From 45c0d3f4620383481323002785823c574bab21d7 Mon Sep 17 00:00:00 2001 From: nilsberglund-orleans <83530463+nilsberglund-orleans@users.noreply.github.com> Date: Sat, 14 May 2022 21:04:33 +0200 Subject: [PATCH] Add files via upload --- Parameters_April22.md | 6528 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 6528 insertions(+) create mode 100644 Parameters_April22.md diff --git a/Parameters_April22.md b/Parameters_April22.md new file mode 100644 index 0000000..95b3384 --- /dev/null +++ b/Parameters_April22.md @@ -0,0 +1,6528 @@ +### Parameter values for YouTube simulations ### + +Created by **Nils Berglund** and optimized by **Marco Mancini** + +C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund + +Below are parameter values used for different simulations, as well as initial conditions used in +function animation. Some simulations use variants of the published code. The list is going to be +updated gradually. + + +### 30 April 22 - Colliding spirals in the Rock-Paper-Scissors equation 3: norm and direction of gradient ### + +**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 0.05 + +#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 3500 /* 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 23 +#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 */ + +#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 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 7.5 /* 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 */ + +``` + +### 29 April 22 - Young’s double-slit experiment with waves, log of energy and cumulative energy ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(-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 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -1.5 +#define XMAX 2.5 /* 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 9 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.5 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling the dimensions of domain */ +#define NPOLY 40 /* number of sides of polygon */ +#define APOLY 0.0 /* 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 0.005 /* 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 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 1100 /* number of frames of movie */ +#define NVID 14 /* 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 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 105 /* wave height */ +#define CPLOT 105 /* 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 0.8 /* 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 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 0.5 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 0.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 400.0 /* 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 3.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT -1.5 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR 1.8 /* 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 10.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 10.0 /* 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 0.05 /* 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 -0.15 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.2 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 28 April 22 - An hourglass with Lennard-Jones particles ### + +**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 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 1000 /* window width */ +#define WINHEIGHT 1000 /* window height */ + +#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 -0.6 +#define INITXMAX 0.6 /* x interval for initial condition */ +#define INITYMIN 0.7 +#define INITYMAX 1.0 /* y interval for initial condition */ + +#define BCXMIN -0.9 +#define BCXMAX 0.9 /* x interval for boundary condition */ +#define BCYMIN -1.1 +#define BCYMAX 1.1 /* 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 30 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* 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 1200 /* 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 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 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 4.0 /* 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 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 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 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 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 */ + +``` + + +### 27 April 22 - 3D waves in a star-shaped domain with log energy plot ### + +**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 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 */ + +#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 42 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.05 /* parameter controlling the dimensions of domain */ +#define NPOLY 40 /* number of sides of polygon */ +#define APOLY 0.0 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 */// #define OSCILLATING_SOURCE_PERIOD 14 /* 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 15 /* 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 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 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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.5 /* 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 103 /* wave height */ +#define CPLOT 103 /* 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 1 /* 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 1 /* 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 0.6 /* 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 10 /* 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 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 0.5 /* 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 300.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.2 /* shift of colors on log scale */ +#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 3.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.0 /* 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, 6.5}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.025 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 3.0 /* 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 -0.05 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 26 April 22 - Colliding spirals in the Rock-Paper-Scissors equation 2: norms of gradient and vorticity ### + +**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 below */ +#define NFIELDS 3 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 3 /* 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 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 0.05 + +#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 BZF 0.667 /* 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 150.0 /* 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 10 /* 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 5 /* initial still time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Plot type - color scheme */ + +#define PLOT 23 + +#define PLOT_B 25 /* plot type for second movie */ + +#define P_AMPLITUDE 0 /* amplitude of first field */ + +#define P_RGB 20 /* RGB plot */ +#define P_POLAR 21 /* polar angle associated with RBG plot */ +#define P_GRADIENT 22 /* gradient of polar angle */ +#define P_GRADIENTX 23 /* direction of gradient of u */ +#define P_GRADIENT_INTENSITY 24 /* gradient and intensity of polar angle */ +#define P_VORTICITY 25 /* curl of polar angle */ + +/* Plot type - height of 3D plot */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ZPLOT 23 /* z coordinate in 3D plot */ +#define ZPLOT_B 22 /* z coordinate in second 3D plot */ + +#define Z_AMPLITUDE 0 /* amplitude of first field */ +#define Z_NORM_GRADIENT 22 /* gradient of polar angle */ +#define Z_NORM_GRADIENTX 23 /* direction of gradient of u */ +#define Z_NORM_GRADIENT_INTENSITY 24 /* gradient and intensity of polar angle */ +#define Z_VORTICITY 25 /* curl of polar angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#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 v */ + +#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 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 11 /* 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 2.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000002 /* 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 P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +/* 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 0.3 /* 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 */ + +#define COMPUTE_THETA ((plot == P_POLAR)||(plot == P_GRADIENT)||(plot == P_GRADIENTX)||(plot == P_GRADIENT_INTENSITY)||(plot == P_VORTICITY)) +#define COMPUTE_THETAZ ((zplot == P_POLAR)||(zplot == P_GRADIENT)||(zplot == P_GRADIENTX)||(zplot == P_GRADIENT_INTENSITY)||(zplot == P_VORTICITY)) + +/* 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 */ + +``` + +### 25 April 22 - A heptagonal parabolic resonator ### + +**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 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 */ + +#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 32 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 7 /* number of sides of polygon */ +#define APOLY 0.0 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 12 /* 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 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 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 0 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.5 /* 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 103 /* wave height */ +#define CPLOT 103 /* color scheme */ + +#define ZPLOT_B 105 +#define CPLOT_B 105 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ + +#define P_3D_PHASE 111 /* phase of wave */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in 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 10 /* 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 0.5 /* 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 300.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 3.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 15.0 /* 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, 6.5}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.02 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 3.0 /* 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 0.05 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 24 April 22 - Vorticity of colliding spirals in 3D in the Rock-Paper-Scissors 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 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 below */ +#define NFIELDS 3 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 3 /* 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 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 0.05 + +#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 150.0 /* 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 3000 /* number of frames of movie */ +#define NVID 10 /* 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 5 /* initial still time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Plot type - color scheme */ + +#define PLOT 25 + +#define PLOT_B 25 /* plot type for second movie */ + +#define P_AMPLITUDE 0 /* amplitude of first field */ + +#define P_RGB 20 /* RGB plot */ +#define P_POLAR 21 /* polar angle associated with RBG plot */ +#define P_GRADIENT 22 /* gradient of polar angle */ +#define P_GRADIENTX 23 /* direction of gradient of u */ +#define P_GRADIENT_INTENSITY 24 /* gradient and intensity of polar angle */ +#define P_VORTICITY 25 /* curl of polar angle */ + +/* Plot type - height of 3D plot */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ZPLOT 25 /* z coordinate in 3D plot */ +#define ZPLOT_B 0 /* z coordinate in second 3D plot */ + +#define Z_AMPLITUDE 0 /* amplitude of first field */ +#define Z_VORTICITY 25 /* curl of polar angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#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 v */ + +#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 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* 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 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 0.000002 /* 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 P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +/* 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, 8.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.25 /* 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 0.0 /* overall y shift for REP_PROJ_3D representation */ + +#define COMPUTE_THETA ((plot == P_POLAR)||(plot == P_GRADIENT)||(plot == P_GRADIENTX)||(plot == P_GRADIENT_INTENSITY)||(plot == P_VORTICITY)) + +/* 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 */ + +``` + +### 23 April 22 - Young’s double-slit experiment with waves: Phase representation in 3D ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(-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 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 */ + +#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 9 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.5 /* parameter controlling the dimensions of domain */ +#define MU 0.05 /* 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 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 1 /* 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 1400 /* 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 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 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 0 /* 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 111 /* color scheme */ + +#define ZPLOT_B 103 +#define CPLOT_B 111 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ + +#define P_3D_PHASE 111 /* phase of wave */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in 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 0 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 17 /* 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 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 300.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 5.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 15.0 /* 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 0.03 /* 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 0.5 /* 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 */ + +``` + +### 22 April 22 - Bed of roses: Spiral energy in the Rock-Paper-Scissors 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 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 below */ +#define NFIELDS 3 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 3 /* 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 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 2.0 + +#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 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 25 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 150.0 /* 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 2400 /* number of frames of movie */ +#define NVID 10 /* 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 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Plot type - color scheme */ + +#define PLOT 23 + +#define PLOT_B 25 /* plot type for second movie */ + +#define P_AMPLITUDE 0 /* amplitude of first field */ + +#define P_RGB 20 /* RGB plot */ +#define P_POLAR 21 /* polar angle associated with RBG plot */ +#define P_GRADIENT 22 /* gradient of polar angle */ +#define P_GRADIENTX 23 /* direction of gradient of u */ +#define P_GRADIENT_INTENSITY 24 /* gradient and intensity of polar angle */ +#define P_VORTICITY 25 /* curl of polar angle */ + +/* Plot type - height of 3D plot */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ZPLOT 23 /* z coordinate in 3D plot */ +#define ZPLOT_B 22 /* z coordinate in second 3D plot */ + +#define Z_AMPLITUDE 0 /* amplitude of first field */ +#define Z_NORM_GRADIENT 22 /* gradient of polar angle */ +#define Z_NORM_GRADIENTX 23 /* direction of gradient of u */ +#define Z_NORM_GRADIENT_INTENSITY 24 /* gradient and intensity of polar angle */ +#define Z_VORTICITY 25 /* curl of polar angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#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 v */ + +#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 11 /* 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 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 0.000002 /* 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 P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +/* 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 0.25 /* 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 */ + +#define COMPUTE_THETA ((plot == P_POLAR)||(plot == P_GRADIENT)||(plot == P_GRADIENTX)||(plot == P_GRADIENT_INTENSITY)||(plot == P_VORTICITY)) +#define COMPUTE_THETAZ ((zplot == P_POLAR)||(zplot == P_GRADIENT)||(zplot == P_GRADIENTX)||(zplot == P_GRADIENT_INTENSITY)||(zplot == P_VORTICITY)) + +/* 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 */ + +``` + +### 21 April 22 - Waves hitting a Mandelbrot set, in 3D (longer version) ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave(-0.9, 0.5, 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 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 -0.925 +#define YMAX 1.325 /* 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 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.2 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* 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 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 -0.2 +#define ISO_YSHIFT_RIGHT 0.15 +#define ISO_SCALE 0.475 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.06 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 20 /* 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 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 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 */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 0 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#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 */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 105 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in 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 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 0.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 5.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 10.0 /* 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] = {2.0, 8.0, 7.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.03 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 3.8 /* 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 1.2 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.35 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 20 April 22 - 3D rendreing of spirals in the Rock-Paper-Scissors 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 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 below */ +#define NFIELDS 3 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 3 /* 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 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 0.05 + +#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 100 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 150.0 /* 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 2900 /* number of frames of movie */ +#define NVID 10 /* 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 5 /* initial still time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Plot type */ + +#define PLOT 103 + +#define PLOT_B 25 /* plot type for second movie */ + +#define P_AMPLITUDE 0 /* amplitude of first field */ + +#define P_RGB 20 /* RGB plot */ +#define P_POLAR 21 /* polar angle associated with RBG plot */ +#define P_GRADIENT 22 /* gradient of polar angle */ +#define P_GRADIENTX 23 /* direction of gradient of u */ +#define P_GRADIENT_INTENSITY 24 /* gradient and intensity of polar angle */ +#define P_VORTICITY 25 /* curl of polar angle */ + + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ + +#define PLOT_3D (PLOT > 100) /* controls whether plot is 2D or 3D */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#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 v */ + +#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 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 /* 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 3.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.00001 /* 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 */ +/* 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] = {2.0, 8.0, 7.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.25 /* 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 */ + +#define COMPUTE_THETA ((plot == P_POLAR)||(plot == P_GRADIENT)||(plot == P_GRADIENTX)||(plot == P_GRADIENT_INTENSITY)||(plot == P_VORTICITY)) + +/* 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 */ + +``` + +### 19 April 22 - 3D rendering of the Buser-Conway-Doyle-Semmler homophonic drums ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_xplusminus(startleft[0], startleft[1], startright[0], startright[1], 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 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 */ + +#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 38 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.2 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* 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 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 -0.2 +#define ISO_YSHIFT_RIGHT 0.15 +#define ISO_SCALE 0.475 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.06 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 20 /* 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 1800 /* number of frames of movie */ +#define NVID 14 /* 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 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 */ +#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 0 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 105 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in 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 14 /* 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 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 0.2 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#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 3.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 10.0 /* 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] = {4.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.02 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.15 /* 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 -0.42 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.05 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 18 April 22 - The 2D Allen-Cahn equation with growing viscosity rendred in 3D ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_random(0.0, 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 1 /* choice of reaction term, see list below */ +#define NFIELDS 1 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 1 /* 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 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 0.0000003 + +#define VISCOSITY 0.05 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ + +#define EPSILON 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 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 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 50 /* 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 10 /* 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 5 /* initial still time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#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 */ + +/* Plot type */ + +#define PLOT 103 + +#define PLOT_B 25 /* plot type for second movie */ + +#define P_AMPLITUDE 0 /* amplitude of first field */ + +#define P_RGB 20 /* RGB plot */ +#define P_POLAR 21 /* polar angle associated with RBG plot */ +#define P_GRADIENT 22 /* gradient of polar angle */ +#define P_GRADIENTX 23 /* direction of gradient of u */ +#define P_GRADIENT_INTENSITY 24 /* gradient and intensity of polar angle */ +#define P_VORTICITY 25 /* curl of polar angle */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ + +#define PLOT_3D (PLOT > 100) /* controls whether plot is 2D or 3D */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + + +/* Field representation */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 1 /* set to 1 to print v */ + +#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 18 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* 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 0.75 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 0.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.00001 /* 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 */ + +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, 7.0}; /* 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 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 0.1 /* 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 */ + +``` + +### 17 April 22 - Interaction pentagons on a surface of genus 2 ### + +**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 4 /* 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 1.0 /* 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 1 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 2 /* pattern of obstacles, 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 0 /* 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 3 /* 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 2.4 /* 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 0.033 /* 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 0.125 /* 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 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 2750 /* number of frames of movie */ +#define NVID 200 /* 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 14 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 3 +#define PLOT_B 4 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* Color schemes */ + +#define COLOR_PALETTE 18 /* 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 135.0 /* hue of particles of type 1 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-7 /* 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 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 0.0002 /* 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 5.0e8 /* 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_RESTORE_TIME 750 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 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 0.15 /* 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 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 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 TRAJECTORY_LENGTH 6000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 0.1 /* 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 16 /* 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 */ + +``` + +### 16 April 22 - 3D waves in a Tokarsky unilluminable room without right angles ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave(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 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 */ + +#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 201 /* 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 1 /* 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 6 /* number of sides of polygon */ +#define APOLY 0.0 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 20 /* 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 2200 /* 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 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 */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 0 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#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 */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 105 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in 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 10 /* 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 0.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 300.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 5.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 15.0 /* 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, 7.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.03 /* 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 */ + +``` + +### 15 April 22 - Interacting squares on a surface of genus 2 ### + +**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 4 /* 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 1.0 /* 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 1 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 2 /* pattern of obstacles, 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 0 /* 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 2 /* 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 4.0 /* 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 2.25 /* 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 0.03 /* 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 0.125 /* 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 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 2400 /* number of frames of movie */ +#define NVID 200 /* 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 14 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#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 0 /* 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 135.0 /* hue of particles of type 1 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-7 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.5 /* 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 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 0.0002 /* 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 5.0e8 /* 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_RESTORE_TIME 750 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 600.0 /* 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 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 0.08 /* 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 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 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 TRAJECTORY_LENGTH 6000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 0.1 /* 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 22 /* 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 */ + +``` + +### 14 April 22 - One cannot always hear the shape of a drum: Isospectral billiards in 3D ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_xplusminus(startleft[0], startleft[1], startright[0], startright[1], 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 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 */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 37 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.6 /* parameter controlling the dimensions of domain */ +#define MU 0.6 /* 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 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 -1.0 +#define ISO_XSHIFT_RIGHT 0.9 +#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 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.06 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 20 /* 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 2550 /* number of frames of movie */ +#define NVID 18 /* 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 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 */ +#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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.5 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 104 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.1 /* vertical scaling in 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 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 15 /* 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 0.1 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 0.25 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* 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 3.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.0 /* 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] = {0.40824829, 0.816496581, 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 0.006 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.4 /* 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 0.1 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 13 April 22 - Waves hitting a Mandelbrot set, in 3D ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave(-0.9, 0.5, 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 HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define WINWIDTH 720 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 1440 /* number of grid points on x axis */ +#define NY 1440 /* number of grid points on y axis */ + +#define XMIN -1.65 +#define XMAX 0.1 /* x interval */ +#define YMIN -0.6 +#define YMAX 1.15 /* 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 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.2 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* 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 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 -0.2 +#define ISO_YSHIFT_RIGHT 0.15 +#define ISO_SCALE 0.475 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.06 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 20 /* 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 700 /* 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 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 */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 0 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#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 */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 105 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ +#define P_3D_LOG_ENERGY 105 /* color depends on logarithm of energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in 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 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 0.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 5.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 10.0 /* 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] = {2.0, 8.0, 7.0}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.03 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 3.5 /* 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 0.9 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.4 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 12 April 22 - Interacting dipoles on a surface of genus 2 ### + +**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 4 /* 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 1.0 /* 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 1 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 2 /* pattern of obstacles, 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 0 /* 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 5 /* 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 2.0 /* 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 1.75 /* 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 0.045 /* 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 0.125 /* 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 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 3400 /* number of frames of movie */ +#define NVID 200 /* 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 14 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#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 0 /* 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 135.0 /* hue of particles of type 1 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-7 /* 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 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 0.0002 /* 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 5.0e8 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 3.0 /* 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_RESTORE_TIME 750 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 600.0 /* 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 50.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* 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 0.1 /* 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 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 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 TRAJECTORY_LENGTH 6000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 0.1 /* 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 36 /* 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 */ + +``` + +### 11 April 22 - 3D waves in a 2D Julia set ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** + +``` + init_circular_wave(0.2, 0.4, phi, psi, xy_in); + add_circular_wave(-1.0, -0.2, -0.4, 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 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 */ + +#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 16 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.6 /* parameter controlling the dimensions of domain */ +#define MU 0.6 /* 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 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 -1.0 +#define ISO_XSHIFT_RIGHT 0.9 +#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 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.06 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 20 /* 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 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 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 */ +#define MID_FRAMES 200 /* 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 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 104 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in 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 14 /* 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 0.2 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 0.35 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.0 /* 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] = {10.0, 6.0, 8.5}; /* location of observer for REP_PROJ_3D representation */ + +#define Z_SCALING_FACTOR 0.018 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 3.75 /* 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 */ + +``` + +``` +double julia_x = 0.37468, julia_y = 0.21115; + +``` + +### 10 April 22 - Brownian particles on a surface of genus 2 ### + +**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 -1.9 +#define INITXMAX 1.9 /* x interval for initial condition */ +#define INITYMIN -1.0 +#define INITYMAX 1.0 /* 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 1 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 2 /* pattern of obstacles, 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 5.75 /* 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 0.015 /* 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 0.125 /* 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 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 5100 /* number of frames of movie */ +#define NVID 200 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#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 */ + +#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 14 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 5 +#define PLOT_B 4 /* 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 1.0e3 /* 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 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 5.0 /* 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 0.0001 /* 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 5.0e8 /* 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_RESTORE_TIME 750 /* 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 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 SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 1 /* 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 34 /* size of hashgrid in x direction */ +#define HASHY 18 /* 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 April 22 - A hexagonal parabolic resonator, in 3D ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave(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 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -1.8 +#define XMAX 2.2 /* 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 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 32 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.0 /* 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 0.0 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.06 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 20 /* 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 2350 /* number of frames of movie */ +#define NVID 18 /* 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 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 */ +#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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.5 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 104 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.15 /* vertical scaling in 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 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 0.1 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 0.25 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* 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 3.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.0 /* 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] = {0.40824829, 0.816496581, 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 0.0075 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 3.0 /* 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 */ + +``` + +### 8 April 22 - Crystal formation on a surface of genus 2 ### + +**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 4 /* 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 1.0 /* 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 1 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 2 /* pattern of obstacles, 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 0 /* 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 3.25 /* 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 0.021 /* 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 0.125 /* 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 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 3400 /* number of frames of movie */ +#define NVID 200 /* 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 14 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#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 0 /* 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 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* 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 135.0 /* hue of particles of type 1 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-7 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 7.5 /* 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 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 0.001 /* 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 5.0e8 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 5.5 /* 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_RESTORE_TIME 750 /* 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 600.0 /* 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 100.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* 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 0.1 /* 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 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 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 TRAJECTORY_LENGTH 6000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 0.1 /* 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 22 /* 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 */ + +``` + +### 7 April 22 - A diffraction grating in 3D ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave(-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 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -1.8 +#define XMAX 2.2 /* 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 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 10 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.18 /* parameter controlling the dimensions of domain */ +#define MU 0.045 /* parameter controlling the dimensions of domain */ +#define NPOLY 4 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.06 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 1 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 20 /* 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 1400 /* number of frames of movie */ +#define NVID 12 /* 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 2 /* width of billiard boundary */ + +#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 */ +#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 */ + +/* 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 0.05 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 104 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.1 /* vertical scaling in 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 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 1.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 3.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* 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 4.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.0 /* 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] = {0.40824829, 0.816496581, 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 0.0075 /* 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 0.5 /* max value of z coordinate for REP_PROJ_3D representation */ + +``` + +### 6 April 22 - Lennard-Jones particles in increasing gravity, long version with gravity reset at the end ### + +**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 4 /* 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 -1.6 +#define INITXMAX 1.6 /* x interval for initial condition */ +#define INITYMIN -0.95 +#define INITYMAX 0.65 /* y interval for initial condition */ + +#define BCXMIN -1.95 +#define BCXMAX 1.95 /* x interval for boundary condition */ +#define BCYMIN -1.05 +#define BCYMAX 0.9 /* 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 0 /* pattern of obstacles, 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 0 /* 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 0.015 /* 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 0.125 /* 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 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 2750 /* number of frames of movie */ +#define NVID 200 /* 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 1 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 6 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* 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 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e3 /* energy of particle with hottest color */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-7 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 7.5 /* 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 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 0.005 /* 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 5.0e7 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 5.5 /* 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 GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_RESTORE_TIME 750 /* 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 600.0 /* 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 500.0 /* 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 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 0.3 /* 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 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 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 TRAJECTORY_LENGTH 6000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 0.1 /* 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 22 /* 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 April 22 - Young’s double-slit experiment with waves, in 3D ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave(-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 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -1.8 +#define XMAX 2.2 /* 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 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 9 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.5 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling the dimensions of domain */ +#define NPOLY 4 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.06 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 1 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 20 /* 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 12 /* 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 2 /* width of billiard boundary */ + +#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 */ +#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 */ + +/* 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 0.05 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +// #define PLOT 104 +#define PLOT 103 + +#define PLOT_B 104 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +#define PLOT_SCALE_ENERGY 0.08 /* vertical scaling in energy plot */ + +/* 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 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 3.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* 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 4.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.0 /* 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 */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; + +``` + +### 4 April 22 - A wave traveling between parabolic reflectors, in 3D ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave(LAMBDA, 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 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -1.8 +#define XMAX 2.2 /* 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 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 19 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.1 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* parameter controlling the dimensions of domain */ +#define NPOLY 4 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-7 /* 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 100 /* 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 1700 /* number of frames of movie */ +#define NVID 15 /* 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 2 /* width of billiard boundary */ + +#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 */ +#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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 104 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ +#define P_3D_ENERGY 104 /* color depends on energy, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +/* 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 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 0.7 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 0.7 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* 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 4.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.0 /* 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 */ + +double u_3d[2] = {-0.75, -0.45}; /* projections of basis vectors */ +double v_3d[2] = {0.75, -0.45}; +double w_3d[2] = {0.0, 0.025}; + +``` + +### 3 April 22 - Shock wave of a narrow wedge moving through & Lennard-Jones gas ### + +**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 4 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.75 +#define XMAX 1.25 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -3.65 +#define INITXMAX 2.15 /* x interval for initial condition */ +#define INITYMIN -1.0 +#define INITYMAX 1.0 /* y interval for initial condition */ + +#define BCXMIN -3.75 +#define BCXMAX 2.25 /* 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 0 /* pattern of obstacles, 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 0 /* 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 5.0 /* 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 0.125 /* 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 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 500 /* number of frames of movie */ +#define NSTEPS 3200 /* number of frames of movie */ +#define NVID 200 /* 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 8 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#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 0 /* 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 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* energy of particle with hottest color */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-7 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#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 5.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 5.0e7 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 5.5 /* 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 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 600.0 /* 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 500.0 /* 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 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 1 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 1 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 1 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.3 /* 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 1 /* 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 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 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 TRAJECTORY_LENGTH 6000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 0.1 /* 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 90 /* 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 */ + +``` + +### 2 April 22 - 3D waves flowing over Sierpinski carpets ### + +**Program:** `wave_3d_sierpinski.c` (variant of `wave_3d.c`) + +**Initial condition in function `animation()`:** `init_circular_wave_sierpinski(1.5, 0.0, phi, psi, xy_in, mdepth);` + +``` +#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 -1.8 +#define XMAX 2.2 /* 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 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 15 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* 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 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.3 /* parameter controlling the dimensions of domain */ +#define NPOLY 4 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-7 /* 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 100 /* 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 1000 /* number of frames of movie */ +#define NVID 15 /* 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 2 /* width of billiard boundary */ + +#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 */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 103 + +#define PLOT_B 102 /* plot type for second movie */ + +#define P_3D_AMPLITUDE 101 /* color depends on amplitude */ +#define P_3D_ANGLE 102 /* color depends on angle with fixed direction */ +#define P_3D_AMP_ANGLE 103 /* color depends on amplitude, luminosity depends on angle */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ + +/* Color schemes */ + +#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 /* 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 0.7 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 300.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* 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 4.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 1.0 /* 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 */ + +``` + +### 1 April 22 - A novel way of generating energy from water ### + +**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 4 /* 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 -1.0 +#define INITYMAX 1.0 /* 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 0 /* pattern of obstacles, 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 0 /* 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 7 /* 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 0.035 /* 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 0.0 /* 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 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 2700 /* number of frames of movie */ +#define NVID 200 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* 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 3 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* 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 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.5e3 /* energy of particle with hottest color */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 1.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 3.75 /* Lennard-Jones equilibrium distance for second type of particle */ +#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 0.0005 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 5.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 5.0e7 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 5.5 /* radius in which to count neighbours */ +#define GRAVITY 2000.0 /* 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 ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 600.0 /* 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 500.0 /* 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 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 0.15 /* 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 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 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 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 TRAJECTORY_LENGTH 6000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 0.1 /* 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 1.0e8 /* maximal force */ +#define FLOOR_OMEGA 1 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 25 /* 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 */ + +``` +