### 31 August 21 - A Sinai pinball with colored pegs ### **Program:** `particle_pinball.c` (variant of `particle_billiard.c`) **Initial condition in function `animation()`:** `init_drop_config(-1.4, 0.0, -0.5*PID, 0.5*PID, 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 21 /* choice of domain shape */ #define CIRCLE_PATTERN 21 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 2000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 48 /* number of circles in x direction */ #define NCY 28 /* number of circles in y direction */ // #define NCX 52 /* number of circles in x direction */ // #define NCY 30 /* number of circles in y direction */ #define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ #define LAMBDA 1.68 /* parameter controlling shape of domain */ #define MU 0.027 /* 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 DRAW_BILLIARD 1 /* set to 1 to draw billiard */ #define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ #define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ #define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ #define DEBUG 0 /* draw trajectories, for debugging purposes */ /* Simulation parameters */ #define NPART 1 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ #define 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 NSTEPS 15000 /* number of frames of movie */ #define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ #define DPHI 0.00004 /* 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 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 0.045 /* 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 ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */ #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 1000 /* final sleeping time */ #define END_FRAMES 100 /* number of still frames at end of movie */ ``` ### 30 August 21 - Erosion of a wave protection ### **Program:** `mangrove.c` **Initial condition in function `animation()`:** `init_wave_flat(phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 8 /* 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 LAMBDA 0.75 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define X_SHIFT -0.8 /* x range on which to apply OSCILLATE_TOPBOT */ #define OMEGA 0.002 /* frequency of periodic excitation */ #define K_BC 3.0 /* spatial period of periodic excitation in y direction */ #define KX_BC 30.0 /* spatial period of periodic excitation in x direction */ #define KY_BC 10.0 /* spatial period of periodic excitation in y direction */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.005 /* Courant number in medium B */ #define GAMMA 2.0e-6 /* damping factor in wave equation */ #define GAMMAB 1.0e-4 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */ #define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ #define KAPPAB 1.0e-6 /* "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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 6500 /* number of frames of movie */ #define NVID 35 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 125 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2500.0 /* scaling factor for energy representation */ #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 */ /* mangrove colors */ #define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */ #define MANGROVE_HUE_MAX 0.0 /* color of saturated mangrove */ // #define MANGROVE_EMAX 5.0e-3 /* max energy for mangrove to survive */ #define MANGROVE_EMAX 1.0e-3 /* max energy for mangrove to survive */ /* 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 */ ``` ### 29 August 21 - Mixing in an ehrenfest-type pinball ### **Program:** `particle_pinball.c` **Initial condition in function `animation()`:** `init_double_drop_config(-1.25, 0.05, 0.0, DPI, 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 21 /* choice of domain shape */ #define CIRCLE_PATTERN 1 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 9 /* number of circles in x direction */ #define NCY 20 /* number of circles in y direction */ #define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ #define LAMBDA 1.8 /* parameter controlling shape of domain */ #define MU 0.03 /* 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 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 5000 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ #define LMAX 0.01 /* minimal segment length triggering resampling */ #define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ #define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ #define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ #define NSTEPS 4500 /* number of frames of movie */ #define TIME 1500 /* 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 NCOLORS 2 /* number of colors */ #define COLORSHIFT 10.0 /* 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 0.02 /* length of velocity vectors */ #define BILLIARD_WIDTH 2 /* width of billiard */ #define PARTICLE_WIDTH 3 /* width of particles */ #define FRONT_WIDTH 3 /* width of wave front */ #define 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 ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular domain */ #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 1000 /* final sleeping time */ #define END_FRAMES 100 /* number of still frames at end of movie */ ``` ### 28 August 21 - Wave protection comparison 8: "Golden spiral" versus Poisson disc sampling with a step input ### **Program:** `wave_comparison.c` **Initial condition in function `animation()`:** `init_wave_flat_comp(phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 11 /* pattern of circles, see list in global_pdes.c */ #define CIRCLE_PATTERN_B 8 /* 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 LAMBDA 0.8 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define MUB 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 20 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.0 /* frequency of periodic excitation */ #define AMPLITUDE 0.025 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.004 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMAB 1.0e-8 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 3200 /* number of frames of movie */ #define NVID 25 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 200 /* time after which to start saving frames */ #define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 END_FRAMES 100 /* number of still frames at end of movie */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 50.0 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2000.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ /* For debugging purposes only */ #define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ #define VMAX 5.0 /* max value of wave amplitude */ ``` ### 27 August 21 - A wave traveling between two parabolic antennas ### **Program:** `wave_billiard.c` **Initial condition in function `animation()`:** `init_wave(-LAMBDA, 0.0, phi, psi, xy_in);` **In `init_wave()`:** `if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.00025)*cos(-sqrt(dist2)/0.005);` ``` #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 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 19 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 8 /* 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 LAMBDA 1.2 /* parameter controlling the dimensions of domain */ #define MU 0.5 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 16 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.002 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.01 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMAB 1.0e-6 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 2 /* Parameters for length and speed of simulation */ #define NSTEPS 4500 /* number of frames of movie */ #define NVID 25 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 0 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard boundary */ #define PAUSE 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 1 #define PLOT_B 0 /* plot type for second movie */ /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 500.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ /* 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 */ ``` ### 26 August 21 - Illustrating the butterfly effect with a laser ### **Program:** `particle_pinball_angles.c` (variant of `particle_billiard.c`) **Initial condition in function `animation()`:** `angle0 = 0.2 + 2.4815e-6, x0 = -1.1, y0 = -0.5625;` ``` #define MOVIE 1 /* set to 1 to generate movie */ #define WINWIDTH 720 /* window width */ #define WINHEIGHT 720 /* window height */ #define XMIN -1.125 #define XMAX 1.125 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ #define 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 20 /* choice of domain shape */ #define CIRCLE_PATTERN 3 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 3 /* number of circles in x direction */ #define NCY 8 /* number of circles in y direction */ #define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ #define LAMBDA 0.5 /* parameter controlling shape of domain */ #define MU 0.11 /* 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 DRAW_BILLIARD 1 /* set to 1 to draw billiard */ #define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ #define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ #define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ #define DEBUG 0 /* draw trajectories, for debugging purposes */ /* Simulation parameters */ #define NPART 1 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ #define 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 NSTEPS 1000 /* number of frames of movie */ #define TIME 4200 /* 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 NCOLORS 128 /* 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 0.02 /* length of velocity vectors */ #define BILLIARD_WIDTH 2 /* width of billiard */ #define PARTICLE_WIDTH 3 /* width of particles */ #define FRONT_WIDTH 3 /* width of wave front */ #define 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 ERASE_OUTSIDE 0 /* set to 1 to erase outside of rectangular domain */ #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 1000 /* final sleeping time */ #define END_FRAMES 50 /* number of still frames at end of movie */ #define LUM_ATTENUATION 0.0025 /* luminosity attenuation */ #include "global_particles.c" #include "sub_part_billiard.c" #include "sub_part_pinball.c" ``` ### 25 August 21 - Wave protection comparison 7: “Golden spiral” versus Poisson disc sampling ### **Program:** `wave_comparison.c` **Initial condition in function `animation()`:** `int_planar_wave_comp(XMIN + 0.015, 0.0, phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 11 /* pattern of circles, see list in global_pdes.c */ #define CIRCLE_PATTERN_B 8 /* 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 LAMBDA 0.8 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define MUB 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 20 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.0035 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.0075 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMAB 1.0e-5 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 3250 /* number of frames of movie */ #define NVID 25 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 200 /* time after which to start saving frames */ #define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 1 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ #define SLOPE 1.5 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2000.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ /* 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 */ ``` ### 24 August 21 - Comparison between 7 non-random and randomized pinballs ### **Program:** `particle_pinball.c` (variant of `particle_billiard.c`) **Initial condition in function `animation()`:** `init_drop_config(-1.25, 0.05, -0.1, 0.1, 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 20 /* choice of domain shape */ #define CIRCLE_PATTERN 3 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 15 /* number of circles in x direction */ #define NCY 20 /* number of circles in y direction */ #define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ #define LAMBDA 0.8 /* parameter controlling shape of domain */ #define MU 0.03 /* 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 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 500 /* 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 NSTEPS 1200 /* number of frames of movie */ #define TIME 1500 /* 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 NCOLORS 10 /* 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 0.02 /* 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 ERASE_OUTSIDE 0 /* set to 1 to erase outside of rectangular domain */ #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 1000 /* final sleeping time */ #define END_FRAMES 100 /* number of still frames at end of movie */ ``` ### 23 August 21 - A self-healing wave protection ### **Program:** `mangrove.c` **Initial condition in function `animation()`:** `init_wave_flat(phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 8 /* 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 LAMBDA 0.75 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define X_SHIFT -0.8 /* x range on which to apply OSCILLATE_TOPBOT */ #define OMEGA 0.0004 /* frequency of periodic excitation */ #define K_BC 3.0 /* spatial period of periodic excitation in y direction */ #define KX_BC 6.0 /* spatial period of periodic excitation in x direction */ #define KY_BC 2.0 /* spatial period of periodic excitation in y direction */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.005 /* Courant number in medium B */ #define GAMMA 2.0e-6 /* damping factor in wave equation */ #define GAMMAB 1.0e-4 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */ #define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ #define KAPPAB 1.0e-6 /* "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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 5800 /* number of frames of movie */ #define NVID 35 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 125 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2500.0 /* scaling factor for energy representation */ #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 */ /* mangrove colors */ #define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */ #define MANGROVE_HUE_MAX 0.0 /* color of saturated mangrove */ #define MANGROVE_EMAX 5.0e-3 /* max energy for mangrove to survive */ // #define MANGROVE_EMAX 1.0e-4 /* max energy for mangrove to survive */ /* For debugging purposes only */ #define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ #define VMAX 10.0 /* max value of wave amplitude */ ``` ### 22 August 21 - Blue noise, baby’s got blue noise: A Poisson disc sampling wave protection ### **Program:** `wave_billiard.c` **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.015, 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 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 8 /* 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 LAMBDA 0.85 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 16 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.002 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.01 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMAB 1.0e-6 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 4000 /* number of frames of movie */ #define NVID 25 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 200 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 1 #define PLOT_B 0 /* plot type for second movie */ /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ #define SLOPE 1.5 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2000.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ /* For debugging purposes only */ #define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ #define VMAX 10.0 /* max value of wave amplitude */ ``` ### 21 August 21 - A Sinai pinball with infinite horizon ### **Program:** Variant of `particle_billiard.c` **Initial condition in function `animation()`:** `init_drop_config(-1.4, 0.0, -0.5*PID, 0.5*PID, 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 21 /* choice of domain shape */ #define CIRCLE_PATTERN 2 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 30 /* number of circles in x direction */ #define NCY 20 /* number of circles in y direction */ #define LAMBDA 1.7 /* parameter controlling shape of domain */ #define MU 0.028 /* 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 DRAW_BILLIARD 1 /* set to 1 to draw billiard */ #define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ #define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ #define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ #define DEBUG 0 /* draw trajectories, for debugging purposes */ /* Simulation parameters */ #define NPART 1 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ #define 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 NSTEPS 11725 /* number of frames of movie */ #define TIME 1400 /* time between movie frames, for fluidity of real-time simulation */ #define DPHI 0.00004 /* 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 NCOLORS 256 /* 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 0.045 /* 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 ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */ #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 1000 /* final sleeping time */ #define END_FRAMES 100 /* number of still frames at end of movie */ ``` ### 20 August 21 - A wave protection alternating square and triangular grids ### **Program:** `wave_billiard.c` **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.015, 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 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 12 /* 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 LAMBDA 0.85 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 16 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.002 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.01 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMAB 1.0e-6 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 3000 /* number of frames of movie */ #define NVID 20 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 250 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 #define PLOT_B 1 /* plot type for second movie */ /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ #define SLOPE 1.5 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2000.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ /* For debugging purposes only */ #define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ #define VMAX 10.0 /* max value of wave amplitude */ ``` ### 19 August 21 - How a parabolic antenna works ### **Program:** `wave_billiard.c` **Initial condition in function `animation()`:** `` ``` #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 720 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 720 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #define XMIN -0.625 #define XMAX 1.625 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ #define JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 18 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 12 /* 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 LAMBDA 0.25 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 16 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.002 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.01 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMAB 1.0e-6 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 2 /* Parameters for length and speed of simulation */ #define NSTEPS 1400 /* number of frames of movie */ #define NVID 25 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 0 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard boundary */ #define PAUSE 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 1 #define PLOT_B 1 /* plot type for second movie */ /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 500.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ /* 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 */ ``` ### 18 August 21 - An pinball Ehrenfest model ### **Program:** Variant of `particle_billiard.c` **Initial condition in function `animation()`:** `init_drop_config(-1.4, 0.0, -0.5*PID, 0.5*PID, 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 21 /* choice of domain shape */ #define CIRCLE_PATTERN 1 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 9 /* number of circles in x direction */ #define NCY 20 /* number of circles in y direction */ #define LAMBDA 1.8 /* parameter controlling shape of domain */ #define MU 0.04 /* 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 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 NSTEPS 3500 /* number of frames of movie */ #define TIME 1500 /* 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 NCOLORS 50 /* 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 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 PAUSE 1000 /* number of frames after which to pause */ #define PSLEEP 1 /* sleep time during pause */ #define SLEEP1 1 /* initial sleeping time */ #define SLEEP2 1000 /* final sleeping time */ ``` ### 17 August 21 - Wave protection comparison 6: randomized square grid vs Sierpinski carpet ### **Program:** `wave_comparison.c` (variant of `wave_billiard.c`) **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.015, 0.0, phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #define XMIN -1.8 #define XMAX 1.8 /* x interval */ #define YMIN -1.0125 #define YMAX 1.0125 /* y interval for 9/16 aspect ratio */ #define JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define B_DOMAIN_B 15 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 2 /* pattern of circles, see list in global_pdes.c */ #define CIRCLE_PATTERN_B 10 /* 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 LAMBDA 0.8 /* parameter controlling the dimensions of domain */ #define MU 0.0346 /* parameter controlling the dimensions of domain */ #define MUB 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 20 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.0035 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.0075 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMAB 1.0e-5 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 4500 /* number of frames of movie */ #define NVID 25 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 200 /* time after which to start saving frames */ #define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 1 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ #define SLOPE 1.5 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2000.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ /* 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 */ ``` ### 16 August 21 - Long-wavelength waves gradually destroying a randomized square grid of obstacles ### **Program:** `mangrove.c` (variant of `wave_billiard.c`) **Initial condition in function `animation()`:** `init_wave_flat(phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 2 /* pattern of circles, 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 LAMBDA 0.75 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define X_SHIFT -0.8 /* x range on which to apply OSCILLATE_TOPBOT */ #define OMEGA 0.0004 /* frequency of periodic excitation */ #define K_BC 3.0 /* spatial period of periodic excitation in y direction */ #define KX_BC 6.0 /* spatial period of periodic excitation in x direction */ #define KY_BC 2.0 /* spatial period of periodic excitation in y direction */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.005 /* Courant number in medium B */ #define GAMMA 5.0e-8 /* damping factor in wave equation */ #define GAMMAB 1.0e-5 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 3300 /* number of frames of movie */ #define NVID 40 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 125 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2500.0 /* scaling factor for energy representation */ #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 */ /* mangrove colors */ #define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */ #define MANGROVE_HUE_MAX 0.0 /* color of saturated mangrove */ #define MANGROVE_EMAX 1.0e-3 /* max energy for mangrove to survive */ // #define MANGROVE_EMAX 1.0e-4 /* max energy for mangrove to survive */ /* 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 */ ``` ### 15 August 21 - How permeable is a pinball? Particles shot at various arrangements of circles ### **Program:** Variant of `particle_billiard.c` **Initial condition in function `animation()`:** `init_drop_config(-1.25, 0.0, -0.1, 0.1, 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 20 /* choice of domain shape */ #define CIRCLE_PATTERN 3 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 15 /* number of circles in x direction */ #define NCY 20 /* number of circles in y direction */ #define LAMBDA 0.8 /* parameter controlling shape of domain */ #define MU 0.03 /* 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 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 500 /* 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 NSTEPS 1000 /* number of frames of movie */ #define TIME 1500 /* 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 NCOLORS 10 /* 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 0.02 /* 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 PAUSE 1000 /* number of frames after which to pause */ #define PSLEEP 1 /* sleep time during pause */ #define SLEEP1 1 /* initial sleeping time */ #define SLEEP2 1000 /* final sleeping time */ ``` ### 14 August 21 - A "golden spiral" wave protection ### **Program:** `wave_billiard.c` **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.015, 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 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 11 /* 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 LAMBDA 0.85 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.002 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.01 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMAB 1.0e-6 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 3500 /* number of frames of movie */ #define NVID 25 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 200 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 #define PLOT_B 1 /* plot type for second movie */ /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2000.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ /* 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 August 21 - Collapse of a triangle lattice wave protection under waves arriving at an angle ### **Program:** `mangrove.c` (variant of `wave_billiard.c`) **Initial condition in function `animation()`:** `init_wave_flat(phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 1 /* pattern of circles, 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 LAMBDA 0.75 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define X_SHIFT -0.8 /* x range on which to apply OSCILLATE_TOPBOT */ #define OMEGA 0.002 /* frequency of periodic excitation */ #define K_BC 3.0 /* spatial period of periodic excitation in y direction */ #define KX_BC 30.0 /* spatial period of periodic excitation in x direction */ #define KY_BC 10.0 /* spatial period of periodic excitation in y direction */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.00666 /* Courant number in medium B */ #define GAMMA 5.0e-8 /* damping factor in wave equation */ #define GAMMAB 1.0e-5 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 6000 /* number of frames of movie */ #define NVID 20 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 250 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2500.0 /* scaling factor for energy representation */ #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 */ /* mangrove colors */ #define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */ #define MANGROVE_HUE_MAX 0.0 /* color of saturated mangrove */ #define MANGROVE_EMAX 2.0e-3 /* max energy for mangrove to survive */ /* 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 */ ``` ### 12 August 21 - Let’s play (frictionless) pinball! ### **Program:** Variant of `particle_billiard.c` **Initial condition in function `animation()`:** `init_drop_config(-0.9, 0.0, 0.117, 1.0, configs);` ``` #define MOVIE 1 /* set to 1 to generate movie */ #define WINWIDTH 720 /* window width */ #define WINHEIGHT 720 /* window height */ #define XMIN -1.125 #define XMAX 1.125 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ #define 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 21 /* choice of domain shape */ #define CIRCLE_PATTERN 3 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 9 /* number of circles in x direction */ #define NCY 20 /* number of circles in y direction */ #define LAMBDA 1.0 /* parameter controlling shape of domain */ #define MU 0.04 /* 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 DRAW_BILLIARD 1 /* set to 1 to draw billiard */ #define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ #define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ #define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ #define DEBUG 0 /* draw trajectories, for debugging purposes */ /* Simulation parameters */ #define NPART 1 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ #define 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 NSTEPS 1150 /* number of frames of movie */ #define TIME 4000 /* 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 NCOLORS 400 /* 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 0.05 /* 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 PAUSE 1000 /* number of frames after which to pause */ #define PSLEEP 1 /* sleep time during pause */ #define SLEEP1 1 /* initial sleeping time */ #define SLEEP2 1000 /* final sleeping time */ ``` ### 11 August 21 - Wave protection comparison 5: Triangular vs "golden mean" lattice ### **Program:** `wave_comparison.c` (variant of `wave_billiard.c`) **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.00, 0.0, phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN_A 20 /* choice of domain shape, see list in global_pdes.c */ #define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN_A 1 /* pattern of circles, see list in global_pdes.c */ #define CIRCLE_PATTERN_B 10 /* 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 LAMBDA 0.8 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define MUB 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* 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 OMEGA 0.0035 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.0075 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 6000 /* number of frames of movie */ #define NVID 20 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 250 /* time after which to start saving frames */ #define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */ #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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 1 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 1500.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ ``` ### 10 August 21 - Collapse of a "golden mean" wave protection under continuous incoming waves ### **Program:** `mangrove.c` (variant of `wave_billiard.c`) **Initial condition in function `animation()`:** `init_wave_flat(phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 10 /* 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 LAMBDA 0.75 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.002 /* frequency of periodic excitation */ #define K_BC 0.0 /* spatial period of periodic excitation in y direction */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.015 /* Courant number in medium B */ #define GAMMA 5.0e-8 /* damping factor in wave equation */ #define GAMMAB 1.0e-5 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 5500 /* number of frames of movie */ #define NVID 20 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 250 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2500.0 /* scaling factor for energy representation */ #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 */ /* mangrove colors */ #define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */ #define MANGROVE_HUE_MAX 0.0 /* color of saturated mangrove */ #define MANGROVE_EMAX 1.2e-3 /* max energy for mangrove to survive */ /* 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 */ ``` ### 9 August 21 - Comparison between a cloaking device and a simple refracting layer ### **Program:** `wave_comparison.c` (variant of `wave_billiard.c`) **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.00, 0.0, phi, psi, xy_in);` **Parameters in function `init_planar_wave()`:** `if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.002*exp(-dist2/0.0005)*cos(-sqrt(dist2)/0.025);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #define XMIN -0.5 #define XMAX 3.5 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ #define JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN_A 20 /* choice of domain shape, see list in global_pdes.c */ #define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN_A 6 /* pattern of circles, see list in global_pdes.c */ #define CIRCLE_PATTERN_B 98 /* 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 LAMBDA 0.12 /* parameter controlling the dimensions of domain */ #define MU 0.1 /* parameter controlling the dimensions of domain */ #define MUB 0.1 /* parameter controlling the dimensions of domain in lower panel */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 3 /* number of grid point for grid of disks */ #define NGRIDY 3 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ #define OMEGA 0.0035 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.0075 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMA_SIDES 0.0 /* damping factor on boundary */ #define GAMMA_TOPBOT 0.0 /* damping factor on boundary */ #define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ #define KAPPA_SIDES 0.0 /* "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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 0 /* Parameters for length and speed of simulation */ #define NSTEPS 1600 /* number of frames of movie */ #define NVID 20 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 30 /* time after which to start saving frames */ #define COMPUTE_ENERGIES 0 /* set to 1 to compute and print energies */ #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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 1.4 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 750.0 /* scaling factor for energy representation */ #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 130.0 /* mean value of hue for color scheme C_HUE */ #define HUEAMP -130.0 /* amplitude of variation of hue for color scheme C_HUE */ ``` ### 8 August 21 - Avoiding a laser in a hexagon with teleporting walls ### **Program:** Variant of `particle_billiard.c` (to be published later on) **Initial condition in function `animation()`:** `init_drop_config(x_shooter, y_shooter, 0.0, DPI, configs);` ``` #define MOVIE 1 /* set to 1 to generate movie */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define XMIN -1.3 #define XMAX 2.7 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ #define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ /* Choice of the billiard table, see global_particles.c */ #define B_DOMAIN 22 /* choice of domain shape */ #define CIRCLE_PATTERN 12 /* pattern of circles */ #define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 15 /* number of circles in x direction */ #define NCY 20 /* number of circles in y direction */ #define LAMBDA 1.0 /* parameter controlling shape of billiard */ #define MU 0.015 /* 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 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 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 5000 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ #define LMAX 0.01 /* minimal segment length triggering resampling */ #define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ #define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ #define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ #define SHOWZOOM 1 /* set to 1 to show a zoom (for laser in room of mirrors) */ #define PRINT_PARTICLE_NUMBER 1 /* set to 1 to print number of non-absorbed particles */ #define NSTEPS 9500 /* number of frames of movie */ #define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ #define DPHI 0.000005 /* 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 NCOLORS 12 /* 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 0.02 /* length of velocity vectors */ #define BILLIARD_WIDTH 6 /* 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 PAUSE 1000 /* number of frames after which to pause */ #define PSLEEP 1 /* sleep time during pause */ #define SLEEP1 1 /* initial sleeping time */ #define SLEEP2 1000 /* final sleeping time */ ``` ### 7 August 21 - Wave protection comparison 4: randomized square grid vs Poisson process ### **Program:** `wave_comparison.c` (variant of `wave_billiard.c`) **Initial condition in function `animation()`:** `nit_planar_wave(XMIN + 0.01, 0.0, phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN_A 20 /* choice of domain shape, see list in global_pdes.c */ #define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN_A 2 /* pattern of circles, see list in global_pdes.c */ #define CIRCLE_PATTERN_B 4 /* 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 LAMBDA 0.85 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* 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 OMEGA 0.9 /* frequency of periodic excitation */ #define COURANT 0.01 /* Courant number */ #define COURANTB 0.0075 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 5500 /* number of frames of movie */ #define NVID 40 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 250 /* time after which to start saving frames */ #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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 1 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 750.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ ``` ### 6 August 21 - A wave protection based on the golden mean ### **Program:** `wave_billiard.c` **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.01, 0.0, phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ /* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */ /* but will multiply run time by 4 */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 10 /* 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 LAMBDA 0.75 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* 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 OMEGA 0.9 /* frequency of periodic excitation */ #define COURANT 0.01 /* Courant number */ #define COURANTB 0.0075 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 4500 /* number of frames of movie */ #define NVID 40 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 250 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 2 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 750.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ ``` ### 5 August 21 - Reflecting stoppers won't protect you in a laser fight ### **Program:** Variant of `particle_billiard.c` (to be published later on) **Initial condition in function `animation()`:** `init_drop_config(x_shooter, y_shooter, 0.0, DPI, configs);` ``` #define MOVIE 1 /* set to 1 to generate movie */ #define WINWIDTH 720 /* window width */ #define WINHEIGHT 720 /* window height */ #define XMIN -1.125 #define XMAX 1.125 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ #define 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 21 /* choice of domain shape */ #define CIRCLE_PATTERN 11 /* pattern of circles */ #define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 15 /* number of circles in x direction */ #define NCY 20 /* number of circles in y direction */ #define LAMBDA 1.0 /* parameter controlling shape of billiard */ #define MU 0.015 /* second parameter controlling shape of billiard */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NPOLY 8 /* number of sides of polygon */ #define APOLY 0.25 /* 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 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 5000 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ #define LMAX 0.01 /* minimal segment length triggering resampling */ #define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ #define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ #define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ #define SHOWZOOM 0 /* set to 1 to show a zoom (for laser in room of mirrors) */ #define NSTEPS 1350 /* number of frames of movie */ #define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ #define DPHI 0.000005 /* 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 NCOLORS 32 /* 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 0.02 /* length of velocity vectors */ #define BILLIARD_WIDTH 6 /* 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 PAUSE 1000 /* number of frames after which to pause */ #define PSLEEP 1 /* sleep time during pause */ #define SLEEP1 1 /* initial sleeping time */ #define SLEEP2 1000 /* final sleeping time */ ``` ### 4 August 21 - Refraction of a wave on a horizontal ellipse ### **Program:** `wave_billiard.c` **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.01, 0.0, phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 1 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 6 /* 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 LAMBDA 1.5 /* parameter controlling the dimensions of domain */ #define MU 0.005 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* 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 OMEGA 0.9 /* frequency of periodic excitation */ #define COURANT 0.0075 /* Courant number in medium B */ #define COURANTB 0.01 /* Courant number */ #define GAMMA 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 2 /* Parameters for length and speed of simulation */ #define NSTEPS 4500 /* number of frames of movie */ #define NVID 40 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 100 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 1 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 750.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ ``` ### 3 August 21 - Wave protection comparison 3: regular vs random square grid ### **Program:** `wave_comparison.c` (variant of `wave_billiard.c`) **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.01, 0.0, phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ /* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */ /* but will multiply run time by 4 */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN_A 20 /* choice of domain shape, see list in global_pdes.c */ #define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN_A 0 /* pattern of circles, see list in global_pdes.c */ #define CIRCLE_PATTERN_B 2 /* 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 LAMBDA 0.75 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* 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 OMEGA 0.9 /* frequency of periodic excitation */ #define COURANT 0.01 /* Courant number */ #define COURANTB 0.0075 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 3000 /* number of frames of movie */ #define NVID 40 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 250 /* time after which to start saving frames */ #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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 1 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 750.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ ``` ### 2 August 21 - Avoiding a laser in a room of mirrors, long version with close-up and particle counter ### **Program:** Variant of `particle_billiard.c` (to be published later on) **Initial condition in function `animation()`:** `init_drop_config(x_shooter, y_shooter, 0.0, DPI, configs);` ``` #define MOVIE 1 /* set to 1 to generate movie */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define XMIN -1.3 #define XMAX 2.7 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ #define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ /* Choice of the billiard table, see global_particles.c */ #define B_DOMAIN 21 /* choice of domain shape */ #define CIRCLE_PATTERN 11 /* pattern of circles */ #define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ #define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */ #define NCX 15 /* number of circles in x direction */ #define NCY 20 /* number of circles in y direction */ #define LAMBDA 1.0 /* parameter controlling shape of billiard */ #define MU 0.015 /* second parameter controlling shape of billiard */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NPOLY 8 /* number of sides of polygon */ #define APOLY 0.25 /* 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 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 5000 /* number of particles */ #define NPARTMAX 100000 /* maximal number of particles after resampling */ #define LMAX 0.01 /* minimal segment length triggering resampling */ #define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ #define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ #define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ #define SHOWZOOM 1 /* set to 1 to show a zoom (for laser in room of mirrors) */ #define NSTEPS 8000 /* number of frames of movie */ #define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ #define DPHI 0.000005 /* 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 NCOLORS 32 /* 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 0.02 /* length of velocity vectors */ #define BILLIARD_WIDTH 6 /* 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 PAUSE 1000 /* number of frames after which to pause */ #define PSLEEP 1 /* sleep time during pause */ #define SLEEP1 1 /* initial sleeping time */ #define SLEEP2 1000 /* final sleeping time */ ``` ### 1 August 21 - A cloaking device, optimized version with longer wavelength ### **Program:** `wave_billiard.c` **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.00, 0.0, phi, psi, xy_in);` **Parameters in `init_planar_wave()`**: `if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.01*exp(-dist2/0.05)*cos(-sqrt(dist2)/0.025);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #define XMIN -1.0 #define XMAX 3.0 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ #define JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 6 /* 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 LAMBDA 0.2 /* parameter controlling the dimensions of domain */ #define MU 0.005 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* 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 OMEGA 0.9 /* frequency of periodic excitation */ #define COURANT 0.01 /* Courant number */ #define COURANTB 0.0075 /* Courant number in medium B */ #define GAMMA 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 2 /* Parameters for length and speed of simulation */ #define NSTEPS 3500 /* number of frames of movie */ #define NVID 40 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 30 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 1 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 750.0 /* scaling factor for energy representation */ #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 -220.0 /* amplitude of variation of hue for color scheme C_HUE */ ``` ### Unpublished - Continuously oscillating plane waves hitting a "golden mean" wave protection ### **Program:** `wave_billiard.c` **Initial condition in function `animation()`:** `init_wave_flat(phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #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 JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 10 /* 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 LAMBDA 0.75 /* parameter controlling the dimensions of domain */ #define MU 0.03 /* parameter controlling the dimensions of domain */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.002 /* frequency of periodic excitation */ #define AMPLITUDE 1.0 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ #define COURANTB 0.01 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMAB 1.0e-6 /* damping factor in wave equation */ #define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ #define GAMMA_TOPBOT 1.0e-6 /* 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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 3 /* Parameters for length and speed of simulation */ #define NSTEPS 5000 /* number of frames of movie */ #define NVID 20 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 250 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard 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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */ #define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ #define SLOPE 2.0 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 2500.0 /* scaling factor for energy representation */ #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 */ ``` ### Unpublished - Cloaking device comparison with longer wavelength ### **Program:** `wave_comparison.c` (variant of `wave_billiard.c`) **Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.00, 0.0, phi, psi, xy_in);` ``` #define MOVIE 1 /* set to 1 to generate movie */ /* General geometrical parameters */ #define WINWIDTH 1280 /* window width */ #define WINHEIGHT 720 /* window height */ #define NX 1280 /* number of grid points on x axis */ #define NY 720 /* number of grid points on y axis */ #define XMIN -0.5 #define XMAX 3.5 /* x interval */ #define YMIN -1.125 #define YMAX 1.125 /* y interval for 9/16 aspect ratio */ #define JULIA_SCALE 1.0 /* scaling for Julia sets */ /* Choice of the billiard table */ #define B_DOMAIN 20 /* choice of top domain shape, see list in global_pdes.c */ #define B_DOMAIN_B 20 /* choice of bottom domain shape, see list in global_pdes.c */ #define CIRCLE_PATTERN 6 /* top pattern of circles, see list in global_pdes.c */ #define CIRCLE_PATTERN_B 98 /* bottom 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 LAMBDA 0.12 /* parameter controlling the dimensions of domain */ #define MU 0.1 /* parameter controlling the dimensions of domain */ #define MUB 0.1 /* parameter controlling the dimensions of domain in bottom panel */ #define NPOLY 3 /* number of sides of polygon */ #define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ #define MDEPTH 4 /* depth of computation of Menger gasket */ #define MRATIO 3 /* ratio defining Menger gasket */ #define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ #define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ #define FOCI 1 /* set to 1 to draw focal points of ellipse */ #define NGRIDX 15 /* number of grid point for grid of disks */ #define NGRIDY 20 /* number of grid point for grid of disks */ /* You can add more billiard tables by adapting the functions */ /* xy_in_billiard and draw_billiard below */ /* Physical parameters of wave equation */ #define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ #define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ #define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */ #define OMEGA 0.0035 /* frequency of periodic excitation */ #define AMPLITUDE 1.5 /* amplitude of periodic excitation */ #define COURANT 0.02 /* Courant number */ // #define COURANT 0.01 /* Courant number */ #define COURANTB 0.0075 /* Courant number in medium B */ #define GAMMA 0.0 /* damping factor in wave equation */ #define GAMMA_SIDES 0.0 /* damping factor on boundary */ #define GAMMA_TOPBOT 0.0 /* damping factor on boundary */ #define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ #define KAPPA_SIDES 0.0 /* "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 */ /* Boundary conditions, see list in global_pdes.c */ #define B_COND 0 /* Parameters for length and speed of simulation */ #define NSTEPS 1600 /* number of frames of movie */ #define NVID 20 /* number of iterations between images displayed on screen */ // #define NVID 40 /* number of iterations between images displayed on screen */ #define NSEG 100 /* number of segments of boundary */ #define INITIAL_TIME 25 /* time after which to start saving frames */ #define BOUNDARY_WIDTH 2 /* width of billiard boundary */ #define COMPUTE_ENERGIES 0 /* set to 1 to compute and print energies */ #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 */ /* Plot type, see list in global_pdes.c */ #define PLOT 0 /* Color schemes */ #define BLACK 1 /* background */ #define COLOR_SCHEME 1 /* 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 1.4 /* sensitivity of color on wave amplitude */ #define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ #define E_SCALE 750.0 /* scaling factor for energy representation */ #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 130.0 /* mean value of hue for color scheme C_HUE */ #define HUEAMP -130.0 /* amplitude of variation of hue for color scheme C_HUE */ ```