.48 /* x interval for initial condition */ -#define INITYMIN -0.77 -#define INITYMAX 0.77 /* y interval for initial condition */ - -#define BCXMIN -1.5 -#define BCXMAX 1.5 /* x interval for boundary condition */ -#define BCYMIN -0.8 -#define BCYMAX 0.8 /* y interval for boundary condition */ - -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ - -#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_ljones.c */ - -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ - -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 0 /* pattern of repelling segments, see list in global_ljones.c */ - -#define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ -#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ -#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ -#define CENTER_PY 0 /* set to 1 to center vertical momentum */ -#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ - -#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ -#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ -#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ -#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 2.75 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ -#define MU 0.016 /* parameter controlling radius of particles */ -#define MU_B 0.0254 /* parameter controlling radius of particles of second type */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 4 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 46 /* number of grid point for grid of disks */ -#define NGRIDY 24 /* number of grid point for grid of disks */ -#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ -#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 1800 /* number of frames of movie */ -#define NVID 550 /* number of iterations between images displayed on screen */ -#define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 10 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 1 /* width of particle boundary */ -#define LINK_WIDTH 2 /* width of links between particles */ -#define CONTAINER_WIDTH 4 /* width of container boundary */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ - -/* Boundary conditions, see list in global_ljones.c */ - -#define BOUNDARY_COND 0 - -/* Plot type, see list in global_ljones.c */ - -#define PLOT 0 -#define PLOT_B 8 /* plot type for second movie */ - -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 1.0e1 /* energy of particle with hottest color */ -#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 135.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 70.0 /* hue of particles of type 1 */ -#define HUE_TYPE3 210.0 /* hue of particles of type 1 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 1.0e-6 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 0.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 0.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.1 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 5.0e5 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 5.0e5 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ -#define GRAVITY 0.0 /* gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 50.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 20.0 /* factor by which to change BETA during simulation */ -#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ -#define NO_OSCILLATION 0 /* set to 1 to have exponential BETA change only */ -#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 1 /* set to 1 to add particles */ -#define ADD_TIME 25 /* time at which to add first particle */ -#define ADD_PERIOD 250 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ -#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ - -#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ - -#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ -#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ -#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ -#define WALL_VMAX 100.0 /* max speed of wall */ -#define WALL_TIME 500 /* time during which to keep wall */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e9 /* maximal force */ -#define FLOOR_OMEGA 1 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 30 /* size of hashgrid in x direction */ -#define HASHY 15 /* size of hashgrid in y direction */ -#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -``` - -### 3 May 22 Colliding spirals in the Rock-Paper-Scissors equation 4: phase and vorticity ### +### 7 June 22 - The 2D quantum hydrogen atom, with smaller angular momentum ### **Program:** `rde.c` -**Initial condition in function `animation()`:** `init_random(0.5, 0.4, phi, xy_in);` +**Initial condition in function `animation()`:** `init_coherent_state(-0.7, 0.0, 2.0, -2.0, 0.15, phi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ @@ -5889,32 +4070,28 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define WINWIDTH 1920 /* window width */ #define WINHEIGHT 1000 /* window height */ -#define NX 1920 /* number of grid points on x axis */ -#define NY 1000 /* number of grid points on y axis */ +#define NX 480 /* number of grid points on x axis */ +#define NY 240 /* number of grid points on y axis */ #define XMIN -2.0 #define XMAX 2.0 /* x interval */ #define YMIN -1.041666667 #define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ - /* Choice of simulated equation */ -#define RDE_EQUATION 4 /* choice of reaction term, see list below */ -#define NFIELDS 3 /* number of fields in reaction-diffusion equation */ -#define NLAPLACIANS 3 /* number of fields for which to compute Laplacian */ +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ -#define E_HEAT 0 /* heat equation */ -#define E_ALLEN_CAHN 1 /* Allen-Cahn equation */ -#define E_CAHN_HILLIARD 2 /* Cahn-Hilliard equation */ -#define E_FHN 3 /* FitzHugh-Nagumo equation */ -#define E_RPS 4 /* rock-paper-scissors equation */ +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 2 /* type of potential, see list in global_3d.c */ #define JULIA_SCALE 0.5 /* scaling for Julia sets */ /* Choice of the billiard table */ -#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ @@ -5923,7 +4100,7 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ #define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ -#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* parameter controlling the dimensions of domain */ #define NPOLY 6 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 5 /* depth of computation of Menger gasket */ @@ -5950,32 +4127,44 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Physical patameters of wave equation */ -#define DT 0.0000005 +#define DT 0.00000002 -#define VISCOSITY 0.5 +#define VISCOSITY 2.0 #define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ #define EPSILON 0.8 /* time scale separation */ #define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.5 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ #define T_OUT 2.0 /* outside temperature */ #define T_IN 0.0 /* inside temperature */ #define SPEED 0.0 /* speed of drift to the right */ #define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.1 /* noise intensity */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ -#define CHANGE_VISCOSITY 1 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 1 /* set to 1 to decrease integration step when viscosity increases */ -#define VISCOSITY_INITIAL_TIME 25 /* initial time during which viscosity remains constant */ -#define VISCOSITY_FACTOR 10.0 /* factor by which to change viscosity */ +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ #define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + /* Boundary conditions, see list in global_pdes.c */ @@ -5983,14 +4172,13 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Parameters for length and speed of simulation */ -#define NSTEPS 2000 /* number of frames of movie */ -#define NVID 5 /* number of iterations between images displayed on screen */ +#define NSTEPS 1200 /* number of frames of movie */ +#define NVID 1000 /* number of iterations between images displayed on screen */ #define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ #define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ #define MAX_DT 0.024 /* maximal value of integration step */ - #define NSEG 100 /* number of segments of boundary */ -#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ +#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ #define PAUSE 100 /* number of frames after which to pause */ #define PSLEEP 2 /* sleep time during pause */ @@ -5998,36 +4186,43 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define SLEEP2 1 /* final sleeping time */ #define INITIAL_TIME 0 /* initial still time */ #define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 100 /* number of still frames at end of movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ #define FADE 1 /* set to 1 to fade at end of movie */ #define PLOT_3D 1 /* controls whether plot is 2D or 3D */ /* Plot type - color scheme */ -#define CPLOT 221 -#define CPLOT_B 21 +#define CPLOT 30 +#define CPLOT_B 31 /* Plot type - height of 3D plot */ -#define ZPLOT 22 /* z coordinate in 3D plot */ -#define ZPLOT_B 25 /* z coordinate in second 3D plot */ +#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ #define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ #define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ #define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ #define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ #define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ #define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 1 /* set to 1 to print viscosity */ +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ #define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ #define FIELD_LINE_WIDTH 1 /* width of field lines */ #define N_FIELD_LINES 120 /* number of field lines */ #define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ /* 3D representation */ @@ -6038,21 +4233,22 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D /* Color schemes, see list in global_pdes.c */ -#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 17 /* Color palette, see list in global_pdes.c */ #define BLACK 1 /* black background */ -#define COLOR_SCHEME 4 /* choice of color scheme */ +#define COLOR_SCHEME 3 /* choice of color scheme */ -#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 1.75 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define CURL_SCALE 0.000015 /* scaling factor for curl representation */ #define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 25.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ #define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ #define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ @@ -6062,11 +4258,11 @@ double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D #define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ #define E_SCALE 100.0 /* scaling factor for energy representation */ #define LOG_SCALE 1.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT 0.0 +#define LOG_SHIFT 0.0 -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 0.55 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 0.75 /* scale of color scheme bar for 2nd part */ #define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ /* only for compatibility with wave_common.c */ @@ -6087,26 +4283,310 @@ double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_ double v_3d[2] = {-0.75, -0.45}; double w_3d[2] = {0.0, 0.015}; double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D representation */ +double observer[3] = {4.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ -#define Z_SCALING_FACTOR 0.035 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 1.7 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ #define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.05 /* overall y shift for REP_PROJ_3D representation */ - +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D -0.1 /* overall y shift for REP_PROJ_3D representation */ /* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ ``` -### 2 May 22 - Olympus Mons: Waves escaping a sunflower spiral of triangles, 3D rendering ### +### 6 June 22 - A centrifuge with rounded bins ### -**Program:** `wave_3d.c` +**Program:** `lennardjones.c` -**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -0.75 +#define INITXMAX 0.75 /* x interval for initial condition */ +#define INITYMIN -0.75 +#define INITYMAX 0.75 /* y interval for initial condition */ + +#define BCXMIN -2.0 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.125 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 7 /* pattern of repelling segments, see list in global_ljones.c */ + +#define TWO_TYPES 1 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.75 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.05 /* parameter controlling the dimensions of domain */ +#define MU 0.012 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* number of frames of movie */ +#define NVID 300 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 50 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 3 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 5 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 1.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 10.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 2.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 1 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.1 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 6.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.002 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 1 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 200 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 200.0 /* maximal rotation speed */ +#define PRINT_OMEGA 1 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 100.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 0 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 1000 /* time at which to deactivate last segment */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 60 /* size of hashgrid in x direction */ +#define HASHY 30 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 5 June 22 - The 2D quantum hydrogen atom ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(-0.7, 0.0, 0.0, -7.5, 0.15, phi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ @@ -6116,13 +4596,258 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D #define WINWIDTH 1920 /* window width */ #define WINHEIGHT 1000 /* window height */ -#define NX 1400 /* number of grid points on x axis */ -#define NY 1400 /* number of grid points on y axis */ +#define NX 480 /* number of grid points on x axis */ +#define NY 250 /* number of grid points on y axis */ -#define XMIN -1.5 -#define XMAX 1.5 /* x interval */ -#define YMIN -1.5 -#define YMAX 1.5 /* y interval for 9/16 aspect ratio */ +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 2 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 15 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000002 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.5 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1400 /* number of frames of movie */ +#define NVID 1000 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +/* Plot type - color scheme */ + +#define CPLOT 30 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 25.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 0.75 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {4.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D -0.1 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 4 June 22 - Square rooms 2: Comparison of an anechoic chamber and a room with flat walls, with dissipation ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** +``` + init_circular_wave_mod(-1.0, 0.0, phi, psi, xy_in); + add_circular_wave_mod(1.0, 1.0, 0.0, phi, psi, xy_in); +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1800 /* number of grid points on x axis */ +#define NY 900 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ #define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ @@ -6130,16 +4855,20 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D /* Choice of the billiard table */ -#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 441 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependece of IoR on Mandelbrot escape speed */ + #define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ #define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ -#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ -#define MU 0.037 /* parameter controlling the dimensions of domain */ +#define LAMBDA 0.19 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 3 /* depth of computation of Menger gasket */ @@ -6171,12 +4900,12 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ -#define OMEGA 0.005 /* frequency of periodic excitation */ -#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ -#define COURANT 0.08 /* Courant number */ -#define COURANTB 0.02 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 1.0e-1 /* damping factor in wave equation */ +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.06 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 2.0e-2 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ #define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ @@ -6196,11 +4925,11 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D /* Parameters for length and speed of simulation */ -#define NSTEPS 2500 /* number of frames of movie */ -#define NVID 8 /* number of iterations between images displayed on screen */ +#define NSTEPS 1600 /* number of frames of movie */ +#define NVID 10 /* number of iterations between images displayed on screen */ #define NSEG 1000 /* number of segments of boundary */ #define INITIAL_TIME 0 /* time after which to start saving frames */ -#define BOUNDARY_WIDTH 3 /* width of billiard boundary */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ #define PAUSE 100 /* number of frames after which to pause */ #define PSLEEP 2 /* sleep time during pause */ @@ -6218,21 +4947,25 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D /* Plot type, see list in global_pdes.c */ -#define ZPLOT 103 /* wave height */ -#define CPLOT 103 /* color scheme */ +#define ZPLOT 109 /* wave height */ +#define CPLOT 109 /* color scheme */ + +#define ZPLOT_B 105 +#define CPLOT_B 105 /* plot type for second movie */ -#define ZPLOT_B 107 -#define CPLOT_B 106 /* plot type for second movie */ #define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ #define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ #define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 1 /* set to 1 to draw only facets with z not too negative */ #define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ #define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ #define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ -#define PLOT_SCALE_LOG_ENERGY 0.7 /* vertical scaling in log energy plot */ +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ /* 3D representation */ @@ -6244,24 +4977,25 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D /* Color schemes */ -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 11 /* Color palette, see list in global_pdes.c */ #define BLACK 1 /* background */ #define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.05 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 30.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ -#define VSCALE_ENERGY 100.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define SLOPE 0.7 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 10.0 /* additional scaling factor for color scheme P_3D_ENERGY */ #define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ #define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 1000.0 /* scaling factor for energy representation */ -#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ -#define LOG_SHIFT 1.5 /* shift of colors on log scale */ -#define LOG_ENERGY_FLOOR -6.0 /* floor value for log of (total) energy */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 1500.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.5 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ #define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ #define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ @@ -6269,12 +5003,12 @@ double observer[3] = {3.0, 7.0, 7.5}; /* location of observer for REP_PROJ_3D #define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ #define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ #define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 150.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 400.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 250.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 250.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ #define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ @@ -6288,23 +5022,23 @@ double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_ double v_3d[2] = {-0.75, -0.45}; double w_3d[2] = {0.0, 0.015}; double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3D representation */ +double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ -#define Z_SCALING_FACTOR 0.16 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.15 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ +#define Z_SCALING_FACTOR 0.05 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ ``` -### 1 May 22 - Lennard-Jones particles under increased gravity, in a container with sides at 120 degrees ### +### 3 June 22 - An almost perfect pool shot ### **Program:** `lennardjones.c` ``` #define MOVIE 1 /* set to 1 to generate movie */ -#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ #define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ /* so far incompatible with double movie */ @@ -6321,29 +5055,29 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ -#define INITXMIN -0.8 +#define INITXMIN 0.6 #define INITXMAX 0.8 /* x interval for initial condition */ -#define INITYMIN -0.9 -#define INITYMAX 0.8 /* y interval for initial condition */ +#define INITYMIN -0.1 +#define INITYMAX 0.1 /* y interval for initial condition */ -#define BCXMIN -1.9 -#define BCXMAX 1.9 /* x interval for boundary condition */ -#define BCYMIN -1.05 -#define BCYMAX 0.9 /* y interval for boundary condition */ +#define BCXMIN -1.6 +#define BCXMAX 1.6 /* x interval for boundary condition */ +#define BCYMIN -0.8 +#define BCYMAX 0.8 /* y interval for boundary condition */ #define OBSXMIN -2.0 #define OBSXMAX 2.0 /* x interval for motion of obstacle */ -#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ +#define CIRCLE_PATTERN 20 /* pattern of circles, see list in global_ljones.c */ -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 2 /* pattern of obstacles, see list in global_ljones.c */ +#define ADD_FIXED_OBSTACLES 1 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ #define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 1 /* pattern of repelling segments, see list in global_ljones.c */ +#define SEGMENT_PATTERN 6 /* pattern of repelling segments, see list in global_ljones.c */ #define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ #define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ #define CENTER_PX 0 /* set to 1 to center horizontal momentum */ #define CENTER_PY 0 /* set to 1 to center vertical momentum */ @@ -6356,22 +5090,22 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 #define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ #define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 2.75 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ #define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ -#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ -#define MU 0.013 /* parameter controlling radius of particles */ -#define MU_B 0.0254 /* parameter controlling radius of particles of second type */ -#define NPOLY 3 /* number of sides of polygon */ +#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */ +#define MU 0.02 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 18 /* number of sides of polygon */ #define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 30 /* number of grid point for grid of disks */ -#define NGRIDY 20 /* number of grid point for grid of disks */ +#define NGRIDX 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ #define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ #define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ @@ -6382,10 +5116,10 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 /* Parameters for length and speed of simulation */ -#define NSTEPS 3500 /* number of frames of movie */ -#define NVID 200 /* number of iterations between images displayed on screen */ +#define NSTEPS 6000 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ #define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 100 /* time after which to start saving frames */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 1 /* width of particle boundary */ #define LINK_WIDTH 2 /* width of links between particles */ #define CONTAINER_WIDTH 4 /* width of container boundary */ @@ -6399,14 +5133,16 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 /* Boundary conditions, see list in global_ljones.c */ -#define BOUNDARY_COND 0 +#define BOUNDARY_COND 20 /* Plot type, see list in global_ljones.c */ #define PLOT 0 -#define PLOT_B 8 /* plot type for second movie */ +#define PLOT_B 9 /* plot type for second movie */ +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ #define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ /* Color schemes */ @@ -6429,39 +5165,40 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 /* particle properties */ -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ #define PARTICLE_HUE_MIN 359.0 /* color of original particle */ #define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e3 /* energy of particle with hottest color */ +#define PARTICLE_EMAX 1.0e3 /* energy of particle with hottest color */ #define HUE_TYPE0 280.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 135.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 70.0 /* hue of particles of type 1 */ -#define HUE_TYPE3 210.0 /* hue of particles of type 1 */ +#define HUE_TYPE1 180.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ #define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 5.0e-7 /* time step for particle displacement */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ #define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST 2.2 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ #define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ #define DAMPING 0.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS 2.0 /* mass of particle of radius MU */ #define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ #define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ #define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 10.0 /* initial velocity range */ +#define V_INITIAL 0.0 /* initial velocity range */ #define OMEGA_INITIAL 10.0 /* initial angular velocity range */ -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ #define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.005 /* initial inverse temperature */ +#define BETA 0.01 /* initial inverse temperature */ #define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 5.0e9 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 5.0e9 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ -#define GRAVITY 4000.0 /* gravity acting on all particles */ -#define INCREASE_GRAVITY 1 /* set to 1 to increase gravity during the simulation */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 6.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ #define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ #define GRAVITY_INITIAL_TIME 500 /* time at start of simulation with constant gravity */ #define GRAVITY_RESTORE_TIME 1000 /* time at end of simulation with gravity restored to initial value */ @@ -6469,7 +5206,7 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 #define ROTATION 0 /* set to 1 to include rotation of particles */ #define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ #define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 50.0 /* force constant in angular dynamics */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ #define KTORQUE_B 10.0 /* force constant in angular dynamics */ #define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ #define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ @@ -6480,9 +5217,9 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 #define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ #define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 20.0 /* factor by which to change BETA during simulation */ +#define BETA_FACTOR 0.002 /* factor by which to change BETA during simulation */ #define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ -#define NO_OSCILLATION 0 /* set to 1 to have exponential BETA change only */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ #define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ #define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ @@ -6505,6 +5242,7 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 #define N_T_AVERAGE 50 /* size of temperature averaging window */ #define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ #define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ #define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ #define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ @@ -6514,10 +5252,10 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 #define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ #define NPART_BOTTOM 100 /* number of particles at the bottom */ -#define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 25 /* time at which to add first particle */ -#define ADD_PERIOD 20 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 250 /* final period where no particles are added */ +#define ADD_PARTICLES 1 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ #define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ #define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ @@ -6526,11 +5264,29 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 #define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ #define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 500 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 365 /* final time without rotation */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 100.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 0 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 1000 /* time at which to deactivate last segment */ + #define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ #define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ #define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + #define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ #define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ @@ -6543,12 +5299,12 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 #define WALL_TIME 500 /* time during which to keep wall */ #define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e9 /* maximal force */ -#define FLOOR_OMEGA 1 /* set to 1 to limit particle momentum to PMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ #define PMAX 1000.0 /* maximal force */ -#define HASHX 60 /* size of hashgrid in x direction */ -#define HASHY 32 /* size of hashgrid in y direction */ +#define HASHX 2 /* size of hashgrid in x direction */ +#define HASHY 2 /* size of hashgrid in y direction */ #define HASHMAX 100 /* maximal number of particles per hashgrid cell */ #define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ @@ -6559,3 +5315,453 @@ double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3 ``` +### 2 June 22 - Quantum pool ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(-1.0, -0.5, 8.0, -8.0, 0.25, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 480 /* number of grid points on x axis */ +#define NY 250 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 1 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 0 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 15 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000001 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.5 /* spring constant of harmonic potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* number of frames of movie */ +#define NVID 2000 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 4 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +/* Plot type - color scheme */ + +#define CPLOT 30 +#define CPLOT_B 32 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT_B 32 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 17 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 1.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 2.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 5.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 0.75 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {4.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 1.9 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D -0.1 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 1 June 22 - Square rooms: Comparison of an anechoic chamber and a room with flat walls ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** +``` + init_circular_wave_mod(-1.0, 0.0, phi, psi, xy_in); + add_circular_wave_mod(1.0, 1.0, 0.0, phi, psi, xy_in); +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1800 /* number of grid points on x axis */ +#define NY 900 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 441 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependece of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.2 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 3 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.025 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 0 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2200 /* number of frames of movie */ +#define NVID 7 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 109 /* wave height */ +#define CPLOT 109 /* color scheme */ + +#define ZPLOT_B 105 +#define CPLOT_B 105 /* plot type for second movie */ + + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 1 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 11 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 10.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 1000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.2 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 240.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 100.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 100.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {6.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.05 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` +