diff --git a/Parameters.md b/Parameters.md index 9bb982b..0edd12f 100644 --- a/Parameters.md +++ b/Parameters.md @@ -9,7 +9,7 @@ function animation. Some simulations use variants of the published code. The lis updated gradually. -### 19 October 22 - Tracking a rocket able to rotate ### +### 20 November 22 - Modeling a cave-in with Lennard-Jones particles ### **Program:** `lennardjones.c` @@ -27,34 +27,34 @@ updated gradually. #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ -#define XMIN -3.3 -#define XMAX 4.7 /* x interval */ -#define YMIN -2.25 -#define YMAX 2.25 /* y interval for 9/16 aspect ratio */ +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ -#define INITXMIN -0.7 -#define INITXMAX 0.7 /* x interval for initial condition */ -#define INITYMIN -1.7 -#define INITYMAX 2.5 /* y interval for initial condition */ +#define INITXMIN -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN 0.05 +#define INITYMAX 1.1 /* y interval for initial condition */ -#define BCXMIN -5.1 -#define BCXMAX 6.1 /* x interval for boundary condition */ -#define BCYMIN -6.5 -#define BCYMAX 44.0 /* y interval for boundary 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 CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ #define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ #define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ #define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 101 /* pattern of repelling segments, see list in global_ljones.c */ -#define ROCKET_SHAPE 1 /* shape of rocket combustion chamber, see list in global_ljones.c */ -#define ROCKET_SHAPE_B 0 /* shape of second rocket */ -#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define SEGMENT_PATTERN 18 /* pattern of repelling segments, see list in global_ljones.c */ +#define ROCKET_SHAPE 2 /* shape of rocket combustion chamber, see list in global_ljones.c */ +#define ROCKET_SHAPE_B 2 /* shape of second rocket */ +#define NOZZLE_SHAPE 2 /* shape of nozzle, see list in global_ljones.c */ #define NOZZLE_SHAPE_B 4 /* shape of nozzle for second rocket, see list in global_ljones.c */ #define TWO_TYPES 0 /* set to 1 to have two types of particles */ @@ -71,12 +71,12 @@ updated gradually. #define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ #define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define PDISC_DISTANCE 2.5 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_DISTANCE 2.7 /* minimal distance in Poisson disc process, controls density of particles */ #define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ #define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ #define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ -#define MU 0.007 /* parameter controlling radius of particles */ +#define MU 0.008 /* parameter controlling radius of particles */ #define MU_B 0.018 /* parameter controlling radius of particles of second type */ #define NPOLY 25 /* number of sides of polygon */ #define APOLY 0.666666666 /* angle by which to turn polygon, in units of Pi/2 */ @@ -99,10 +99,10 @@ updated gradually. /* Parameters for length and speed of simulation */ -#define NSTEPS 2750 /* number of frames of movie */ +#define NSTEPS 5000 /* number of frames of movie */ #define NVID 100 /* 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 INITIAL_TIME 200 /* time after which to start saving frames */ #define OBSTACLE_INITIAL_TIME 200 /* time after which to start moving obstacle */ #define BOUNDARY_WIDTH 1 /* width of particle boundary */ #define LINK_WIDTH 2 /* width of links between particles */ @@ -117,7 +117,7 @@ updated gradually. /* Boundary conditions, see list in global_ljones.c */ -#define BOUNDARY_COND 20 +#define BOUNDARY_COND 1 /* Plot type, see list in global_ljones.c */ @@ -126,7 +126,9 @@ updated gradually. #define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ #define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ -#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ +#define ALTITUDE_LINES 0 /* set to 1 to add horizontal lines to show altitude */ +#define COLOR_SEG_GROUPS 0 /* set to 1 to collor segment groups differently */ /* Color schemes */ @@ -153,7 +155,7 @@ updated gradually. #define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ #define PARTICLE_HUE_MIN 359.0 /* color of original particle */ #define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define PARTICLE_EMAX 1.5e2 /* energy of particle with hottest color */ #define HUE_TYPE0 70.0 /* hue of particles of type 0 */ #define HUE_TYPE1 280.0 /* hue of particles of type 1 */ #define HUE_TYPE2 .0 /* hue of particles of type 2 */ @@ -162,10 +164,10 @@ updated gradually. #define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ #define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ #define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST 3.7 /* Lennard-Jones equilibrium distance */ #define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 5.0 /* damping coefficient of particles */ +#define REPEL_RADIUS 15.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 100.0 /* 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 */ @@ -173,15 +175,15 @@ updated gradually. #define V_INITIAL 0.0 /* initial velocity range */ #define OMEGA_INITIAL 10.0 /* initial angular velocity range */ -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ #define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ #define SIGMA 5.0 /* noise intensity in thermostat */ #define BETA 0.02 /* initial inverse temperature */ #define MU_XI 0.01 /* friction constant in thermostat */ #define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ #define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ -#define GRAVITY 15.0 /* gravity acting on all particles */ +#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ +#define GRAVITY 2500.0 /* gravity acting on all particles */ #define GRAVITY_X 0.0 /* horizontal gravity acting on all particles */ #define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ #define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ @@ -202,13 +204,13 @@ updated gradually. #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 INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ #define BETA_FACTOR 0.025 /* 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 MIDDLE_CONSTANT_PHASE 1050 /* final phase in which temperature is constant */ -#define FINAL_DECREASE_PHASE 1500 /* final phase in which temperature decreases */ -#define FINAL_CONSTANT_PHASE -1 /* final phase in which temperature is constant */ +#define MIDDLE_CONSTANT_PHASE 2000 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 1300 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE -1 /* 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 */ @@ -270,23 +272,23 @@ updated gradually. #define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ #define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ #define RELEASE_ROCKET_AT_DEACTIVATION 1 /* set to 1 to limit segments velocity before segment release */ -#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_X0 1.5 /* initial position of segments */ #define SEGMENTS_Y0 0.0 /* initial position of segments */ #define SEGMENTS_VX0 0.0 /* initial velocity of segments */ #define SEGMENTS_VY0 0.0 /* initial velocity of segments */ #define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ #define MOVE_SEGMENT_GROUPS 1 /* set to 1 to group segments into moving units */ -#define SEGMENT_GROUP_MASS 1000.0 /* mass of segment group */ -#define SEGMENT_GROUP_I 25.0 /* moment of inertia of segment group */ +#define SEGMENT_GROUP_MASS 1000.0 /* mass of segment group */ +#define SEGMENT_GROUP_I 1000.0 /* moment of inertia of segment group */ #define SEGMENT_GROUP_DAMPING 0.0 /* damping of segment groups */ -#define GROUP_REPULSION 0 /* set to 1 for groups of segments to repel each other */ -#define KSPRING_GROUPS 1.0e8 /* harmonic potential between segment groups */ +#define GROUP_REPULSION 1 /* set to 1 for groups of segments to repel each other */ +#define KSPRING_GROUPS 1.0e11 /* harmonic potential between segment groups */ #define GROUP_WIDTH 0.05 /* interaction width of groups */ -#define GROUP_G_REPEL 0 /* set to 1 to add repulsion between centers of mass of groups */ -#define GROUP_G_REPEL_RADIUS 0.12 /* radius within which centers of mass of groups repel each other */ +#define GROUP_G_REPEL 1 /* set to 1 to add repulsion between centers of mass of groups */ +#define GROUP_G_REPEL_RADIUS 1.2 /* radius within which centers of mass of groups repel each other */ #define TRACK_SEGMENT_GROUPS 1 /* set to 1 for view to track group of segments */ -#define TRACK_X_PADDING 1.2 /* distance from x boundary where tracking starts */ +#define TRACK_X_PADDING 2.0 /* distance from x boundary where tracking starts */ #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 horizontal */ @@ -297,8 +299,9 @@ updated gradually. #define REACTION_PROB 0.0045 /* probability controlling reaction term */ #define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ -#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ -#define PLOT_SPEEDS 1 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ +#define PRINT_LEFT 0 /* set to 1 to print certain parameters at the top left instead of right */ +#define PLOT_SPEEDS 0 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ +#define PLOT_TRAJECTORIES 0 /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */ #define VMAX_PLOT_SPEEDS 0.6 /* vertical scale of plot of obstacle speeds */ #define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ @@ -322,8 +325,8 @@ updated gradually. #define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ #define PMAX 1000.0 /* maximal force */ -#define HASHX 160 /* size of hashgrid in x direction */ -#define HASHY 600 /* size of hashgrid in y direction */ +#define HASHX 180 /* size of hashgrid in x direction */ +#define HASHY 90 /* 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 */ @@ -334,785 +337,11 @@ updated gradually. ``` -### 18 October 22 - A circular wave starting off center in a hexagon-bestagon ### - -**Program:** `wave_billiard.c` - -**Initial condition in function `animation()`:** `init_circular_wave(0.1, 0.1, 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 3840 /* number of grid points on x axis */ -#define NY 2000 /* 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 1 /* 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 8 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 1 /* pattern of circles or polygons, see list in global_pdes.c */ - -#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ -#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ -#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ - -#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 6 /* number of sides of polygon */ -#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 6 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 12 /* number of grid point for grid of disks */ -#define NGRIDY 15 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -2.9 -#define ISO_XSHIFT_RIGHT 1.4 -#define ISO_YSHIFT_LEFT -0.15 -#define ISO_YSHIFT_RIGHT -0.15 -#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard below */ - -/* Physical parameters of wave equation */ - -#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ -#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ -#define OSCILLATION_SCHEDULE 1 /* oscillation schedule, see list in global_pdes.c */ - -#define OMEGA 0.0005 /* frequency of periodic excitation */ -#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ -#define ACHIRP 0.25 /* acceleration coefficient in chirp */ -#define DAMPING 0.0 /* damping of periodic excitation */ -#define COURANT 0.06 /* Courant number */ -#define COURANTB 0.12 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 0.0 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ -#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ -/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ -/* The physical damping coefficient is given by GAMMA/(DT)^2 */ -/* Increasing COURANT speeds up the simulation, but decreases accuracy */ -/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ - -#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ -#define OSCILLATING_SOURCE_PERIOD 25 /* 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 3400 /* number of frames of movie */ -#define NVID 20 /* 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 PRINT_SPEED 0 /* print speed of moving source */ - -#define PAUSE 200 /* 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 */ -#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 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define PLOT 0 - -#define PLOT_B 5 /* plot type for second movie */ - -/* Color schemes */ - -#define COLOR_PALETTE 15 /* 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 PHASE_FACTOR 1.0 /* 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 125.0 /* 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 2.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 1.5 /* 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 */ - -#define NXMAZE 7 /* width of maze */ -#define NYMAZE 7 /* height of maze */ -#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ -#define RAND_SHIFT 24 /* seed of random number generator */ -#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ - -/* 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 October 22 - Two vortices in the incompressible Euler equation (short version) ### - -**Program:** `rde.c` - -**Initial condition in function `animation()`:** - -``` - init_vortex_state(0.4, 0.0, 0.1, phi, xy_in); - add_vortex_state(-0.4, 0.0, 0.1, 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 900 /* window width */ -#define WINHEIGHT 900 /* window height */ -#define NX 450 /* number of grid points on x axis */ -#define NY 450 /* number of grid points on y axis */ - -#define XMIN -1.0 -#define XMAX 1.0 /* x interval */ -#define YMIN -1.0 -#define YMAX 1.0 /* y interval for 9/16 aspect ratio */ - -/* Choice of simulated equation */ - -#define RDE_EQUATION 6 /* choice of reaction term, see list in global_3d.c */ -#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ -#define NLAPLACIANS 1 /* number of fields for which to compute Laplacian */ - -#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */ -#define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */ -#define POTENTIAL 101 /* type of potential or vector potential, see list in global_3d.c */ - -#define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */ - -#define JULIA_SCALE 0.5 /* scaling for Julia sets */ - -/* Choice of the billiard table */ - -#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ - -#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ -#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ -#define MU 1.0 /* parameter controlling the dimensions of domain */ -#define NPOLY 5 /* number of sides of polygon */ -#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define MDEPTH 7 /* depth of computation of Menger gasket */ -#define MRATIO 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 0.0000012 - -#define VISCOSITY 2.0 - -#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ -#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ - -#define EPSILON 0.8 /* time scale separation */ -#define DELTA 0.1 /* time scale separation */ -#define FHNA 1.0 /* parameter in FHN equation */ -#define FHNC -0.01 /* parameter in FHN equation */ -#define K_HARMONIC 1.0 /* spring constant of harmonic potential */ -#define K_COULOMB 0.5 /* constant in Coulomb potential */ -#define BZQ 0.0008 /* parameter in BZ equation */ -#define BZF 1.2 /* parameter in BZ equation */ -#define B_FIELD 10.0 /* magnetic field */ -#define AB_RADIUS 0.2 /* radius of region with magnetic field for Aharonov-Bohm effect */ -#define K_EULER 50.0 /* constant in stream function integration of Euler equation */ - -#define SMOOTHEN_VORTICITY 1 /* set to 1 to smoothen vorticity field in Euler equation */ -#define SMOOTHEN_PERIOD 12 /* period between smoothenings */ -#define SMOOTH_FACTOR 0.01 /* factor by which to smoothen */ - -#define T_OUT 2.0 /* outside temperature */ -#define T_IN 0.0 /* inside temperature */ -#define SPEED 0.0 /* speed of drift to the right */ - -#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ -#define NOISE_INTENSITY 0.005 /* noise intensity */ -#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ -#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ -#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ - -#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ -#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ -#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ -#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ -#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, - for numerical stability */ - -#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ -#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ -#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ -#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ - - -/* Boundary conditions, see list in global_pdes.c */ - -#define B_COND 1 - -/* Parameters for length and speed of simulation */ - -#define NSTEPS 1200 /* number of frames of movie */ -#define NVID 350 /* 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 5 /* width of billiard boundary */ - -#define PAUSE 100 /* number of frames after which to pause */ -#define PSLEEP 2 /* sleep time during pause */ -#define SLEEP1 2 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define INITIAL_TIME 0 /* initial still time */ -#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ -#define END_FRAMES 50 /* number of still frames at end of movie */ -#define FADE 1 /* set to 1 to fade at end of movie */ - -/* Visualisation */ - -#define PLOT_3D 0 /* controls whether plot is 2D or 3D */ - -#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */ -#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ - -/* Plot type - color scheme */ - -#define CPLOT 50 -#define CPLOT_B 51 - -/* Plot type - height of 3D plot */ - -#define ZPLOT 50 /* z coordinate in 3D plot */ -#define ZPLOT_B 51 /* z coordinate in second 3D plot */ - -#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ -#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ -#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ -#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ -#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ -#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ -#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ -#define ADD_POT_CONSTANT 0.5 /* constant in front of added potential */ - -#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ - -#define PRINT_TIME 0 /* set to 1 to print running time */ -#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ -#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ -#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ -#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ - -#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ -#define FIELD_LINE_WIDTH 1 /* width of field lines */ -#define N_FIELD_LINES 120 /* number of field lines */ -#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ -#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ -#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ -#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ - -/* 3D representation */ - -#define REPRESENTATION_3D 1 /* choice of 3D representation */ - -#define REP_AXO_3D 0 /* linear projection (axonometry) */ -#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ - -/* Color schemes, see list in global_pdes.c */ - -#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 14 /* Color palette, see list in global_pdes.c */ - -#define BLACK 1 /* black background */ - -#define COLOR_SCHEME 3 /* choice of color scheme */ - -#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 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 0.000015 /* scaling factor for curl representation */ -#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ -#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ -#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ -#define E_SCALE 100.0 /* scaling factor for energy representation */ -#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT 1.0 - -#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 2.5 /* 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 */ -#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */ -#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ -#define ACHIRP 0.2 /* acceleration coefficient in chirp */ -#define DAMPING 0.0 /* damping of periodic excitation */ -#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ -#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ -#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ -#define NXMAZE 8 /* width of maze */ -#define NYMAZE 8 /* height of maze */ -#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ -#define RAND_SHIFT 58 /* seed of random number generator */ -#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ -/* end of constants added only for compatibility with wave_common.c */ - - -double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ -double v_3d[2] = {-0.75, -0.45}; -double w_3d[2] = {0.0, 0.015}; -double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ -int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ - -#define Z_SCALING_FACTOR 1.0 /* overall scaling factor of z axis for REP_PROJ_3D representation */ -#define XY_SCALING_FACTOR 1.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ -#define BORDER_PADDING 2 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */ - -/* For debugging purposes only */ -#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ -#define TEST_GRADIENT 0 /* print norm squared of gradient */ - -``` - -### 16 October 22 - A rocket that can rotate ### - -**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 */ -#define TIME_LAPSE_FIRST 1 /* set to 1 to show time-lapse version first */ - -/* General geometrical parameters */ - -#define WINWIDTH 1280 /* window width */ -#define WINHEIGHT 720 /* window height */ - -#define XMIN -3.3 -#define XMAX 4.7 /* x interval */ -#define YMIN -2.25 -#define YMAX 2.25 /* y interval for 9/16 aspect ratio */ - -#define INITXMIN -0.7 -#define INITXMAX 0.7 /* x interval for initial condition */ -#define INITYMIN -1.7 -#define INITYMAX 2.5 /* y interval for initial condition */ - -#define BCXMIN -5.1 -#define BCXMAX 6.1 /* x interval for boundary condition */ -#define BCYMIN -6.5 -#define BCYMAX 15.5 /* y interval for boundary condition */ - -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ - -#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ - -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ - -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 101 /* pattern of repelling segments, see list in global_ljones.c */ -#define ROCKET_SHAPE 1 /* shape of rocket combustion chamber, see list in global_ljones.c */ -#define ROCKET_SHAPE_B 0 /* shape of second rocket */ -#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ -#define NOZZLE_SHAPE_B 4 /* shape of nozzle for second rocket, see list in global_ljones.c */ - -#define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.5 /* 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 2.5 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ -#define MU 0.0075 /* parameter controlling radius of particles */ -#define MU_B 0.018 /* parameter controlling radius of particles of second type */ -#define NPOLY 25 /* 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 90 /* number of grid point for grid of disks */ -#define NGRIDY 100 /* 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 TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ -#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment 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 1750 /* number of frames of movie */ -#define NVID 100 /* 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 OBSTACLE_INITIAL_TIME 200 /* time after which to start moving obstacle */ -#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 20 - -/* Plot type, see list in global_ljones.c */ - -#define PLOT 0 -#define PLOT_B 8 /* plot type for second movie */ - -#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ -#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ -#define HUE_TYPE0 70.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 280.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 .0 /* hue of particles of type 2 */ -#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 5.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 0.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ -#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.02 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ -#define GRAVITY 15.0 /* gravity acting on all particles */ -#define GRAVITY_X 0.0 /* horizontal gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 100.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 0.025 /* 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 MIDDLE_CONSTANT_PHASE 850 /* final phase in which temperature is constant */ -#define FINAL_DECREASE_PHASE 700 /* final phase in which temperature decreases */ -#define FINAL_CONSTANT_PHASE -1 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ -#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ -#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ -#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 0 /* time at which to add first particle */ -#define ADD_PERIOD 10000 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ -#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ -#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ -#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 100 /* final time without rotation */ -#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ -#define OMEGAMAX 100.0 /* maximal rotation speed */ -#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ -#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ -#define PRINT_SEGMENTS_SPEEDS 1 /* set to 1 to print velocity of moving segments */ - -#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ -#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ -#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ -#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ -#define RELEASE_ROCKET_AT_DEACTIVATION 1 /* set to 1 to limit segments velocity before segment release */ -#define SEGMENTS_X0 0.0 /* initial position of segments */ -#define SEGMENTS_Y0 0.0 /* initial position of segments */ -#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ -#define SEGMENTS_VY0 0.0 /* initial velocity of segments */ -#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ - -#define MOVE_SEGMENT_GROUPS 1 /* set to 1 to group segments into moving units */ -#define SEGMENT_GROUP_MASS 900.0 /* mass of segment group */ -#define SEGMENT_GROUP_I 25.0 /* moment of inertia of segment group */ -#define SEGMENT_GROUP_DAMPING 0.0 /* damping of segment groups */ -#define GROUP_REPULSION 0 /* set to 1 for groups of segments to repel each other */ -#define KSPRING_GROUPS 1.0e8 /* harmonic potential between segment groups */ -#define GROUP_WIDTH 0.05 /* interaction width of groups */ -#define GROUP_G_REPEL 0 /* set to 1 to add repulsion between centers of mass of groups */ -#define GROUP_G_REPEL_RADIUS 0.12 /* radius within which centers of mass of groups repel each other */ - -#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 horizontal */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ -#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ -#define REACTION_PROB 0.0045 /* probability controlling reaction term */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ -#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ -#define PLOT_SPEEDS 1 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ -#define VMAX_PLOT_SPEEDS 0.5 /* vertical scale of plot of obstacle speeds */ - -#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 0 /* time during which to keep wall */ - -#define NXMAZE 10 /* width of maze */ -#define NYMAZE 10 /* height of maze */ -#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ -#define RAND_SHIFT 200 /* seed of random number generator */ -#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e12 /* maximal force */ -#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 160 /* size of hashgrid in x direction */ -#define HASHY 320 /* size of hashgrid in y direction */ -#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -``` - -### 15 October 22 - And the winner is: The fastest particles solving a maze ### +### 19 November 22 - Solving a 30 by 30 maze with laser beams ### **Program:** `particle_billiard.c` -**Initial condition in function `animation()`:** `init_drop_config(-1.3, 0.2, -0.25*PI, 0.25*PI, configs);` +**Initial condition in function `animation()`:** `init_drop_config(-1.15, -0.01, 0.15*PI, 0.3*PI, configs);` ``` #define MOVIE 1 /* set to 1 to generate movie */ @@ -1160,7 +389,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Simulation parameters */ -#define NPART 1000 /* number of particles */ +#define NPART 10000 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ #define LMAX 0.01 /* minimal segment length triggering resampling */ #define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ @@ -1172,9 +401,9 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */ #define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ -#define TEST_INITIAL_COND 1 /* set to 1 to allow only initial conditions that pass a test */ +#define TEST_INITIAL_COND 0 /* set to 1 to allow only initial conditions that pass a test */ -#define NSTEPS 6000 /* number of frames of movie */ +#define NSTEPS 8600 /* number of frames of movie */ #define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ #define DPHI 0.00002 /* integration step */ #define NVID 25 /* number of iterations between images displayed on screen */ @@ -1188,7 +417,598 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Colors and other graphical parameters */ -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 0 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 1024 /* number of colors */ +#define COLORSHIFT 0 /* hue of initial color */ +#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ +#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ +#define NSEG 100 /* number of segments of boundary */ +#define LENGTH 0.04 /* length of velocity vectors */ +#define BILLIARD_WIDTH 3 /* width of billiard */ +#define PARTICLE_WIDTH 3 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ + +#define NXMAZE 30 /* width of maze */ +#define NYMAZE 30 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 1 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +``` + +### 18 November 22 - 2D view of an annular waveguide ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(-0.85, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ +#define SAVE_MEMORY 0 /* set to 1 to save memory when writing tiff images */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 3840 /* number of grid points on x axis */ +#define NY 2000 /* 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 1 /* 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 7 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 1 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ +#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ +#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ + +#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 0.7 /* parameter controlling the dimensions of domain */ +#define MU 0.0 /* 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 6 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 12 /* number of grid point for grid of disks */ +#define NGRIDY 15 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ +#define OSCILLATION_SCHEDULE 1 /* oscillation schedule, see list in global_pdes.c */ + +#define OMEGA 0.0005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define ACHIRP 0.25 /* acceleration coefficient in chirp */ +#define DAMPING 0.0 /* damping of periodic excitation */ +#define COURANT 0.06 /* Courant number */ +#define COURANTB 0.15 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 0.015 /* 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 1 /* period of oscillating source */ +#define ALTERNATE_OSCILLATING_SOURCE 1 /* set to 1 to alternate sign of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* number of frames of movie */ +#define NVID 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 PRINT_SPEED 0 /* print speed of moving source */ + +#define PAUSE 200 /* 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 */ +#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 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 4 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 17 /* 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 PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 500.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define FLUX_SCALE 1.0e4 /* scaling factor for enegy flux represtnation */ +#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 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 20.0 /* 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 */ + +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +/* for compatibility with sub_wave and sub_maze */ +#define ADD_POTENTIAL 0 +#define POT_MAZE 7 +#define POTENTIAL 0 +/* end of constants only used by sub_wave and sub_maze */ + +/* 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 November 22 - A visualisation with tracers of interacting vortices in the Euler equation ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** +``` + init_vortex_state(0.25, 0.25, 0.15, phi, xy_in); + add_vortex_state(0.8, 0.3, -0.15, phi, xy_in); + add_vortex_state(1.5, 0.25, 0.15, phi, xy_in); + add_vortex_state(-0.3, 0.3, -0.15, phi, xy_in); + add_vortex_state(-0.75, 0.25, 0.15, phi, xy_in); + add_vortex_state(-1.55, 0.3, -0.15, phi, xy_in); + + add_vortex_state(0.3, -0.3, -0.15, phi, xy_in); + add_vortex_state(0.75, -0.25, 0.15, phi, xy_in); + add_vortex_state(1.55, -0.3, -0.15, phi, xy_in); + add_vortex_state(-0.25, -0.25, 0.15, phi, xy_in); + add_vortex_state(-0.8, -0.3, -0.15, phi, xy_in); + add_vortex_state(-1.5, -0.25, 0.15, phi, xy_in); +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 960 /* number of grid points on x axis */ +#define NY 500 /* 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 6 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 1 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */ +#define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */ +#define POTENTIAL 7 /* type of potential or vector potential, see list in global_3d.c */ + +#define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 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 0.0000012 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.0 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define V_MAZE 0.4 /* potential in walls of maze */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ +#define B_FIELD 10.0 /* magnetic field */ +#define AB_RADIUS 0.2 /* radius of region with magnetic field for Aharonov-Bohm effect */ +#define K_EULER 50.0 /* constant in stream function integration of Euler equation */ + +#define SMOOTHEN_VORTICITY 1 /* set to 1 to smoothen vorticity field in Euler equation */ +#define SMOOTHEN_PERIOD 10 /* period between smoothenings */ +#define SMOOTH_FACTOR 0.01 /* factor by which to smoothen */ + +#define ADD_TRACERS 1 /* set to 1 to add tracer particles (for Euler equations) */ +#define N_TRACERS 1000 /* number of tracer particles */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2800 /* number of frames of movie */ +#define NVID 120 /* 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 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 0 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +#define DRAW_PERIODICISED 1 /* set to 1 to repeat wave periodically in x and y directions */ + +/* Plot type - color scheme */ + +#define CPLOT 52 +#define CPLOT_B 51 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 52 /* z coordinate in 3D plot */ +// #define ZPLOT 32 /* z coordinate in 3D plot */ +#define ZPLOT_B 51 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 0.35 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define FLUX_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.75 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 +#define LOG_MIN 1.0e-3 /* floor value for log vorticity plot */ + +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define ACHIRP 0.2 /* acceleration coefficient in chirp */ +#define DAMPING 0.0 /* damping of periodic excitation */ +#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ +#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ +#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.08 /* 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 -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.1 /* overall y shift for REP_PROJ_3D representation */ +#define BORDER_PADDING 0 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */ + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ +#define TEST_GRADIENT 0 /* print norm squared of gradient */ + +``` + +### 16 November 22 - Solving a 16 by 16 maze with laser beams ### + +**Program:** `particle_billiard.c` + +**Initial condition in function `animation()`:** `init_drop_config(-1.15, 0.07, -0.3*PI, 0.3*PI, configs);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +#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 SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ + +/* Choice of the billiard table, see global_particles.c */ + +#define B_DOMAIN 30 /* choice of domain shape */ + +#define CIRCLE_PATTERN 1 /* pattern of circles */ +#define POLYLINE_PATTERN 10 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 100000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 100000 /* total number of sides of polygonal line */ +#define NCX 30 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 1 /* Sierpinski gastket depth */ + +#define LAMBDA 1.5 /* parameter controlling shape of domain */ +#define MU 0.5 /* second parameter controlling shape of billiard */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define PENROSE_RATIO 2.5 /* parameter controlling the shape of small ellipses in Penrose room */ + +#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ +#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ + +#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ +#define DEBUG 0 /* draw trajectories, for debugging purposes */ + +/* Simulation parameters */ + +#define NPART 10000 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 1 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */ +#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */ +#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ + +#define TEST_INITIAL_COND 0 /* set to 1 to allow only initial conditions that pass a test */ + +#define NSTEPS 7500 /* number of frames of movie */ +#define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.00002 /* integration step */ +#define NVID 25 /* number of iterations between images displayed on screen */ +#define END_FRAMES 25 /* number of still frames at the end of the movie */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ #define NCOLORS 16 /* number of colors */ #define COLORSHIFT 0 /* hue of initial color */ @@ -1211,26 +1031,631 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define SLEEP1 1 /* initial sleeping time */ #define SLEEP2 1 /* final sleeping time */ -#define NXMAZE 8 /* width of maze */ -#define NYMAZE 8 /* height of maze */ +#define NXMAZE 16 /* width of maze */ +#define NYMAZE 16 /* height of maze */ #define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ -#define RAND_SHIFT 58 /* seed of random number generator */ +#define RAND_SHIFT 1 /* seed of random number generator */ #define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ ``` -### 14 October 22 - solving a maze with waves: Average energy ### +### 15 November 22 - Rocket comparison 12: Glas-shaped vs trumpet-shaped nozzle, with a background grid ### + +**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 */ +#define TIME_LAPSE_FIRST 1 /* set to 1 to show time-lapse version first */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -3.3 +#define XMAX 4.7 /* x interval */ +#define YMIN -2.25 +#define YMAX 2.25 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.5 +#define INITXMAX 2.5 /* x interval for initial condition */ +#define INITYMIN -1.7 +#define INITYMAX 0.7 /* y interval for initial condition */ + +#define BCXMIN -5.1 +#define BCXMAX 6.1 /* x interval for boundary condition */ +#define BCYMIN -6.5 +#define BCYMAX 44.0 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 102 /* pattern of repelling segments, see list in global_ljones.c */ +#define ROCKET_SHAPE 2 /* shape of rocket combustion chamber, see list in global_ljones.c */ +#define ROCKET_SHAPE_B 2 /* shape of second rocket */ +#define NOZZLE_SHAPE 2 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 4 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.5 /* 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 2.7 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.009 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* 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 90 /* number of grid point for grid of disks */ +#define NGRIDY 100 /* 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 TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ +#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment 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 3500 /* number of frames of movie */ +#define NVID 100 /* 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 OBSTACLE_INITIAL_TIME 200 /* time after which to start moving obstacle */ +#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 20 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ +#define ALTITUDE_LINES 1 /* set to 1 to add horizontal lines to show altitude */ +#define COLOR_SEG_GROUPS 1 /* set to 1 to collor segment groups differently */ + +/* 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 70.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 280.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 .0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 5.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ +#define GRAVITY 15.0 /* gravity acting on all particles */ +#define GRAVITY_X 0.0 /* horizontal gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.025 /* 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 MIDDLE_CONSTANT_PHASE 2000 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 1300 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE -1 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 1 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ +#define RELEASE_ROCKET_AT_DEACTIVATION 1 /* set to 1 to limit segments velocity before segment release */ +#define SEGMENTS_X0 1.5 /* initial position of segments */ +#define SEGMENTS_Y0 0.0 /* initial position of segments */ +#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ +#define SEGMENTS_VY0 0.0 /* initial velocity of segments */ +#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ + +#define MOVE_SEGMENT_GROUPS 1 /* set to 1 to group segments into moving units */ +#define SEGMENT_GROUP_MASS 1000.0 /* mass of segment group */ +#define SEGMENT_GROUP_I 1000.0 /* moment of inertia of segment group */ +#define SEGMENT_GROUP_DAMPING 0.0 /* damping of segment groups */ +#define GROUP_REPULSION 1 /* set to 1 for groups of segments to repel each other */ +#define KSPRING_GROUPS 1.0e11 /* harmonic potential between segment groups */ +#define GROUP_WIDTH 0.05 /* interaction width of groups */ +#define GROUP_G_REPEL 1 /* set to 1 to add repulsion between centers of mass of groups */ +#define GROUP_G_REPEL_RADIUS 1.2 /* radius within which centers of mass of groups repel each other */ +#define TRACK_SEGMENT_GROUPS 1 /* set to 1 for view to track group of segments */ +#define TRACK_X_PADDING 2.0 /* distance from x boundary where tracking starts */ + +#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 horizontal */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 0 /* set to 1 to print certain parameters at the top left instead of right */ +#define PLOT_SPEEDS 1 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ +#define PLOT_TRAJECTORIES 1 /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */ +#define VMAX_PLOT_SPEEDS 0.6 /* vertical scale of plot of obstacle speeds */ + +#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 0 /* time during which to keep wall */ + +#define NXMAZE 10 /* width of maze */ +#define NYMAZE 10 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 200 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 120 /* size of hashgrid in x direction */ +#define HASHY 450 /* 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 November 22 - A visualisation of a shear flow with tracers ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_shear_flow(1.0, 0.02, 0.03, 1, 1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ +#define SAVE_MEMORY 1 /* set to 1 to save memory when writing tiff images */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 960 /* number of grid points on x axis */ +#define NY 500 /* 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 6 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 1 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */ +#define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */ +#define POTENTIAL 7 /* type of potential or vector potential, see list in global_3d.c */ + +#define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 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 0.0000012 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.0 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define V_MAZE 0.4 /* potential in walls of maze */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ +#define B_FIELD 10.0 /* magnetic field */ +#define AB_RADIUS 0.2 /* radius of region with magnetic field for Aharonov-Bohm effect */ +#define K_EULER 50.0 /* constant in stream function integration of Euler equation */ + +#define SMOOTHEN_VORTICITY 1 /* set to 1 to smoothen vorticity field in Euler equation */ +#define SMOOTHEN_PERIOD 10 /* period between smoothenings */ +#define SMOOTH_FACTOR 0.03 /* factor by which to smoothen */ + +#define ADD_TRACERS 1 /* set to 1 to add tracer particles (for Euler equations) */ +#define N_TRACERS 1000 /* number of tracer particles */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3700 /* number of frames of movie */ +#define NVID 60 /* 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 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 0 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +#define DRAW_PERIODICISED 1 /* set to 1 to repeat wave periodically in x and y directions */ + +/* Plot type - color scheme */ + +#define CPLOT 52 +#define CPLOT_B 51 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 52 /* z coordinate in 3D plot */ +#define ZPLOT_B 51 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 0.35 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 17 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define FLUX_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.75 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 +#define LOG_MIN 1.0e-3 /* floor value for log vorticity plot */ + +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define ACHIRP 0.2 /* acceleration coefficient in chirp */ +#define DAMPING 0.0 /* damping of periodic excitation */ +#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ +#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ +#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.08 /* 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 -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.1 /* overall y shift for REP_PROJ_3D representation */ +#define BORDER_PADDING 0 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */ + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ +#define TEST_GRADIENT 0 /* print norm squared of gradient */ + +``` + +### 13 November 22 - Energy flux of waves crossing a maze ### **Program:** `wave_billiard.c` -**Initial condition in function `animation()`:** - -``` - init_circular_wave(-1.5, 0.0, phi, psi, xy_in); - - add_circular_wave(sign, -1.5, 0.0, phi, psi, xy_in); - sign = -sign; -``` +**Initial condition in function `animation()`:** `init_circular_wave(-1.5, 0.0, phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ @@ -1240,15 +1665,15 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define WINWIDTH 1920 /* window width */ #define WINHEIGHT 1000 /* window height */ -#define NX 3840 /* number of grid points on x axis */ -#define NY 2000 /* number of grid points on y axis */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on x 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 1 /* set to 1 if resolution of grid is double that of displayed image */ +#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 */ @@ -1266,8 +1691,8 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #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 0.3 /* parameter controlling the dimensions of domain */ +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.3 /* 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 6 /* depth of computation of Menger gasket */ @@ -1303,10 +1728,10 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define AMPLITUDE 0.8 /* amplitude of periodic excitation */ #define ACHIRP 0.25 /* acceleration coefficient in chirp */ #define DAMPING 0.0 /* damping of periodic excitation */ -#define COURANT 0.12 /* Courant number */ -#define COURANTB 0.06 /* Courant number in medium B */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.1 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-3 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ #define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ @@ -1318,7 +1743,8 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* 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 25 /* period of oscillating source */ +#define OSCILLATING_SOURCE_PERIOD 1 /* period of oscillating source */ +#define ALTERNATE_OSCILLATING_SOURCE 1 /* set to 1 to alternate sign of oscillating source */ /* Boundary conditions, see list in global_pdes.c */ @@ -1326,7 +1752,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Parameters for length and speed of simulation */ -#define NSTEPS 2500 /* number of frames of movie */ +#define NSTEPS 2400 /* number of frames of movie */ #define NVID 20 /* 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 */ @@ -1343,19 +1769,20 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Parameters of initial condition */ -#define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ /* Plot type, see list in global_pdes.c */ -#define PLOT 3 -#define PLOT_B 5 /* plot type for second movie */ +#define PLOT 7 + +#define PLOT_B 6 /* plot type for second movie */ /* Color schemes */ -#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 14 /* Color palette, 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 /* background */ @@ -1366,9 +1793,10 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define PHASE_FACTOR 1.0 /* 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 125.0 /* scaling factor for energy representation */ +#define E_SCALE 5000.0 /* 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 LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define FLUX_SCALE 1.0e4 /* scaling factor for enegy flux represtnation */ #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 */ @@ -1379,7 +1807,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #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 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */ #define COLORBAR_RANGE_B 1.5 /* scale of color scheme bar for 2nd part */ #define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ @@ -1391,21 +1819,365 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define RAND_SHIFT 24 /* seed of random number generator */ #define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ +/* for compatibility with sub_wave and sub_maze */ +#define ADD_POTENTIAL 0 +#define POT_MAZE 7 +#define POTENTIAL 0 +/* end of constants only used by sub_wave and sub_maze */ + + /* 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 */ ``` -### 13 October 22 - 3D rendering of two interacting vortices in the 2D incompressible Euler equation ### +### 12 November 22 - Deep impact 4: Dropping a rectangle in a Lennard-Jones fluid ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ +#define TIME_LAPSE_FIRST 0 /* set to 1 to show time-lapse version first */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.05 +#define INITYMAX -0.25 /* y interval for initial condition */ + +#define BCXMIN -2.0 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.125 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 16 /* pattern of repelling segments, see list in global_ljones.c */ +#define ROCKET_SHAPE 2 /* shape of rocket combustion chamber, see list in global_ljones.c */ +#define ROCKET_SHAPE_B 2 /* shape of second rocket */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 0 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.3 /* parameter controlling the dimensions of domain */ +#define MU 0.009 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* 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 90 /* number of grid point for grid of disks */ +#define NGRIDY 100 /* 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 TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ +#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1800 /* number of frames of movie */ +#define NVID 100 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 300 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ +#define COLOR_SEG_GROUPS 1 /* set to 1 to collor segment groups differently */ + +/* 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 3.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 70.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 280.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 .0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 15.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ +#define GRAVITY 1000.0 /* gravity acting on all particles */ +#define GRAVITY_X 0.0 /* horizontal gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.025 /* 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 MIDDLE_CONSTANT_PHASE 1600 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 1500 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE -1 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 0 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ +#define RELEASE_ROCKET_AT_DEACTIVATION 1 /* set to 1 to limit segments velocity before segment release */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 0.8 /* initial position of segments */ +#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ +#define SEGMENTS_VY0 0.0 /* initial velocity of segments */ +#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ + +#define MOVE_SEGMENT_GROUPS 1 /* set to 1 to group segments into moving units */ +#define SEGMENT_GROUP_MASS 1000.0 /* mass of segment group */ +#define SEGMENT_GROUP_I 1000.0 /* moment of inertia of segment group */ +#define SEGMENT_GROUP_DAMPING 0.0 /* damping of segment groups */ +#define GROUP_REPULSION 0 /* set to 1 for groups of segments to repel each other */ +#define KSPRING_GROUPS 1.0e11 /* harmonic potential between segment groups */ +#define GROUP_WIDTH 0.05 /* interaction width of groups */ +#define GROUP_G_REPEL 0 /* set to 1 to add repulsion between centers of mass of groups */ +#define GROUP_G_REPEL_RADIUS 1.2 /* radius within which centers of mass of groups repel each other */ +#define TRACK_SEGMENT_GROUPS 0 /* set to 1 for view to track group of segments */ +#define TRACK_X_PADDING 2.0 /* distance from x boundary where tracking starts */ + +#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 horizontal */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 0 /* set to 1 to print certain parameters at the top left instead of right */ +#define PLOT_SPEEDS 0 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ +#define PLOT_TRAJECTORIES 0 /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */ +#define VMAX_PLOT_SPEEDS 0.6 /* vertical scale of plot of obstacle speeds */ + +#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 0 /* time during which to keep wall */ + +#define NXMAZE 10 /* width of maze */ +#define NYMAZE 10 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 200 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 120 /* size of hashgrid in x direction */ +#define HASHY 60 /* 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 November 22 - Several interacting vortices in the Euler equation ### **Program:** `rde.c` **Initial condition in function `animation()`:** - ``` - init_vortex_state(0.5, 0.0, 0.2, phi, xy_in); - add_vortex_state(-0.5, 0.0, 0.2, phi, xy_in); + init_vortex_state(0.25, 0.25, 0.15, phi, xy_in); + add_vortex_state(0.8, 0.3, -0.15, phi, xy_in); + add_vortex_state(1.5, 0.25, 0.15, phi, xy_in); + add_vortex_state(-0.3, 0.3, -0.15, phi, xy_in); + add_vortex_state(-0.75, 0.25, 0.15, phi, xy_in); + add_vortex_state(-1.55, 0.3, -0.15, phi, xy_in); + + add_vortex_state(0.3, -0.3, -0.15, phi, xy_in); + add_vortex_state(0.75, -0.25, 0.15, phi, xy_in); + add_vortex_state(1.55, -0.3, -0.15, phi, xy_in); + add_vortex_state(-0.25, -0.25, 0.15, phi, xy_in); + add_vortex_state(-0.8, -0.3, -0.15, phi, xy_in); + add_vortex_state(-1.5, -0.25, 0.15, phi, xy_in); ``` ``` @@ -1416,8 +2188,8 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define WINWIDTH 1920 /* window width */ #define WINHEIGHT 1000 /* window height */ -#define NX 920 /* number of grid points on x axis */ -#define NY 450 /* number of grid points on y axis */ +#define NX 960 /* number of grid points on x axis */ +#define NY 500 /* number of grid points on y axis */ #define XMIN -2.0 #define XMAX 2.0 /* x interval */ @@ -1432,7 +2204,1702 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */ #define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */ -#define POTENTIAL 101 /* type of potential or vector potential, see list in global_3d.c */ +#define POTENTIAL 7 /* type of potential or vector potential, see list in global_3d.c */ + +#define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 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 0.0000012 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.0 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define V_MAZE 0.4 /* potential in walls of maze */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ +#define B_FIELD 10.0 /* magnetic field */ +#define AB_RADIUS 0.2 /* radius of region with magnetic field for Aharonov-Bohm effect */ +#define K_EULER 50.0 /* constant in stream function integration of Euler equation */ + +#define SMOOTHEN_VORTICITY 1 /* set to 1 to smoothen vorticity field in Euler equation */ +#define SMOOTHEN_PERIOD 10 /* period between smoothenings */ +#define SMOOTH_FACTOR 0.05 /* factor by which to smoothen */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1800 /* number of frames of movie */ +#define NVID 80 /* 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 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 0 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +#define DRAW_PERIODICISED 1 /* set to 1 to repeat wave periodically in x and y directions */ + +/* Plot type - color scheme */ + +#define CPLOT 52 +#define CPLOT_B 51 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 52 /* z coordinate in 3D plot */ +#define ZPLOT_B 51 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 0.35 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.75 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 +#define LOG_MIN 1.0e-3 /* floor value for log vorticity plot */ + +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define ACHIRP 0.2 /* acceleration coefficient in chirp */ +#define DAMPING 0.0 /* damping of periodic excitation */ +#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ +#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ +#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ +/* end of constants added only for compatibility with wave_common.c */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.08 /* 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 -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.1 /* overall y shift for REP_PROJ_3D representation */ +#define BORDER_PADDING 0 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */ + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ +#define TEST_GRADIENT 0 /* print norm squared of gradient */ + +``` + +### 10 November 22 - Refraction of a wave on a grid of triangles ### + +**Program:** `wave_billiard.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 3840 /* number of grid points on x axis */ +#define NY 2000 /* 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 1 /* 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 56 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 1 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ +#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ +#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ + +#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 0.75 /* parameter controlling the dimensions of domain */ +#define MU 0.3 /* 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 6 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 12 /* number of grid point for grid of disks */ +#define NGRIDY 15 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ +#define OSCILLATION_SCHEDULE 1 /* oscillation schedule, see list in global_pdes.c */ + +#define OMEGA 0.0005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define ACHIRP 0.25 /* acceleration coefficient in chirp */ +#define DAMPING 0.0 /* damping of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.1 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 0.0 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 50 /* 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 2800 /* 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 PRINT_SPEED 0 /* print speed of moving source */ + +#define PAUSE 200 /* 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 */ +#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 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 5 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* 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 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define 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 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.5 /* 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 */ + +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +/* for compatibility with sub_wave and sub_maze */ +#define ADD_POTENTIAL 0 +#define POT_MAZE 7 +#define POTENTIAL 0 +/* end of constants only used by sub_wave and sub_maze */ + + +/* 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 */ + +``` + +### 9 November 22 - Deep impact 3: Dropping a disc in a Lennard-Jones fluid ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 0 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ +#define TIME_LAPSE_FIRST 0 /* set to 1 to show time-lapse version first */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.05 +#define INITYMAX -0.25 /* y interval for initial condition */ + +#define BCXMIN -2.0 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.125 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 9 /* pattern of repelling segments, see list in global_ljones.c */ +#define ROCKET_SHAPE 2 /* shape of rocket combustion chamber, see list in global_ljones.c */ +#define ROCKET_SHAPE_B 2 /* shape of second rocket */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 0 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.2 /* parameter controlling the dimensions of domain */ +#define MU 0.009 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* 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 90 /* number of grid point for grid of disks */ +#define NGRIDY 100 /* 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 TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ +#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1600 /* number of frames of movie */ +#define NVID 100 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 300 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ +#define COLOR_SEG_GROUPS 1 /* set to 1 to collor segment groups differently */ + +/* 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 3.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 70.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 280.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 .0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 15.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ +#define GRAVITY 1000.0 /* gravity acting on all particles */ +#define GRAVITY_X 0.0 /* horizontal gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.025 /* 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 MIDDLE_CONSTANT_PHASE 1600 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 1500 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE -1 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 0 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ +#define RELEASE_ROCKET_AT_DEACTIVATION 1 /* set to 1 to limit segments velocity before segment release */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 0.8 /* initial position of segments */ +#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ +#define SEGMENTS_VY0 0.0 /* initial velocity of segments */ +#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ + +#define MOVE_SEGMENT_GROUPS 1 /* set to 1 to group segments into moving units */ +#define SEGMENT_GROUP_MASS 1000.0 /* mass of segment group */ +#define SEGMENT_GROUP_I 1000.0 /* moment of inertia of segment group */ +#define SEGMENT_GROUP_DAMPING 0.0 /* damping of segment groups */ +#define GROUP_REPULSION 0 /* set to 1 for groups of segments to repel each other */ +#define KSPRING_GROUPS 1.0e11 /* harmonic potential between segment groups */ +#define GROUP_WIDTH 0.05 /* interaction width of groups */ +#define GROUP_G_REPEL 0 /* set to 1 to add repulsion between centers of mass of groups */ +#define GROUP_G_REPEL_RADIUS 1.2 /* radius within which centers of mass of groups repel each other */ +#define TRACK_SEGMENT_GROUPS 0 /* set to 1 for view to track group of segments */ +#define TRACK_X_PADDING 2.0 /* distance from x boundary where tracking starts */ + +#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 horizontal */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 0 /* set to 1 to print certain parameters at the top left instead of right */ +#define PLOT_SPEEDS 0 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ +#define PLOT_TRAJECTORIES 0 /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */ +#define VMAX_PLOT_SPEEDS 0.6 /* vertical scale of plot of obstacle speeds */ + +#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 0 /* time during which to keep wall */ + +#define NXMAZE 10 /* width of maze */ +#define NYMAZE 10 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 200 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 120 /* size of hashgrid in x direction */ +#define HASHY 60 /* 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 */ + +``` + +### 8 November 22 - Periodicised view of a 2D shear flow rendered in 3D ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_shear_flow(-1.0, 0.02, 0.05, 1, 1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 960 /* number of grid points on x axis */ +#define NY 500 /* 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 6 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 1 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */ +#define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */ +#define POTENTIAL 7 /* type of potential or vector potential, see list in global_3d.c */ + +#define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 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 0.0000012 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.0 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define V_MAZE 0.4 /* potential in walls of maze */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ +#define B_FIELD 10.0 /* magnetic field */ +#define AB_RADIUS 0.2 /* radius of region with magnetic field for Aharonov-Bohm effect */ +#define K_EULER 50.0 /* constant in stream function integration of Euler equation */ + +#define SMOOTHEN_VORTICITY 1 /* set to 1 to smoothen vorticity field in Euler equation */ +#define SMOOTHEN_PERIOD 10 /* period between smoothenings */ +#define SMOOTH_FACTOR 0.05 /* factor by which to smoothen */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* number of frames of movie */ +#define NVID 80 /* 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 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +#define DRAW_PERIODICISED 1 /* set to 1 to repeat wave periodically in x and y directions */ + +/* Plot type - color scheme */ + +#define CPLOT 52 +#define CPLOT_B 51 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 52 /* z coordinate in 3D plot */ +#define ZPLOT_B 51 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 0.35 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 17 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 0.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.75 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 +#define LOG_MIN 1.0e-3 /* floor value for log vorticity plot */ + +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 6.0 /* 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 */ + +/* 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 */ +#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define ACHIRP 0.2 /* acceleration coefficient in chirp */ +#define DAMPING 0.0 /* damping of periodic excitation */ +#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ +#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ +#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.08 /* 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 -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.1 /* overall y shift for REP_PROJ_3D representation */ +#define BORDER_PADDING 0 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */ + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ +#define TEST_GRADIENT 0 /* print norm squared of gradient */ + +``` + +### 7 November 22 - Phase space representation of a Bunimovich flower billiard ### + +**Program:** `billiard_phase_space.c` + +**Initial condition in function `animation()`:** `lyap_exponents[i] = draw_phase_portrait(14, 20, 200, 20, 0.1);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +#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 XPHASEMAX 0.0 /* max x coordinate of phase portrait */ + +#define PIXELIZE 0 /* set to 1 to pixelize phase portrait (beta) */ +#define NGRID 200 /* size of grid to draw orbits with positive Lyapunov exponent */ + +#define SYMMETRIZE_S 1 /* set to 1 to symmetrize orbits wrt s */ + +#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ + +/* Choice of the billiard table, see global_particles.c */ + +#define B_DOMAIN 10 /* choice of domain shape */ + +#define CIRCLE_PATTERN 6 /* pattern of circles */ +#define POLYLINE_PATTERN 4 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 50000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 50000 /* total number of sides of polygonal line */ +#define NCX 9 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 2 /* Sierpinski gastket depth */ + +#define LAMBDAMIN 0.5 /* parameter controlling shape of domain */ +#define LAMBDA 1.2 /* parameter controlling shape of domain */ +#define MU 0.1 /* second parameter controlling shape of billiard */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NPOLY 7 /* number of sides of polygon */ +#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ +#define DRAW_CONSTRUCTION_LINES 1 /* set to 1 to draw additional construction lines for billiard */ +#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ +#define PENROSE_RATIO 1.0 /* parameter controlling the shape of small ellipses in Penrose room */ + +#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ +#define DEBUG 0 /* draw trajectories, for debugging purposes */ + +/* Simulation parameters */ + +#define NPART 1 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define TRAJ_LENGTH 10000 /* length of trajectory */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ +#define PRINT_TRAJECTORY_LENGTH 0 /* set to 1 to print length of trajectory 0 */ +#define PRINT_TRAJECTORY_PERIOD 0 /* set to 1 to print period of trajectory 0 */ +#define DRAW_LENGTHS_PLOT 0 /* set to 1 to plot trajectory lengths */ +#define LENGTHS_LOG_SCALE 1 /* set to 1 to use log scale for plot of lengths */ +#define MAX_ANGLE 90.0 /* range of angles of trajectory */ + +#define NSTEPS 3400 /* number of frames of movie */ +// #define NSTEPS 500 /* number of frames of movie */ +#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.00001 /* integration step */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define SYMMETRIC_PARAMETER 1 /* set to 1 if parameters depend symmetrically on time */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 64 /* number of colors */ +#define CFACTOR 3 /* color step */ +#define COLORSHIFT 0 /* hue of initial color */ +#define LYAP_PLOT_COLOR 100.0 /* color hue of Lyapunov exponent plot */ +#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ +#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ +#define NSEG 100 /* number of segments of boundary */ +#define LENGTH 0.03 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 2 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PRINT_LAMBDA 1 /* set to 1 to print value of lambda */ +#define PRINT_MU 0 /* set to 1 to print value of mu */ +#define PRINT_PENROSE_RATIO 0 /* set to 1 to print value of the Penrose billiard ratio */ +#define PRINT_LYAPUNOV 1 /* set to 1 to print mean Lyapunov exponent */ +#define PLOT_LYAPUNOV 1 /* set to 1 to add plot of Lyapunov exponents */ +#define LOGSCALEX_LYAP 0 /* set to 1 to use log scale on parameter axis of Lyapunov exponents */ +#define LYAP_MAX 0.7 /* maximal Lyapunov exponent */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define END_FRAMES 100 /* number of frames at end of movie */ + +``` + +### 6 November 22 - Refraction of a wave on a chessboard ### + +**Program:** `wave_billiard.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 3840 /* number of grid points on x axis */ +#define NY 2000 /* 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 1 /* 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 55 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 1 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ +#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ +#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ + +#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 0.3 /* 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 6 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 12 /* number of grid point for grid of disks */ +#define NGRIDY 15 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ +#define OSCILLATION_SCHEDULE 1 /* oscillation schedule, see list in global_pdes.c */ + +#define OMEGA 0.0005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define ACHIRP 0.25 /* acceleration coefficient in chirp */ +#define DAMPING 0.0 /* damping of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.1 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 0.0 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 50 /* 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 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 PRINT_SPEED 0 /* print speed of moving source */ + +#define PAUSE 200 /* 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 */ +#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 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 5 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* 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 200.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define 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 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.5 /* 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 */ + +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +/* for compatibility with sub_wave and sub_maze */ +#define ADD_POTENTIAL 0 +#define POT_MAZE 7 +#define POTENTIAL 0 +/* end of constants only used by sub_wave and sub_maze */ + + +/* 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 */ + +``` + +### 5 November 22 - Rocket comparison 11: Bell-shaped vs narrow straight nozzle, with higher moments of inertia ### + +**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 */ +#define TIME_LAPSE_FIRST 1 /* set to 1 to show time-lapse version first */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -3.3 +#define XMAX 4.7 /* x interval */ +#define YMIN -2.25 +#define YMAX 2.25 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.5 +#define INITXMAX 2.5 /* x interval for initial condition */ +#define INITYMIN -1.7 +#define INITYMAX 0.7 /* y interval for initial condition */ + +#define BCXMIN -5.1 +#define BCXMAX 6.1 /* x interval for boundary condition */ +#define BCYMIN -6.5 +#define BCYMAX 44.0 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 102 /* pattern of repelling segments, see list in global_ljones.c */ +#define ROCKET_SHAPE 2 /* shape of rocket combustion chamber, see list in global_ljones.c */ +#define ROCKET_SHAPE_B 2 /* shape of second rocket */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 0 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.5 /* 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 2.7 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.009 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* 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 90 /* number of grid point for grid of disks */ +#define NGRIDY 100 /* 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 TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ +#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment 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 3300 /* number of frames of movie */ +#define NVID 100 /* 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 OBSTACLE_INITIAL_TIME 200 /* time after which to start moving obstacle */ +#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 20 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ +#define COLOR_SEG_GROUPS 1 /* set to 1 to collor segment groups differently */ + +/* 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 70.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 280.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 .0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 5.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ +#define GRAVITY 15.0 /* gravity acting on all particles */ +#define GRAVITY_X 0.0 /* horizontal gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.025 /* 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 MIDDLE_CONSTANT_PHASE 1600 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 1500 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE -1 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 1 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ +#define RELEASE_ROCKET_AT_DEACTIVATION 1 /* set to 1 to limit segments velocity before segment release */ +#define SEGMENTS_X0 1.5 /* initial position of segments */ +#define SEGMENTS_Y0 0.0 /* initial position of segments */ +#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ +#define SEGMENTS_VY0 0.0 /* initial velocity of segments */ +#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ + +#define MOVE_SEGMENT_GROUPS 1 /* set to 1 to group segments into moving units */ +#define SEGMENT_GROUP_MASS 1000.0 /* mass of segment group */ +#define SEGMENT_GROUP_I 1000.0 /* moment of inertia of segment group */ +#define SEGMENT_GROUP_DAMPING 0.0 /* damping of segment groups */ +#define GROUP_REPULSION 1 /* set to 1 for groups of segments to repel each other */ +#define KSPRING_GROUPS 1.0e11 /* harmonic potential between segment groups */ +#define GROUP_WIDTH 0.05 /* interaction width of groups */ +#define GROUP_G_REPEL 1 /* set to 1 to add repulsion between centers of mass of groups */ +#define GROUP_G_REPEL_RADIUS 1.2 /* radius within which centers of mass of groups repel each other */ +#define TRACK_SEGMENT_GROUPS 1 /* set to 1 for view to track group of segments */ +#define TRACK_X_PADDING 2.0 /* distance from x boundary where tracking starts */ + +#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 horizontal */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 0 /* set to 1 to print certain parameters at the top left instead of right */ +#define PLOT_SPEEDS 1 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ +#define PLOT_TRAJECTORIES 1 /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */ +#define VMAX_PLOT_SPEEDS 0.6 /* vertical scale of plot of obstacle speeds */ + +#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 0 /* time during which to keep wall */ + +#define NXMAZE 10 /* width of maze */ +#define NYMAZE 10 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 200 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 120 /* size of hashgrid in x direction */ +#define HASHY 450 /* 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 */ + +``` + +### 4 November 22 - A 2D shear flow rendered in 3D ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_shear_flow(-1.0, 0.02, 0.05, 1, 1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 960 /* number of grid points on x axis */ +#define NY 500 /* 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 6 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 1 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */ +#define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */ +#define POTENTIAL 7 /* type of potential or vector potential, see list in global_3d.c */ #define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */ @@ -1489,6 +3956,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define FHNC -0.01 /* parameter in FHN equation */ #define K_HARMONIC 1.0 /* spring constant of harmonic potential */ #define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define V_MAZE 0.4 /* potential in walls of maze */ #define BZQ 0.0008 /* parameter in BZ equation */ #define BZF 1.2 /* parameter in BZ equation */ #define B_FIELD 10.0 /* magnetic field */ @@ -1496,8 +3964,8 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define K_EULER 50.0 /* constant in stream function integration of Euler equation */ #define SMOOTHEN_VORTICITY 1 /* set to 1 to smoothen vorticity field in Euler equation */ -#define SMOOTHEN_PERIOD 12 /* period between smoothenings */ -#define SMOOTH_FACTOR 0.01 /* factor by which to smoothen */ +#define SMOOTHEN_PERIOD 10 /* period between smoothenings */ +#define SMOOTH_FACTOR 0.05 /* factor by which to smoothen */ #define T_OUT 2.0 /* outside temperature */ #define T_IN 0.0 /* inside temperature */ @@ -1528,8 +3996,8 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Parameters for length and speed of simulation */ -#define NSTEPS 2500 /* number of frames of movie */ -#define NVID 250 /* number of iterations between images displayed on screen */ +#define NSTEPS 1600 /* number of frames of movie */ +#define NVID 100 /* 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 */ @@ -1554,12 +4022,12 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Plot type - color scheme */ -#define CPLOT 50 +#define CPLOT 52 #define CPLOT_B 51 /* Plot type - height of 3D plot */ -#define ZPLOT 50 /* z coordinate in 3D plot */ +#define ZPLOT 52 /* z coordinate in 3D plot */ #define ZPLOT_B 51 /* z coordinate in second 3D plot */ #define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ @@ -1569,7 +4037,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ #define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ #define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ -#define ADD_POT_CONSTANT 0.5 /* constant in front of added potential */ +#define ADD_POT_CONSTANT 0.35 /* constant in front of added potential */ #define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ @@ -1597,7 +4065,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Color schemes, see list in global_pdes.c */ #define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 14 /* 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 */ @@ -1606,8 +4074,8 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ -#define VSCALE_AMPLITUDE 2.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#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 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) */ @@ -1619,14 +4087,21 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #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 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 0.75 /* scaling factor for energy log representation */ #define LOG_SHIFT 1.0 +#define LOG_MIN 1.0e-3 /* floor value for log vorticity plot */ + +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ #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 2.5 /* scale of color scheme bar for 2nd part */ +#define COLORBAR_RANGE 6.0 /* 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 */ /* only for compatibility with wave_common.c */ @@ -1647,11 +4122,6 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ #define B_DOMAIN_B 20 /* second domain shape, for comparisons */ #define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ -#define NXMAZE 8 /* width of maze */ -#define NYMAZE 8 /* height of maze */ -#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ -#define RAND_SHIFT 58 /* seed of random number generator */ -#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ /* end of constants added only for compatibility with wave_common.c */ @@ -1662,11 +4132,11 @@ double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "lig double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ -#define Z_SCALING_FACTOR 1.0 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define Z_SCALING_FACTOR 0.08 /* overall scaling factor of z axis for REP_PROJ_3D representation */ #define XY_SCALING_FACTOR 1.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ #define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ #define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ -#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.1 /* overall y shift for REP_PROJ_3D representation */ #define BORDER_PADDING 2 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */ /* For debugging purposes only */ @@ -1676,433 +4146,338 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO ``` -### 12 October 22 - Phase space representation of a Penrose unilluminable room ### +### 3 November 22 - Rocket comparison 10: Bell-shaped vs narrow straight nozzle ### -**Program:** `billiard_phase_space.c` - -**In function `animation()`:** `lyap_exponents[i] = draw_phase_portrait(20, 20, 100, 20, 0.2);` +**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 */ +#define TIME_LAPSE_FIRST 1 /* set to 1 to show time-lapse version first */ + +/* 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 XMIN -3.3 +#define XMAX 4.7 /* x interval */ +#define YMIN -2.25 +#define YMAX 2.25 /* y interval for 9/16 aspect ratio */ -#define XPHASEMAX 0.0 /* max x coordinate of phase portrait */ +#define INITXMIN -2.5 +#define INITXMAX 2.5 /* x interval for initial condition */ +#define INITYMIN -1.7 +#define INITYMAX 0.7 /* y interval for initial condition */ -#define PIXELIZE 1 /* set to 1 to pixelize phase portrait (beta) */ -#define NGRID 200 /* size of grid to draw orbits with positive Lyapunov exponent */ +#define BCXMIN -5.1 +#define BCXMAX 6.1 /* x interval for boundary condition */ +#define BCYMIN -6.5 +#define BCYMAX 44.0 /* y interval for boundary condition */ -#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ -/* Choice of the billiard table, see global_particles.c */ +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ -#define B_DOMAIN 16 /* choice of domain shape */ +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ -#define CIRCLE_PATTERN 6 /* pattern of circles */ -#define POLYLINE_PATTERN 4 /* pattern of polyline */ +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 102 /* pattern of repelling segments, see list in global_ljones.c */ +#define ROCKET_SHAPE 2 /* shape of rocket combustion chamber, see list in global_ljones.c */ +#define ROCKET_SHAPE_B 2 /* shape of second rocket */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 0 /* shape of nozzle for second rocket, see list in global_ljones.c */ -#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.5 /* 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 NMAXCIRCLES 50000 /* total number of circles (must be at least NCX*NCY for square grid) */ -#define NMAXPOLY 50000 /* total number of sides of polygonal line */ -#define NCX 9 /* number of circles in x direction */ -#define NCY 20 /* number of circles in y direction */ -#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ -#define SDEPTH 2 /* Sierpinski gastket depth */ - -#define LAMBDA 1.5 /* parameter controlling shape of domain */ -#define MU 0.3 /* second parameter controlling shape of billiard */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NPOLY 4 /* number of sides of polygon */ -#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ -#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ -#define PENROSE_RATIO 9.0 /* parameter controlling the shape of small ellipses in Penrose room */ - -#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ -#define DEBUG 0 /* draw trajectories, for debugging purposes */ - -/* Simulation parameters */ - -#define NPART 1 /* number of particles */ -#define NPARTMAX 100000 /* maximal number of particles after resampling */ -#define TRAJ_LENGTH 10000 /* length of trajectory */ -#define LMAX 0.01 /* minimal segment length triggering resampling */ -#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ -#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ -#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ -#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ -#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ -#define PRINT_TRAJECTORY_LENGTH 0 /* set to 1 to print length of trajectory 0 */ -#define PRINT_TRAJECTORY_PERIOD 0 /* set to 1 to print period of trajectory 0 */ -#define DRAW_LENGTHS_PLOT 0 /* set to 1 to plot trajectory lengths */ -#define LENGTHS_LOG_SCALE 1 /* set to 1 to use log scale for plot of lengths */ -#define MAX_ANGLE 90.0 /* range of angles of trajectory */ - -#define NSTEPS 2800 /* number of frames of movie */ -#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00001 /* integration step */ -#define NVID 150 /* number of iterations between images displayed on screen */ -#define SYMMETRIC_PARAMETER 1 /* set to 1 if parameters depend symmetrically on time */ - -/* Decreasing TIME accelerates the animation and the movie */ -/* For constant speed of movie, TIME*DPHI should be kept constant */ -/* However, increasing DPHI too much deterioriates quality of simulation */ -/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ -/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ - -/* Colors and other graphical parameters */ - -#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ - -#define NCOLORS 64 /* number of colors */ -#define CFACTOR 3 /* color step */ -#define COLORSHIFT 0 /* hue of initial color */ -#define LYAP_PLOT_COLOR 200.0 /* color hue of Lyapunov exponent plot */ -#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ -#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ -#define NSEG 100 /* number of segments of boundary */ -#define LENGTH 0.03 /* length of velocity vectors */ -#define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 2 /* width of particles */ -#define FRONT_WIDTH 3 /* width of wave front */ - -#define BLACK 1 /* set to 1 for black background */ -#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ -#define OUTER_COLOR 270.0 /* color outside billiard */ -#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ -#define PAINT_EXT 1 /* set to 1 to paint exterior */ - -#define PRINT_LAMBDA 0 /* set to 1 to print value of lambda */ -#define PRINT_MU 0 /* set to 1 to print value of mu */ -#define PRINT_PENROSE_RATIO 1 /* set to 1 to print value of the Penrose billiard ratio */ -#define PRINT_LYAPUNOV 1 /* set to 1 to print mean Lyapunov exponent */ -#define PLOT_LYAPUNOV 1 /* set to 1 to add plot of Lyapunov exponents */ -#define LOGSCALEX_LYAP 0 /* set to 1 to use log scale on parameter axis of Lyapunov exponents */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define END_FRAMES 100 /* number of frames at end of movie */ - -``` - -### 11 October 22 - solving a maze with waves ### - -**Program:** `wave_billiard.c` - -**Initial condition in function `animation()`:** - -``` - init_circular_wave(-1.5, 0.0, phi, psi, xy_in); - - add_circular_wave(sign, -1.5, 0.0, phi, psi, xy_in); - sign = -sign; -``` - -``` -#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 3840 /* number of grid points on x axis */ -#define NY 2000 /* 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 1 /* 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 53 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 1 /* pattern of circles or polygons, see list in global_pdes.c */ - -#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ -#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ -#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ +#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 300 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 2.7 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ -#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */ -#define MU 0.3 /* 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 6 /* depth of computation of Menger gasket */ +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.009 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* 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 12 /* number of grid point for grid of disks */ -#define NGRIDY 15 /* number of grid point for grid of disks */ +#define NGRIDX 90 /* number of grid point for grid of disks */ +#define NGRIDY 100 /* 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 TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ +#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment 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 */ -#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 OSCILLATION_SCHEDULE 1 /* oscillation schedule, see list in global_pdes.c */ - -#define OMEGA 0.0005 /* frequency of periodic excitation */ -#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ -#define ACHIRP 0.25 /* acceleration coefficient in chirp */ -#define DAMPING 0.0 /* damping of periodic excitation */ -#define COURANT 0.12 /* Courant number */ -#define COURANTB 0.06 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 0.0 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ -#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ -/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ -/* The physical damping coefficient is given by GAMMA/(DT)^2 */ -/* Increasing COURANT speeds up the simulation, but decreases accuracy */ -/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ - -#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */ -#define OSCILLATING_SOURCE_PERIOD 25 /* 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 3000 /* 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 2 /* width of billiard boundary */ -#define PRINT_SPEED 0 /* print speed of moving source */ +#define NSTEPS 3300 /* number of frames of movie */ +#define NVID 100 /* 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 OBSTACLE_INITIAL_TIME 200 /* time after which to start moving obstacle */ +#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 200 /* number of frames after which to pause */ +#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 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 */ -#define FADE 1 /* set to 1 to fade at end of movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ -/* Parameters of initial condition */ +/* Boundary conditions, see list in global_ljones.c */ -#define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ +#define BOUNDARY_COND 20 -/* Plot type, see list in global_pdes.c */ +/* Plot type, see list in global_ljones.c */ #define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ -#define PLOT_B 4 /* plot type for second movie */ +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ +#define COLOR_SEG_GROUPS 1 /* set to 1 to collor segment groups differently */ /* Color schemes */ -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE 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_pdes.c */ +#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 1.0 /* sensitivity of color on wave amplitude */ -#define PHASE_FACTOR 1.0 /* 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 SLOPE 0.5 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 125.0 /* 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 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 */ -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 1.5 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ +/* particle properties */ -#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ +#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 70.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 280.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 .0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ -#define NXMAZE 7 /* width of maze */ -#define NYMAZE 7 /* height of maze */ +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 5.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ +#define GRAVITY 15.0 /* gravity acting on all particles */ +#define GRAVITY_X 0.0 /* horizontal gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.025 /* 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 MIDDLE_CONSTANT_PHASE 1600 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 1500 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE -1 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 1 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ +#define RELEASE_ROCKET_AT_DEACTIVATION 1 /* set to 1 to limit segments velocity before segment release */ +#define SEGMENTS_X0 1.5 /* initial position of segments */ +#define SEGMENTS_Y0 0.0 /* initial position of segments */ +#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ +#define SEGMENTS_VY0 0.0 /* initial velocity of segments */ +#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ + +#define MOVE_SEGMENT_GROUPS 1 /* set to 1 to group segments into moving units */ +#define SEGMENT_GROUP_MASS 1000.0 /* mass of segment group */ +#define SEGMENT_GROUP_I 100.0 /* moment of inertia of segment group */ +#define SEGMENT_GROUP_DAMPING 0.0 /* damping of segment groups */ +#define GROUP_REPULSION 1 /* set to 1 for groups of segments to repel each other */ +#define KSPRING_GROUPS 1.0e11 /* harmonic potential between segment groups */ +#define GROUP_WIDTH 0.05 /* interaction width of groups */ +#define GROUP_G_REPEL 1 /* set to 1 to add repulsion between centers of mass of groups */ +#define GROUP_G_REPEL_RADIUS 1.2 /* radius within which centers of mass of groups repel each other */ +#define TRACK_SEGMENT_GROUPS 1 /* set to 1 for view to track group of segments */ +#define TRACK_X_PADDING 2.0 /* distance from x boundary where tracking starts */ + +#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 horizontal */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 0 /* set to 1 to print certain parameters at the top left instead of right */ +#define PLOT_SPEEDS 1 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ +#define PLOT_TRAJECTORIES 1 /* set to 1 to add a plot of obstacle trajectories (e.g. for rockets) */ +#define VMAX_PLOT_SPEEDS 0.6 /* vertical scale of plot of obstacle speeds */ + +#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 0 /* time during which to keep wall */ + +#define NXMAZE 10 /* width of maze */ +#define NYMAZE 10 /* height of maze */ #define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ -#define RAND_SHIFT 24 /* seed of random number generator */ +#define RAND_SHIFT 200 /* seed of random number generator */ #define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ -/* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 120 /* size of hashgrid in x direction */ +#define HASHY 450 /* 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 */ ``` -### 10 October 22 - Shining a rotating laser beam into a maze with mirrored walls ### - -**Program:** `particle_trajectory.c` - -**Initial condition in function `animation()`:** - -``` - time = (double)i/(double)(NSTEPS-1); - x = -1.65; - y = 0.22; - alpha = angle_schedule(time); -``` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ - -#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 SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ - -/* Choice of the billiard table, see global_particles.c */ - -#define B_DOMAIN 30 /* choice of domain shape */ - -#define CIRCLE_PATTERN 6 /* pattern of circles */ -#define POLYLINE_PATTERN 10 /* pattern of polyline */ - -#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ - -#define NMAXCIRCLES 50000 /* total number of circles (must be at least NCX*NCY for square grid) */ -#define NMAXPOLY 50000 /* total number of sides of polygonal line */ -#define NCX 9 /* number of circles in x direction */ -#define NCY 20 /* number of circles in y direction */ -#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ -#define SDEPTH 2 /* Sierpinski gastket depth */ - -#define LAMBDA -1.1 /* parameter controlling shape of domain */ -#define MU 0.1 /* second parameter controlling shape of billiard */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NPOLY 3 /* number of sides of polygon */ -#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ -#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ -#define PENROSE_RATIO 2.5 /* parameter controlling the shape of small ellipses in Penrose room */ - -#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ -#define DEBUG 0 /* draw trajectories, for debugging purposes */ - -/* Simulation parameters */ - -#define NPART 1 /* number of particles */ -#define NPARTMAX 100000 /* maximal number of particles after resampling */ -#define TRAJ_LENGTH 10000 /* length of trajectory */ -#define LMAX 0.01 /* minimal segment length triggering resampling */ -#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ -#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ -#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ -#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ -#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ -#define PRINT_TRAJECTORY_LENGTH 1 /* set to 1 to print length of trajectory 0 */ -#define PRINT_TRAJECTORY_ANGLE 1 /* set to 1 to print angle of trajectory 0 */ -#define PRINT_TRAJECTORY_PERIOD 0 /* set to 1 to print period of trajectory 0 */ -#define DRAW_LENGTHS_PLOT 1 /* set to 1 to plot trajectory lengths */ -#define LENGTHS_LOG_SCALE 1 /* set to 1 to use log scale for plot of lengths */ -#define MAX_ANGLE 45.0 /* range of angles of trajectory */ - -#define NSTEPS 3600 /* number of frames of movie */ -#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00001 /* integration step */ -#define NVID 150 /* number of iterations between images displayed on screen */ - -/* Decreasing TIME accelerates the animation and the movie */ -/* For constant speed of movie, TIME*DPHI should be kept constant */ -/* However, increasing DPHI too much deterioriates quality of simulation */ -/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ -/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ - -/* Colors and other graphical parameters */ - -#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ - -#define NCOLORS 64 /* number of colors */ -#define COLORSHIFT 0 /* hue of initial color */ -#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ -#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ -#define NSEG 100 /* number of segments of boundary */ -#define LENGTH 0.03 /* length of velocity vectors */ -#define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 2 /* width of particles */ -#define FRONT_WIDTH 3 /* width of wave front */ - -#define BLACK 1 /* set to 1 for black background */ -#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ -#define OUTER_COLOR 270.0 /* color outside billiard */ -#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ -#define PAINT_EXT 1 /* set to 1 to paint exterior */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define END_FRAMES 100 /* number of frames at end of movie */ - -#define NXMAZE 8 /* width of maze */ -#define NYMAZE 8 /* height of maze */ -#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ -#define RAND_SHIFT 58 /* seed of random number generator */ -#define MAZE_XSHIFT -0.5 /* horizontal shift of maze */ - -``` - -### 9 October 22 - Video #600: Incompressible Euler equation with two vortices ### +### 2 November 22 - A shear flow at 60 fps ### **Program:** `rde.c` -**Initial condition in function `animation()`:** -``` - init_vortex_state(0.4, 0.0, 0.2, phi, xy_in); - add_vortex_state(-0.4, 0.0, 0.2, phi, xy_in);` -``` +**Initial condition in function `animation()`:** `init_shear_flow(1.0, 0.02, 0.03, 1, 1, phi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ @@ -2114,7 +4489,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define WINHEIGHT 1000 /* window height */ #define NX 960 /* number of grid points on x axis */ #define NY 500 /* number of grid points on y axis */ - + #define XMIN -2.0 #define XMAX 2.0 /* x interval */ #define YMIN -1.041666667 @@ -2128,7 +4503,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */ #define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */ -#define POTENTIAL 101 /* type of potential or vector potential, see list in global_3d.c */ +#define POTENTIAL 7 /* type of potential or vector potential, see list in global_3d.c */ #define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */ @@ -2161,7 +4536,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define X_TARGET 0.4 #define Y_TARGET 0.7 /* shooter and target positions in laser fight */ -#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_LEFT -1.65 #define ISO_XSHIFT_RIGHT 0.4 #define ISO_YSHIFT_LEFT -0.05 #define ISO_YSHIFT_RIGHT -0.05 @@ -2172,7 +4547,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Physical patameters of wave equation */ -#define DT 0.000001 +#define DT 0.0000012 #define VISCOSITY 2.0 @@ -2185,12 +4560,17 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define FHNC -0.01 /* parameter in FHN equation */ #define K_HARMONIC 1.0 /* spring constant of harmonic potential */ #define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define V_MAZE 0.4 /* potential in walls of maze */ #define BZQ 0.0008 /* parameter in BZ equation */ #define BZF 1.2 /* parameter in BZ equation */ #define B_FIELD 10.0 /* magnetic field */ #define AB_RADIUS 0.2 /* radius of region with magnetic field for Aharonov-Bohm effect */ #define K_EULER 50.0 /* constant in stream function integration of Euler equation */ +#define SMOOTHEN_VORTICITY 1 /* set to 1 to smoothen vorticity field in Euler equation */ +#define SMOOTHEN_PERIOD 10 /* period between smoothenings */ +#define SMOOTH_FACTOR 0.015 /* factor by which to smoothen */ + #define T_OUT 2.0 /* outside temperature */ #define T_IN 0.0 /* inside temperature */ #define SPEED 0.0 /* speed of drift to the right */ @@ -2220,8 +4600,8 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Parameters for length and speed of simulation */ -#define NSTEPS 3000 /* number of frames of movie */ -#define NVID 200 /* number of iterations between images displayed on screen */ +#define NSTEPS 4000 /* number of frames of movie */ +#define NVID 50 /* 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 */ @@ -2246,12 +4626,12 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Plot type - color scheme */ -#define CPLOT 50 +#define CPLOT 52 #define CPLOT_B 51 /* Plot type - height of 3D plot */ -#define ZPLOT 50 /* z coordinate in 3D plot */ +#define ZPLOT 52 /* z coordinate in 3D plot */ #define ZPLOT_B 51 /* z coordinate in second 3D plot */ #define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ @@ -2261,7 +4641,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ #define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ #define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ -#define ADD_POT_CONSTANT 0.5 /* constant in front of added potential */ +#define ADD_POT_CONSTANT 0.35 /* constant in front of added potential */ #define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ @@ -2289,7 +4669,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO /* Color schemes, see list in global_pdes.c */ #define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 14 /* 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 */ @@ -2299,7 +4679,7 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #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_AMPLITUDE 0.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define CURL_SCALE 0.000015 /* scaling factor for curl representation */ #define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ @@ -2311,13 +4691,19 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #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 2.0 /* scaling factor for energy log representation */ -#define LOG_SHIFT -1.0 +#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 0.75 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 + +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ #define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */ #define COLORBAR_RANGE_B 2.5 /* scale of color scheme bar for 2nd part */ #define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ @@ -2339,11 +4725,6 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ #define B_DOMAIN_B 20 /* second domain shape, for comparisons */ #define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ -#define NXMAZE 8 /* width of maze */ -#define NYMAZE 8 /* height of maze */ -#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ -#define RAND_SHIFT 58 /* seed of random number generator */ -#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ /* end of constants added only for compatibility with wave_common.c */ @@ -2351,15 +4732,15 @@ double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_ double v_3d[2] = {-0.75, -0.45}; double w_3d[2] = {0.0, 0.015}; double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ -double observer[3] = {8.0, 8.0, 12.0}; /* location of observer for REP_PROJ_3D representation */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ -#define Z_SCALING_FACTOR 1.25 /* overall scaling factor of z axis 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 1.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ -#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ -#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ #define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ - +#define BORDER_PADDING 2 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */ /* For debugging purposes only */ #define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ @@ -2368,1047 +4749,11 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO ``` -### 8 October 22 - An example of a simulation gone wrong: Dam break with interacting bricks and no thermostat ### +### 1 November 22 - A quantum particle tunneling through a maze ### -**Program:** `lennardjones.c` +**Program:** `rde.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 */ -#define TIME_LAPSE_FIRST 1 /* set to 1 to show time-lapse version first */ - -/* 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 -2.0 -#define INITXMAX -0.04 /* x interval for initial condition */ -#define INITYMIN -1.125 -#define INITYMAX 0.65 /* y interval for initial condition */ - -#define BCXMIN -2.05 -#define BCXMAX 2.0 /* x interval for boundary condition */ -#define BCYMIN -1.125 -#define BCYMAX 1.25 /* y interval for boundary condition */ - -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ - -#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_ljones.c */ - -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ - -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 17 /* pattern of repelling segments, see list in global_ljones.c */ -#define ROCKET_SHAPE 0 /* shape of rocket combustion chamber, see list in global_ljones.c */ -#define ROCKET_SHAPE_B 0 /* shape of second rocket */ -#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ -#define NOZZLE_SHAPE_B 4 /* shape of nozzle for second rocket, see list in global_ljones.c */ - -#define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.5 /* 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 2.5 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ -#define MU 0.0075 /* parameter controlling radius of particles */ -#define MU_B 0.018 /* parameter controlling radius of particles of second type */ -#define NPOLY 25 /* 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 90 /* number of grid point for grid of disks */ -#define NGRIDY 100 /* 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 TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ -#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment 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 60 /* 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 OBSTACLE_INITIAL_TIME 250 /* time after which to start moving obstacle */ -#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 11 -#define PLOT_B 11 /* plot type for second movie */ - -#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ -#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ -#define HUE_TYPE0 70.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 280.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 .0 /* hue of particles of type 2 */ -#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 3.5 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 20.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 0.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ -#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.005 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ -#define GRAVITY 2000.0 /* gravity acting on all particles */ -#define GRAVITY_X 0.0 /* horizontal gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 100.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 0.1 /* 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 MIDDLE_CONSTANT_PHASE 3000 /* final phase in which temperature is constant */ -#define FINAL_DECREASE_PHASE -1 /* final phase in which temperature decreases */ -#define FINAL_CONSTANT_PHASE -1 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ -#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ -#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ -#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 0 /* time at which to add first particle */ -#define ADD_PERIOD 10000 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ -#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ -#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ -#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 100 /* final time without rotation */ -#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ -#define OMEGAMAX 100.0 /* maximal rotation speed */ -#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ -#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ -#define PRINT_SEGMENTS_SPEEDS 0 /* set to 1 to print velocity of moving segments */ - -#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ -#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ -#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ -#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ -#define RELEASE_ROCKET_AT_DEACTIVATION 1 /* set to 1 to limit segments velocity before segment release */ -#define SEGMENTS_X0 0.0 /* initial position of segments */ -#define SEGMENTS_Y0 0.0 /* initial position of segments */ -#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ -#define SEGMENTS_VY0 0.0 /* initial velocity of segments */ -#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ - -#define MOVE_SEGMENT_GROUPS 1 /* set to 1 to group segments into moving units */ -#define SEGMENT_GROUP_MASS 75.0 /* mass of segment group */ -#define SEGMENT_GROUP_I 15.0 /* moment of inertia of segment group */ -#define SEGMENT_GROUP_DAMPING 25.0 /* damping of segment groups */ -#define GROUP_REPULSION 1 /* set to 1 for groups of segments to repel each other */ -#define KSPRING_GROUPS 5.0e8 /* harmonic potential between segment groups */ -#define GROUP_WIDTH 0.05 /* interaction width of groups */ -#define GROUP_G_REPEL 1 /* set to 1 to add repulsion between centers of mass of groups */ -#define GROUP_G_REPEL_RADIUS 0.15 /* radius within which centers of mass of groups repel each other */ - -#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 horizontal */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ -#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ -#define REACTION_PROB 0.0045 /* probability controlling reaction term */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ -#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ -#define PLOT_SPEEDS 0 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ -#define VMAX_PLOT_SPEEDS 5.0 /* vertical scale of plot of obstacle speeds */ - -#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 0 /* time during which to keep wall */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e12 /* maximal force */ -#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 160 /* size of hashgrid in x direction */ -#define HASHY 80 /* 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 October 22 - Total internal reflection (short version) ### - -**Program:** `wave_billiard.c` - -**Initial condition in function `animation()`:** - -``` - init_circular_wave(-0.6, -0.3, phi, psi, xy_in); - - add_circular_wave(sign, -0.6, -0.3, phi, psi, xy_in); - sign = -sign; -``` - -``` -#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 1000 /* window width */ -#define WINHEIGHT 1000 /* window height */ -#define NX 2000 /* number of grid points on x axis */ -#define NY 2000 /* number of grid points on y axis */ - -#define XMIN -1.0 -#define XMAX 1.0 /* x interval */ -#define YMIN -1.0 -#define YMAX 1.0 /* y interval for 9/16 aspect ratio */ - -#define HIGHRES 1 /* 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 6 /* choice of domain shape, see list in global_pdes.c */ - -#define CIRCLE_PATTERN 1 /* pattern of circles or polygons, see list in global_pdes.c */ - -#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ -#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ -#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ - -#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 0.3 /* 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 6 /* depth of computation of Menger gasket */ -#define MRATIO 3 /* ratio defining Menger gasket */ -#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ -#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NGRIDX 12 /* number of grid point for grid of disks */ -#define NGRIDY 15 /* number of grid point for grid of disks */ - -#define X_SHOOTER -0.2 -#define Y_SHOOTER -0.6 -#define X_TARGET 0.4 -#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ - -#define ISO_XSHIFT_LEFT -2.9 -#define ISO_XSHIFT_RIGHT 1.4 -#define ISO_YSHIFT_LEFT -0.15 -#define ISO_YSHIFT_RIGHT -0.15 -#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ - -/* You can add more billiard tables by adapting the functions */ -/* xy_in_billiard and draw_billiard below */ - -/* Physical parameters of wave equation */ - -#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ -#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ -#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ -#define OSCILLATION_SCHEDULE 3 /* oscillation schedule, see list in global_pdes.c */ - -#define OMEGA 0.0005 /* frequency of periodic excitation */ -#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ -#define ACHIRP 0.25 /* acceleration coefficient in chirp */ -#define DAMPING 0.0 /* damping of periodic excitation */ -#define COURANT 0.12 /* Courant number */ -#define COURANTB 0.06 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 0.0 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ -#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ -/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ -/* The physical damping coefficient is given by GAMMA/(DT)^2 */ -/* Increasing COURANT speeds up the simulation, but decreases accuracy */ -/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ - -#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */ -#define OSCILLATING_SOURCE_PERIOD 50 /* 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 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 2 /* width of billiard boundary */ -#define PRINT_SPEED 0 /* print speed of moving source */ - -#define PAUSE 200 /* 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 */ -#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 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ - -/* Plot type, see list in global_pdes.c */ - -#define PLOT 1 - -#define PLOT_B 4 /* plot type for second movie */ - -/* Color schemes */ - -#define COLOR_PALETTE 12 /* 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 PHASE_FACTOR 1.0 /* 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 125.0 /* 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 3.0 /* 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 */ - -``` - -### 6 October 22 - Phase space representation of parabolic resonators ### - -**Program:** `billiard_phase_space.c` - -**In function `animation()`:** `lyap_exponents[i] = draw_phase_portrait(16, 20, 100, 20, 0.2);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ - -#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 XPHASEMAX 0.0 /* max x coordinate of phase portrait */ - -#define PIXELIZE 1 /* set to 1 to pixelize phase portrait (beta) */ -#define NGRID 200 /* size of grid to draw orbits with positive Lyapunov exponent */ - -#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ - -/* Choice of the billiard table, see global_particles.c */ - -#define B_DOMAIN 15 /* choice of domain shape */ - -#define CIRCLE_PATTERN 6 /* pattern of circles */ -#define POLYLINE_PATTERN 4 /* pattern of polyline */ - -#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ - -#define NMAXCIRCLES 50000 /* total number of circles (must be at least NCX*NCY for square grid) */ -#define NMAXPOLY 50000 /* total number of sides of polygonal line */ -#define NCX 9 /* number of circles in x direction */ -#define NCY 20 /* number of circles in y direction */ -#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ -#define SDEPTH 2 /* Sierpinski gastket depth */ - -#define LAMBDA 0.0 /* parameter controlling shape of domain */ -#define MU 1.0 /* second parameter controlling shape of billiard */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NPOLY 4 /* number of sides of polygon */ -#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ -#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ -#define PENROSE_RATIO 2.5 /* parameter controlling the shape of small ellipses in Penrose room */ - -#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ -#define DEBUG 0 /* draw trajectories, for debugging purposes */ - -/* Simulation parameters */ - -#define NPART 1 /* number of particles */ -#define NPARTMAX 100000 /* maximal number of particles after resampling */ -#define TRAJ_LENGTH 10000 /* length of trajectory */ -#define LMAX 0.01 /* minimal segment length triggering resampling */ -#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ -#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ -#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ -#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ -#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ -#define PRINT_TRAJECTORY_LENGTH 0 /* set to 1 to print length of trajectory 0 */ -#define PRINT_TRAJECTORY_PERIOD 0 /* set to 1 to print period of trajectory 0 */ -#define DRAW_LENGTHS_PLOT 0 /* set to 1 to plot trajectory lengths */ -#define LENGTHS_LOG_SCALE 1 /* set to 1 to use log scale for plot of lengths */ -#define MAX_ANGLE 90.0 /* range of angles of trajectory */ - -#define NSTEPS 3200 /* number of frames of movie */ -// #define NSTEPS 500 /* number of frames of movie */ -#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00001 /* integration step */ -#define NVID 150 /* number of iterations between images displayed on screen */ -#define SYMMETRIC_PARAMETER 1 /* set to 1 if parameters depend symmetrically on time */ - -/* Decreasing TIME accelerates the animation and the movie */ -/* For constant speed of movie, TIME*DPHI should be kept constant */ -/* However, increasing DPHI too much deterioriates quality of simulation */ -/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ -/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ - -/* Colors and other graphical parameters */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ - -#define NCOLORS 64 /* number of colors */ -#define CFACTOR 3 /* color step */ -#define COLORSHIFT 0 /* hue of initial color */ -#define LYAP_PLOT_COLOR 200.0 /* color hue of Lyapunov exponent plot */ -#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ -#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ -#define NSEG 100 /* number of segments of boundary */ -#define LENGTH 0.03 /* length of velocity vectors */ -#define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 2 /* width of particles */ -#define FRONT_WIDTH 3 /* width of wave front */ - -#define BLACK 1 /* set to 1 for black background */ -#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ -#define OUTER_COLOR 270.0 /* color outside billiard */ -#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ -#define PAINT_EXT 1 /* set to 1 to paint exterior */ - -#define PRINT_LAMBDA 1 /* set to 1 to print value of lambda */ -#define PRINT_MU 0 /* set to 1 to print value of mu */ -#define PRINT_LYAPUNOV 1 /* set to 1 to print mean Lyapunov exponent */ -#define PLOT_LYAPUNOV 1 /* set to 1 to add plot of Lyapunov exponents */ -#define LOGSCALEX_LYAP 0 /* set to 1 to use log scale on parameter axis of Lyapunov exponents */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define END_FRAMES 100 /* number of frames at end of movie */ - -``` - -### 5 October 22 - Solving a maze by shooting particles at it ### - -**Program:** `particle_billiard.c` - -**Initial condition in function `animation()`:** `init_drop_config(-1.3, 0.2, -0.25*PI, 0.25*PI, configs);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ - -#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 SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ - -/* Choice of the billiard table, see global_particles.c */ - -#define B_DOMAIN 30 /* choice of domain shape */ - -#define CIRCLE_PATTERN 1 /* pattern of circles */ -#define POLYLINE_PATTERN 10 /* pattern of polyline */ - -#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ - -#define NMAXCIRCLES 100000 /* total number of circles (must be at least NCX*NCY for square grid) */ -#define NMAXPOLY 100000 /* total number of sides of polygonal line */ -#define NCX 30 /* number of circles in x direction */ -#define NCY 20 /* number of circles in y direction */ -#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ -#define SDEPTH 1 /* Sierpinski gastket depth */ - -#define LAMBDA 1.5 /* parameter controlling shape of domain */ -#define MU 0.5 /* second parameter controlling shape of billiard */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define PENROSE_RATIO 2.5 /* parameter controlling the shape of small ellipses in Penrose room */ - -#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ -#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ - -#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ -#define DEBUG 0 /* draw trajectories, for debugging purposes */ - -/* Simulation parameters */ - -#define NPART 1000 /* number of particles */ -#define NPARTMAX 100000 /* maximal number of particles after resampling */ -#define LMAX 0.01 /* minimal segment length triggering resampling */ -#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ -#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ -#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ -#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */ -#define PRINT_LEFT_RIGHT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles on left and right side */ -#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */ -#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ - -#define NSTEPS 7000 /* number of frames of movie */ -#define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00002 /* integration step */ -#define NVID 25 /* number of iterations between images displayed on screen */ -#define END_FRAMES 25 /* number of still frames at the end of the movie */ - -/* Decreasing TIME accelerates the animation and the movie */ -/* For constant speed of movie, TIME*DPHI should be kept constant */ -/* However, increasing DPHI too much deterioriates quality of simulation */ -/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ -/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ - -/* Colors and other graphical parameters */ - -#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ - -#define NCOLORS 16 /* number of colors */ -#define COLORSHIFT 0 /* hue of initial color */ -#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */ -#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ -#define NSEG 100 /* number of segments of boundary */ -#define LENGTH 0.04 /* length of velocity vectors */ -#define BILLIARD_WIDTH 3 /* width of billiard */ -#define PARTICLE_WIDTH 3 /* width of particles */ -#define FRONT_WIDTH 3 /* width of wave front */ - -#define BLACK 1 /* set to 1 for black background */ -#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ -#define OUTER_COLOR 270.0 /* color outside billiard */ -#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ -#define PAINT_EXT 1 /* set to 1 to paint exterior */ - -#define PAUSE 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 NXMAZE 8 /* width of maze */ -#define NYMAZE 8 /* height of maze */ -#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ -#define RAND_SHIFT 58 /* seed of random number generator */ -#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ - -``` - -### 4 October 22 - Just another sim in the hall: A breaking dam made of interacting bricks ### - -**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 */ -#define TIME_LAPSE_FIRST 1 /* set to 1 to show time-lapse version first */ - -/* 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 -2.0 -#define INITXMAX -0.04 /* x interval for initial condition */ -#define INITYMIN -1.125 -#define INITYMAX 0.65 /* y interval for initial condition */ - -#define BCXMIN -2.05 -#define BCXMAX 2.0 /* x interval for boundary condition */ -#define BCYMIN -1.125 -#define BCYMAX 1.25 /* y interval for boundary condition */ - -#define OBSXMIN -2.0 -#define OBSXMAX 2.0 /* x interval for motion of obstacle */ - -#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_ljones.c */ - -#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ -#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ - -#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ -#define SEGMENT_PATTERN 17 /* pattern of repelling segments, see list in global_ljones.c */ -#define ROCKET_SHAPE 0 /* shape of rocket combustion chamber, see list in global_ljones.c */ -#define ROCKET_SHAPE_B 0 /* shape of second rocket */ -#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ -#define NOZZLE_SHAPE_B 4 /* shape of nozzle for second rocket, see list in global_ljones.c */ - -#define TWO_TYPES 0 /* set to 1 to have two types of particles */ -#define TPYE_PROPORTION 0.5 /* 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 2.5 /* minimal distance in Poisson disc process, controls density of particles */ -#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ -#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ - -#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ -#define MU 0.0075 /* parameter controlling radius of particles */ -#define MU_B 0.018 /* parameter controlling radius of particles of second type */ -#define NPOLY 25 /* 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 90 /* number of grid point for grid of disks */ -#define NGRIDY 100 /* 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 TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ -#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment 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 60 /* number of iterations between images displayed on screen */ -#define NSEG 250 /* number of segments of boundary */ -#define INITIAL_TIME 150 /* time after which to start saving frames */ -#define OBSTACLE_INITIAL_TIME 400 /* time after which to start moving obstacle */ -#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 11 -#define PLOT_B 11 /* plot type for second movie */ - -#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ -#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ -#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ - -/* Color schemes */ - -#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ - -#define BLACK 1 /* background */ - -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ - -#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ - -#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ -#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ -#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ -#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ -#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ - -/* particle properties */ - -#define ENERGY_HUE_MIN 330.0 /* color of original particle */ -#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ -#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ -#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ -#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ -#define HUE_TYPE0 70.0 /* hue of particles of type 0 */ -#define HUE_TYPE1 280.0 /* hue of particles of type 1 */ -#define HUE_TYPE2 .0 /* hue of particles of type 2 */ -#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ - -#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ -#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ -#define KREPEL 12.0 /* constant in repelling force between particles */ -#define EQUILIBRIUM_DIST 3.5 /* Lennard-Jones equilibrium distance */ -#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ -#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ -#define DAMPING 50.0 /* damping coefficient of particles */ -#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ -#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ -#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ -#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ -#define V_INITIAL 0.0 /* initial velocity range */ -#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ - -#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ -#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ -#define SIGMA 5.0 /* noise intensity in thermostat */ -#define BETA 0.003 /* initial inverse temperature */ -#define MU_XI 0.01 /* friction constant in thermostat */ -#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ -#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ -#define NBH_DIST_FACTOR 7.5 /* radius in which to count neighbours */ -#define GRAVITY 2000.0 /* gravity acting on all particles */ -#define GRAVITY_X 0.0 /* horizontal gravity acting on all particles */ -#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ -#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ -#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ -#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ -#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ - -#define ROTATION 0 /* set to 1 to include rotation of particles */ -#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ -#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ -#define KTORQUE 100.0 /* force constant in angular dynamics */ -#define KTORQUE_B 10.0 /* force constant in angular dynamics */ -#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ -#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ -#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ -#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ -#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ -#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ - -#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ -#define BETA_FACTOR 0.1 /* 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 MIDDLE_CONSTANT_PHASE 3000 /* final phase in which temperature is constant */ -#define FINAL_DECREASE_PHASE -1 /* final phase in which temperature decreases */ -#define FINAL_CONSTANT_PHASE -1 /* final phase in which temperature is constant */ - -#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ -#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ -#define COMPRESSION_RATIO 0.3 /* final size of container */ -#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ -#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ - -#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ -#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ -#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ -#define NTRIALS 2000 /* number of trials when resampling */ -#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ -#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ -#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ -#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ -#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ -#define N_PRESSURES 100 /* number of intervals to record pressure */ -#define N_P_AVERAGE 100 /* size of pressure averaging window */ -#define N_T_AVERAGE 50 /* size of temperature averaging window */ -#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ -#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ -#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ -#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ -#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ -#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ - -#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ -#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ - -#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ -#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ -#define NPART_BOTTOM 100 /* number of particles at the bottom */ - -#define ADD_PARTICLES 0 /* set to 1 to add particles */ -#define ADD_TIME 0 /* time at which to add first particle */ -#define ADD_PERIOD 10000 /* time interval between adding further particles */ -#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ -#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ - -#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ -#define N_TRACER_PARTICLES 3 /* number of tracer particles */ -#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ -#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ -#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ - -#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ -#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ -#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ -#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ -#define ROTATE_FINAL_TIME 100 /* final time without rotation */ -#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ -#define OMEGAMAX 100.0 /* maximal rotation speed */ -#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ -#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ -#define PRINT_SEGMENTS_SPEEDS 0 /* set to 1 to print velocity of moving segments */ - -#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ -#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ -#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ -#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ -#define RELEASE_ROCKET_AT_DEACTIVATION 1 /* set to 1 to limit segments velocity before segment release */ -#define SEGMENTS_X0 0.0 /* initial position of segments */ -#define SEGMENTS_Y0 0.0 /* initial position of segments */ -#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ -#define SEGMENTS_VY0 0.0 /* initial velocity of segments */ -#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ - -#define MOVE_SEGMENT_GROUPS 1 /* set to 1 to group segments into moving units */ -#define SEGMENT_GROUP_MASS 100.0 /* mass of segment group */ -#define SEGMENT_GROUP_I 15.0 /* moment of inertia of segment group */ -#define SEGMENT_GROUP_DAMPING 50.0 /* damping of segment groups */ -#define GROUP_REPULSION 1 /* set to 1 for groups of segments to repel each other */ -#define KSPRING_GROUPS 1.0e8 /* harmonic potential between segment groups */ -#define GROUP_WIDTH 0.05 /* interaction width of groups */ -#define GROUP_G_REPEL 1 /* set to 1 to add repulsion between centers of mass of groups */ -#define GROUP_G_REPEL_RADIUS 0.12 /* radius within which centers of mass of groups repel each other */ - -#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 horizontal */ -#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ - -#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ -#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ -#define REACTION_PROB 0.0045 /* probability controlling reaction term */ - -#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ -#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ -#define PLOT_SPEEDS 0 /* set to 1 to add a plot of obstacle speeds (e.g. for rockets) */ -#define VMAX_PLOT_SPEEDS 5.0 /* vertical scale of plot of obstacle speeds */ - -#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 0 /* time during which to keep wall */ - -#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ -#define FMAX 1.0e12 /* maximal force */ -#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ -#define PMAX 1000.0 /* maximal force */ - -#define HASHX 160 /* size of hashgrid in x direction */ -#define HASHY 80 /* size of hashgrid in y direction */ -#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ -#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ - -#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ -#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ - -``` - -### 3 October 22 - Total internal reflection, with an index of refraction of 1.33 ### - -**Program:** `wave_billiard.c` - -**Initial condition in function `animation()`:** `init_circular_wave(-1.2, -0.5, phi, psi, xy_in);` +**Initial condition in function `animation()`:** `init_coherent_state(-1.2, 0.35, 5.0, -2.0, 0.1, phi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ @@ -3418,374 +4763,265 @@ int reset_view = 0; /* switch to reset 3D view parameters (for option RO #define WINWIDTH 1920 /* window width */ #define WINHEIGHT 1000 /* window height */ -#define NX 3840 /* number of grid points on x axis */ -#define NY 2000 /* number of grid points on y axis */ -#define XMIN -1.9 -#define XMAX 2.1 /* x interval */ +#define NX 480 /* number of grid points on x axis */ +#define NY 250 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ #define YMIN -1.041666667 #define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ -#define HIGHRES 1 /* set to 1 if resolution of grid is double that of displayed image */ +/* Choice of simulated equation */ -#define JULIA_SCALE 1.0 /* scaling for Julia sets */ +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodinger equation) */ +#define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */ +#define POTENTIAL 7 /* type of potential or vector potential, see list in global_3d.c */ + +#define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ /* Choice of the billiard table */ -#define B_DOMAIN 6 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ -#define CIRCLE_PATTERN 1 /* pattern of circles or polygons, see list in global_pdes.c */ - -#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ -#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ -#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ +#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 1 /* set to 1 to randomize angle of polygons */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ -#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */ -#define MU 0.3 /* 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 6 /* 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 LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 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 12 /* number of grid point for grid of disks */ -#define NGRIDY 15 /* number of grid point for grid of disks */ +#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 -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 */ +#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 below */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ -/* Physical parameters of wave equation */ +/* Physical patameters 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 OSCILLATION_SCHEDULE 3 /* oscillation schedule, see list in global_pdes.c */ +#define DT 0.00000002 -#define OMEGA 0.0005 /* frequency of periodic excitation */ -#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ -#define ACHIRP 0.25 /* acceleration coefficient in chirp */ -#define DAMPING 0.0 /* damping of periodic excitation */ -#define COURANT 0.12 /* Courant number */ -#define COURANTB 0.09 /* Courant number in medium B */ -#define GAMMA 0.0 /* damping factor in wave equation */ -#define GAMMAB 0.0 /* damping factor in wave equation */ -#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ -#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ -#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ -#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ -#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ -/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ -/* The physical damping coefficient is given by GAMMA/(DT)^2 */ -/* Increasing COURANT speeds up the simulation, but decreases accuracy */ -/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ +#define VISCOSITY 2.0 -#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */ -#define OSCILLATING_SOURCE_PERIOD 50 /* period of oscillating source */ +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 1.0 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define V_MAZE 0.4 /* potential in walls of maze */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ +#define B_FIELD 10.0 /* magnetic field */ +#define AB_RADIUS 0.2 /* radius of region with magnetic field for Aharonov-Bohm effect */ +#define K_EULER 50.0 /* constant in stream function integration of Euler equation */ + +#define SMOOTHEN_VORTICITY 1 /* set to 1 to smoothen vorticity field in Euler equation */ +#define SMOOTHEN_PERIOD 10 /* period between smoothenings */ +#define SMOOTH_FACTOR 0.015 /* factor by which to smoothen */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + /* Boundary conditions, see list in global_pdes.c */ -#define B_COND 2 +#define B_COND 0 /* 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 2 /* width of billiard boundary */ -#define PRINT_SPEED 0 /* print speed of moving source */ +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 500 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ -#define PAUSE 200 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ +#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 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 */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ #define FADE 1 /* set to 1 to fade at end of movie */ -/* Parameters of initial condition */ +/* Visualisation */ -#define INITIAL_AMP 0.75 /* amplitude of initial condition */ -#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ -#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ -/* Plot type, see list in global_pdes.c */ +#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ -#define PLOT 0 +/* Plot type - color scheme */ -#define PLOT_B 4 /* plot type for second movie */ +#define CPLOT 30 +#define CPLOT_B 31 -/* Color schemes */ +/* Plot type - height of 3D plot */ + +#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 0.35 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ #define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ -#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 0 /* Color palette, see list in global_pdes.c */ -#define BLACK 1 /* background */ +#define BLACK 1 /* black background */ -#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ -#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ -#define PHASE_FACTOR 1.0 /* 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 SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 30.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ -#define E_SCALE 125.0 /* 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 CURL_SCALE 0.000015 /* scaling factor for curl representation */ #define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/ #define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ #define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ #define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ #define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ -#define HUEMEAN 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 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 0.75 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 -#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ -#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */ -#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define NXMAZE 7 /* width of maze */ +#define NYMAZE 7 /* height of maze */ +#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */ +#define RAND_SHIFT 24 /* seed of random number generator */ +#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */ + +#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 2.5 /* 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 */ +/* 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 */ +#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define ACHIRP 0.2 /* acceleration coefficient in chirp */ +#define DAMPING 0.0 /* damping of periodic excitation */ +#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */ +#define B_DOMAIN_B 20 /* second domain shape, for comparisons */ +#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 1.25 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 1.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ +#define BORDER_PADDING 2 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */ /* For debugging purposes only */ -#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ -#define VMAX 10.0 /* max value of wave amplitude */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ +#define TEST_GRADIENT 0 /* print norm squared of gradient */ ``` -### 2 October 22 - Phase space representation of billiards interpolating between a circle and a hexagon ### - -**Program:** `billiard_phase_space.c` - -**In function `animation()`:** `lyap_exponents[i] = draw_phase_portrait(12, 20, 100, 20, 0.2);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ - -#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 XPHASEMAX 0.0 /* max x coordinate of phase portrait */ - -#define PIXELIZE 1 /* set to 1 to pixelize phase portrait (beta) */ -#define NGRID 200 /* size of grid to draw orbits with positive Lyapunov exponent */ - -#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ - -/* Choice of the billiard table, see global_particles.c */ - -#define B_DOMAIN 9 /* choice of domain shape */ - -#define CIRCLE_PATTERN 6 /* pattern of circles */ -#define POLYLINE_PATTERN 4 /* pattern of polyline */ - -#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ - -#define NMAXCIRCLES 50000 /* total number of circles (must be at least NCX*NCY for square grid) */ -#define NMAXPOLY 50000 /* total number of sides of polygonal line */ -#define NCX 9 /* number of circles in x direction */ -#define NCY 20 /* number of circles in y direction */ -#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ -#define SDEPTH 2 /* Sierpinski gastket depth */ - -#define LAMBDA 1000.0 /* parameter controlling shape of domain */ -#define MU 1.0 /* second parameter controlling shape of billiard */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ -#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ -#define PENROSE_RATIO 2.5 /* parameter controlling the shape of small ellipses in Penrose room */ - -#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ -#define DEBUG 0 /* draw trajectories, for debugging purposes */ - -/* Simulation parameters */ - -#define NPART 1 /* number of particles */ -#define NPARTMAX 100000 /* maximal number of particles after resampling */ -#define TRAJ_LENGTH 10000 /* length of trajectory */ -#define LMAX 0.01 /* minimal segment length triggering resampling */ -#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ -#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ -#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ -#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ -#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ -#define PRINT_TRAJECTORY_LENGTH 0 /* set to 1 to print length of trajectory 0 */ -#define PRINT_TRAJECTORY_PERIOD 0 /* set to 1 to print period of trajectory 0 */ -#define DRAW_LENGTHS_PLOT 0 /* set to 1 to plot trajectory lengths */ -#define LENGTHS_LOG_SCALE 1 /* set to 1 to use log scale for plot of lengths */ -#define MAX_ANGLE 90.0 /* range of angles of trajectory */ - -#define NSTEPS 4000 /* number of frames of movie */ -#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00001 /* integration step */ -#define NVID 150 /* number of iterations between images displayed on screen */ -#define SYMMETRIC_PARAMETER 1 /* set to 1 if parameters depend symmetrically on time */ - -/* Decreasing TIME accelerates the animation and the movie */ -/* For constant speed of movie, TIME*DPHI should be kept constant */ -/* However, increasing DPHI too much deterioriates quality of simulation */ -/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ -/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ - -/* Colors and other graphical parameters */ - -#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ - -#define NCOLORS 64 /* number of colors */ -#define CFACTOR 3 /* color step */ -#define COLORSHIFT 0 /* hue of initial color */ -#define LYAP_PLOT_COLOR 200.0 /* color hue of Lyapunov exponent plot */ -#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ -#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ -#define NSEG 100 /* number of segments of boundary */ -#define LENGTH 0.03 /* length of velocity vectors */ -#define BILLIARD_WIDTH 2 /* width of billiard */ -#define PARTICLE_WIDTH 2 /* width of particles */ -#define FRONT_WIDTH 3 /* width of wave front */ - -#define BLACK 1 /* set to 1 for black background */ -#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ -#define OUTER_COLOR 270.0 /* color outside billiard */ -#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ -#define PAINT_EXT 1 /* set to 1 to paint exterior */ - -#define PRINT_LAMBDA 1 /* set to 1 to print value of lambda */ -#define PRINT_MU 0 /* set to 1 to print value of mu */ -#define PRINT_LYAPUNOV 1 /* set to 1 to print mean Lyapunov exponent */ -#define PLOT_LYAPUNOV 1 /* set to 1 to add plot of Lyapunov exponents */ - -#define PAUSE 1000 /* number of frames after which to pause */ -#define PSLEEP 1 /* sleep time during pause */ -#define SLEEP1 1 /* initial sleeping time */ -#define SLEEP2 1 /* final sleeping time */ -#define END_FRAMES 100 /* number of frames at end of movie */ - -``` - -### 1 October 22 - Solving a maze with laser beams ### - -**Program:** `particle_billiard.c` - -**Initial condition in function `animation()`:** `init_drop_config(-1.3, 0.2, -0.25*PI, 0.25*PI, configs);` - -``` -#define MOVIE 1 /* set to 1 to generate movie */ - -#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 SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ - -/* Choice of the billiard table, see global_particles.c */ - -#define B_DOMAIN 30 /* choice of domain shape */ - -#define CIRCLE_PATTERN 1 /* pattern of circles */ -#define POLYLINE_PATTERN 10 /* pattern of polyline */ - -#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ - -#define NMAXCIRCLES 100000 /* total number of circles (must be at least NCX*NCY for square grid) */ -#define NMAXPOLY 100000 /* total number of sides of polygonal line */ -#define NCX 30 /* number of circles in x direction */ -#define NCY 20 /* number of circles in y direction */ -#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ -#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ -#define SDEPTH 1 /* Sierpinski gastket depth */ - -#define LAMBDA 1.5 /* parameter controlling shape of domain */ -#define MU 0.5 /* second parameter controlling shape of billiard */ -#define FOCI 1 /* set to 1 to draw focal points of ellipse */ -#define NPOLY 6 /* number of sides of polygon */ -#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ -#define PENROSE_RATIO 2.5 /* parameter controlling the shape of small ellipses in Penrose room */ - -#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ -#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ -#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ - -#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ -#define DEBUG 0 /* draw trajectories, for debugging purposes */ - -/* Simulation parameters */ - -#define NPART 1000 /* number of particles */ -#define NPARTMAX 100000 /* maximal number of particles after resampling */ -#define LMAX 0.01 /* minimal segment length triggering resampling */ -#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ -#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ -#define SHOWTRAILS 1 /* set to 1 to keep trails of the particles */ -#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ -#define PRINT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles */ -#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */ -#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ - -#define NSTEPS 5250 /* number of frames of movie */ -#define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ -#define DPHI 0.00002 /* integration step */ -#define NVID 25 /* number of iterations between images displayed on screen */ -#define END_FRAMES 25 /* number of still frames at the end of the movie */ - -/* Decreasing TIME accelerates the animation and the movie */ -/* For constant speed of movie, TIME*DPHI should be kept constant */ -/* However, increasing DPHI too much deterioriates quality of simulation */ -/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ -/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ - -/* Colors and other graphical parameters */ - -#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ - -#define NCOLORS 16 /* number of colors */ -#define COLORSHIFT 0 /* hue of initial color */ -#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */ -#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ -#define NSEG 100 /* number of segments of boundary */ -#define LENGTH 0.03 /* length of velocity vectors */ -#define BILLIARD_WIDTH 3 /* width of billiard */ -#define PARTICLE_WIDTH 3 /* width of particles */ -#define FRONT_WIDTH 3 /* width of wave front */ - -#define BLACK 1 /* set to 1 for black background */ -#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ -#define OUTER_COLOR 270.0 /* color outside billiard */ -#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ -#define PAINT_EXT 1 /* set to 1 to paint exterior */ - -#define PAUSE 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 */ - -```