From 3e1b198ed13413ee5b099986993f63958968f284 Mon Sep 17 00:00:00 2001 From: nilsberglund-orleans <83530463+nilsberglund-orleans@users.noreply.github.com> Date: Sat, 5 Feb 2022 18:45:19 +0100 Subject: [PATCH] Add files via upload --- Parameters_December21.md | 4495 +++++++++++++++++++++++++++++++++ Parameters_January22.md | 5082 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 9577 insertions(+) create mode 100644 Parameters_December21.md create mode 100644 Parameters_January22.md diff --git a/Parameters_December21.md b/Parameters_December21.md new file mode 100644 index 0000000..2c306a2 --- /dev/null +++ b/Parameters_December21.md @@ -0,0 +1,4495 @@ +### Parameter values for YouTube simulations ### + +Created by **Nils Berglund** and optimized by **Marco Mancini** + +C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund + +Below are parameter values used for different simulations, as well as initial conditions used in +function animation. Some simulations use variants of the published code. The list is going to be +updated gradually. + + + +### 31 December 21 - Four waves in a nine-pointed star ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** + +``` + init_circular_wave(0.0, 0.0, phi, psi, xy_in); + for (i=0; i<3; i++) + { + add_circular_wave(-1.0, 0.6*cos(PID + (double)(i)*DPI/3.0), 0.6*sin(PID + (double)(i)*DPI/3.0), phi, psi, xy_in); + } +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 42 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 20 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.4 /* parameter controlling the dimensions of domain */ +#define NPOLY 18 /* number of sides of polygon */ +#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 4250 /* 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 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 5 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.125 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 16.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 24.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 30 December 21 - Molecular Tetris: interface growth with anisotropic interaction ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -0.8 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 2 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 26 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3850 /* number of frames of movie */ +#define NVID 250 /* 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 */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 1.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 3.5 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 5.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ +#define GRAVITY 100.0 /* gravity acting on all particles */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 2.0e2 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.5 /* number of temperature oscillations in BETA schedule */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 300 /* time at which to add first particle */ +#define ADD_PERIOD 2000 /* time interval between adding further particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 December 21 - Waves escaping a ring of triangular obstacles ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ + +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 20 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.04 /* 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-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 2500 /* number of frames of movie */ +#define NVID 15 /* 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 + +#define PLOT_B 0 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 4.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 2.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 28 December 21 - Let it snow: interface growth with molecular dynamics ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -0.8 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 26 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3600 /* number of frames of movie */ +#define NVID 250 /* 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 */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 1.0e-2 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ +#define GRAVITY 300.0 /* gravity acting on all particles */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e1 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.25 /* number of temperature oscillations in BETA schedule */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 1 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 1 /* set to 1 to add particles */ +#define ADD_TIME 50 /* time at which to add first particle */ +#define ADD_PERIOD 7 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 27 December 21 - Molecular dynamics with pentagonal symmetry, a representation with atomic bonds ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +/* Choice of the billiard table */ + +// #define B_DOMAIN 20 /* choice of domain shape, see list in global_ljones.c */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 3 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 2.5 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.02 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 26 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3600 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 3 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 20.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 5.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e2 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 300 /* time at which to add first particle */ +#define ADD_PERIOD 2000 /* time interval between adding further particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 26 December 21 - Wave protection comparison 12: Triangles pointing right vs randomly rotated triangles ### + +**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 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ + +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ +#define YMID 500 /* mid point of display */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.0729 +#define YMAX 1.0729 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN_B 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_pdes.c */ +#define CIRCLE_PATTERN_B 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 RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ +#define RANDOM_POLY_ANGLE_B 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.04665361 /* parameter controlling the dimensions of domain */ +#define MUB 0.04665361 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define APOLY_B 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 20 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 0.0 /* 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 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 150 /* 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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 4 + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 2000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ + +#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 */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 100.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + + +/* 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 */ + +``` + + +### 25 December 21 - Mystery billiard 12 ### + +**Program:** `mystery_billiard.c` (variant of `particle_billiard.c`) + +**Initial condition in function `animation()`:** `init_drop_config(0.0, -0.7, -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 30 /* choice of domain shape */ + +#define CIRCLE_PATTERN 1 /* pattern of circles */ +#define POLYLINE_PATTERN 7 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 10000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 10000 /* total number of sides of polygonal line */ +#define NCX 30 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 4 /* Sierpinski gastket depth */ + +#define LAMBDA 1.8 /* parameter controlling shape of domain */ +#define MU 0.01 /* second parameter controlling shape of billiard */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define DRAW_BILLIARD 0 /* 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 2000 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ + +#define NSTEPS 4825 /* number of frames of movie */ +#define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.0000075 /* integration step */ +#define NVID 250 /* number of iterations between images displayed on screen */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 16 /* 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 0.025 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 2 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 0 /* set to 1 to paint exterior */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1000 /* final sleeping time */ +#define FINALFRAMES 100 /* number of still frames at the end */ + +``` + +### 24 December 21 - Waves in a seven-pointed star ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1030 /* window height */ + +#define NX 1920 /* number of grid points on x axis */ +#define NY 1030 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.0329 +#define YMAX 1.1129 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 42 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 2 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.1 /* parameter controlling the dimensions of domain */ +#define MU 0.4 /* parameter controlling the dimensions of domain */ +#define NPOLY 14 /* number of sides of polygon */ +#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.04 /* 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-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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2100 /* 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 3 /* 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 + +#define PLOT_B 0 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 12 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 6.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 10.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 23 December 21 - Freezing and melting at the molecular scale: A representation with atomic bonds ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +/* Choice of the billiard table */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.25 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 26 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 5500 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 3 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 100.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 5.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e2 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 4.5 /* number of temperature oscillations in BETA schedule */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 300 /* time at which to add first particle */ +#define ADD_PERIOD 2000 /* time interval between adding further particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 December 21 - An attempt at growing a quasicrystal ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 3 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 2.5 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.02 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 26 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 4800 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 20.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 2.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.5 /* number of temperature oscillations in BETA schedule */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 300 /* time at which to add first particle */ +#define ADD_PERIOD 2000 /* time interval between adding further particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 21 December 21 - Trajectory of a single particle in an unilluminable room without right angles ### + +**Program:** `particle_billiard.c` + +**Initial condition in function `animation()`:** +``` + alphamax = 2.50949; + init_drop_config(x_shooter, y_shooter, alphamax, alphamax + 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 30 /* choice of domain shape */ + +#define CIRCLE_PATTERN 1 /* pattern of circles */ +#define POLYLINE_PATTERN 6 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 100000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 100000 /* total number of sides of polygonal line */ +#define NCX 30 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 1 /* Sierpinski gastket depth */ + +#define LAMBDA 0.8 /* parameter controlling shape of domain */ +#define MU 0.0025 /* 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 SHOWZOOM 1 /* set to 1 to show zoom on specific area */ +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */ +#define PRINT_COLLISION_NUMBER 1 /* set to 1 to print number of collisions */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ + +#define NSTEPS 9000 /* 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 300 /* number of iterations between images displayed on screen */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 32 /* 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 0.015 /* 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 PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1000 /* final sleeping time */ + +``` + +### 20 December 21 - Freezing and melting of particles with anisotropic Lennard-Jones interaction ### + +**Program:** `lennardjones.c` + + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +/* Choice of the billiard table */ + +// #define B_DOMAIN 20 /* choice of domain shape, see list in global_ljones.c */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 2 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.5 /* minimal distance in Poisson disc process */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling 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 32 /* number of grid point for grid of disks */ +#define NGRIDY 26 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2775 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 1.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e2 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2 /* number of temperature oscillations in BETA schedule */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 300 /* time at which to add first particle */ +#define ADD_PERIOD 2000 /* time interval between adding further particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 19 December 21 - Wave protection comparison 11: triangles on a triangular grid vs triangles on a square grid ### + +**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 1920 /* window width */ +#define WINHEIGHT 1030 /* window height */ + +#define NX 1920 /* number of grid points on x axis */ +#define NY 1030 /* number of grid points on y axis */ +#define YMID 500 /* mid point of display */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.0729 +#define YMAX 1.0729 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN_B 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 0 /* pattern of circles, see list in global_pdes.c */ +#define CIRCLE_PATTERN_B 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 RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.04665361 /* parameter controlling the dimensions of domain */ +#define MUB 0.04665361 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define APOLY_B 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 20 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 0.0 /* 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 2500 /* 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 150 /* 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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 4 + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 2000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ + +#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 */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 100.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + + +/* 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 */ + +``` + +### 18 December 21 - Grain boundary dynamics under temperature cycling in a system with Lennard-Jones interaction ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define 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_ljones.c */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +// #define NSTEPS 4000 /* number of frames of movie */ +#define NSTEPS 6500 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 2500.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.0 /* scaling factor for energy log 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 */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 100.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 5.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e2 /* factor by which to change BETA during simulation */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e18 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 17 December 21 - Video #300: Waves in a star-shaped domain ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1080 /* window height */ + +#define NX 1920 /* number of grid points on x axis */ +#define NY 1080 /* 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 42 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 2 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.025 /* parameter controlling the dimensions of domain */ +#define NPOLY 128 /* number of sides of polygon */ +#define APOLY 0.33333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.04 /* 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-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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3450 /* 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 6.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 10.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + + +### 16 December 21 - Waves in a unilluminable room without right angles ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(polyline[85].x, polyline[85].y, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 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 36 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 2 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.2 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.33333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3750 /* 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 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 5 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 250.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 6.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 10.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + + +### 15 December 21 - Inserting an atom in a crystal ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#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 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_ljones.c */ + +#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.025 /* 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 32 /* number of grid point for grid of disks */ +#define NGRIDY 26 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1300 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 50.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 2.0e-1 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e2 /* factor by which to change BETA during simulation */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define ADD_PARTICLES 1 /* set to 1 to add particles */ +#define ADD_TIME 300 /* time at which to add first particle */ +#define ADD_PERIOD 2000 /* time interval between adding further particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 14 December 21 - 6 out of phase waves in a von Koch snowflake fractal ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** + +``` + init_circular_wave(0.7, 0.0, phi, psi, xy_in); + sign = 1.0; + for (i=1; i<6; i++) + { + sign = - sign; + add_circular_wave(sign, 0.7*cos((double)(2*i)*PI/6.0), 0.7*sin((double)(2*i)*PI/6.0), phi, psi, xy_in); + } +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 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 41 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 2 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.2 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.33333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 4500 /* 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 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 4 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.25 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.0 /* scaling factor for energy log 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 10.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 13 December 21 - Spreading of an epidemic: A spatial SIR model ### + +**Program:** `sir.c` (variant of `lennardjones.c`) + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +/* Choice of the billiard table */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.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 PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.025 /* 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 32 /* number of grid point for grid of disks */ +#define NGRIDY 26 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3500 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 2 + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 5.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 100.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 3.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define SIGMA 10.0 /* noise intensity in thermostat */ +#define BETA 3.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e2 /* factor by which to change BETA during simulation */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 300 /* time at which to add first particle */ +#define ADD_PERIOD 2000 /* time interval between adding further particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define P_PROTECTED 0.5 /* probability of being protected */ +#define CONTAMINATION_RADIUS 2.8 /* radius in which people can contiminate others */ +#define P_INFECTION 0.1 /* probability of getting infected */ +#define P_INFECTION_PROTECTED 0.01 /* probability of getting infected if protected */ +#define INFECTION_CHANGE 0.2 /* time change of infection */ +#define RECOVER_THRESHOLD 100.0 /* threshold for getting recovered */ + +#define HASHX 16 /* size of hashgrid in x direction */ +#define HASHY 9 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 December 21 - Advent, advent... Average energy in a von Koch snowflake (log scale) ### + +**Program:** `wave_billiard_vonKoch.c` (variant of `wave_billiard.c`) + +**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 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 41 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 2 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.2 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MAXDEPTH 5 /* max 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 1070 /* 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 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 25 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 5 + +#define PLOT_B 0 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 12 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 6.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 11 December 21 - Temperature cycling: Lennard-Jones interacting particles with oscillating temperature ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 640 /* number of grid points on x axis */ +#define NY 360 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#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 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.03 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 X_SHIFT -0.9 /* x range on which to apply OSCILLATE_TOPBOT */ + +#define OMEGA 0.00133333333 /* frequency of periodic excitation */ +#define K_BC 3.0 /* spatial period of periodic excitation in y direction */ +#define KX_BC 10.0 /* spatial period of periodic excitation in x direction */ +#define KY_BC 3.3333 /* 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 3.0e-6 /* damping factor in wave equation */ +#define GAMMAB 5.0e-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 5500 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.2 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ + +#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 LOG_SCALE 2.0 /* scaling factor for energy log 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 */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 50.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 2.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e18 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 10 December 21 - A polygonal unilluminable room without right angles ### + +**Program:** `particle_billiard.c` + +**Initial condition in function `animation()`:** `init_drop_config(x_shooter, y_shooter, 0.0, 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 30 /* choice of domain shape */ + +#define CIRCLE_PATTERN 1 /* pattern of circles */ +#define POLYLINE_PATTERN 6 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 100000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 100000 /* total number of sides of polygonal line */ +#define NCX 30 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 1 /* Sierpinski gastket depth */ + +#define LAMBDA 0.8 /* parameter controlling shape of domain */ +#define MU 0.007 /* 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 10000 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 1 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 1 /* set to 1 to show zoom on specific area */ +#define PRINT_PARTICLE_NUMBER 1 /* set to 1 to print number of particles */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ + +#define NSTEPS 2500 /* 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 COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 16 /* number of colors */ +#define COLORSHIFT 0 /* hue of initial color */ +#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */ +#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ +#define NSEG 100 /* number of segments of boundary */ +#define LENGTH 0.015 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 2 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1000 /* final sleeping time */ + +``` + +### 9 December 21 - Crystal formation in a Lennard-Jones interacting particle system with a thermostat ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 640 /* number of grid points on x axis */ +#define NY 360 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#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 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.03 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 X_SHIFT -0.9 /* x range on which to apply OSCILLATE_TOPBOT */ + +#define OMEGA 0.00133333333 /* frequency of periodic excitation */ +#define K_BC 3.0 /* spatial period of periodic excitation in y direction */ +#define KX_BC 10.0 /* spatial period of periodic excitation in x direction */ +#define KY_BC 3.3333 /* 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 3.0e-6 /* damping factor in wave equation */ +#define GAMMAB 5.0e-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 4000 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.2 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ + +#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 LOG_SCALE 2.0 /* scaling factor for energy log 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 */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 50.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 1.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e5 /* factor by which to change BETA during simulation */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e18 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 8 December 21 - Heavily peated: wave starting off center in a von Koch snowflake, average energy on log scale ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(0.6*cos(PI/6.0), 0.6*sin(PI/6.0), 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 41 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 2 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2500 /* 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 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 5 + +#define PLOT_B 4 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.0 /* scaling factor for energy log 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 7 December 21 - A lighthouse beam in a mirrored heptagon ### + +**Program:** `particle_trajectory.c` + +**Initial condition in function `animation()`:** +``` + time = (double)i/(double)(NSTEPS-1); + x = 0.0; + y = 0.0; + alpha = (DPI/(double)NPOLY)*time; +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ + +/* Choice of the billiard table, see global_particles.c */ + +#define B_DOMAIN 30 /* choice of domain shape */ + +#define CIRCLE_PATTERN 5 /* pattern of circles */ +#define POLYLINE_PATTERN 5 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 10000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 10000 /* total number of sides of polygonal line */ +#define NCX 9 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 4 /* Sierpinski gastket depth */ + +#define LAMBDA 1.0 /* parameter controlling shape of domain */ +#define MU 0.005 /* second parameter controlling shape of billiard */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NPOLY 7 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ +#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ + +#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ +#define DEBUG 0 /* draw trajectories, for debugging purposes */ + +/* Simulation parameters */ + +#define NPART 1 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define TRAJ_LENGTH 128 /* length of trajectory */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ +#define PRINT_TRAJECTORY_LENGTH 0 /* set to 1 to print length of trajectory 0 */ + +#define NSTEPS 4000 /* number of frames of movie */ +#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.00001 /* integration step */ +#define NVID 150 /* number of iterations between images displayed on screen */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 64 /* number of colors */ +#define COLORSHIFT 0 /* hue of initial color */ +#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ +#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ +#define NSEG 100 /* number of segments of boundary */ +#define LENGTH 0.03 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 2 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1000 /* final sleeping time */ +#define END_FRAMES 100 /* number of frames at end of movie */ + +``` + +### 6 December 21 - A crude model of seismic waves ### + +**Program:** `wave_diffraction.c` (variant of `wave_billiard.c`) + +**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.98, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 2560 /* number of grid points on x axis */ +#define NY 1440 /* 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 2 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.03 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2800 /* number of frames of movie */ +#define NVID 50 /* 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 + +#define PLOT_B 0 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 15 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 2.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 100.0 /* 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 5 December 21 - Grain boundary dynamics in a particle system with Lennard-Jones interaction of increasing strength ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 640 /* number of grid points on x axis */ +#define NY 360 Crack dynamics in a particle system with Lennard-Jones interaction of increasing constant /* 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 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.02 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 X_SHIFT -0.9 /* x range on which to apply OSCILLATE_TOPBOT */ + +#define OMEGA 0.00133333333 /* frequency of periodic excitation */ +#define K_BC 3.0 /* spatial period of periodic excitation in y direction */ +#define KX_BC 10.0 /* spatial period of periodic excitation in x direction */ +#define KY_BC 3.3333 /* 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 3.0e-6 /* damping factor in wave equation */ +#define GAMMAB 5.0e-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 3000 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.2 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ + +#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 */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.5e9 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-10 /* time step for particle displacement */ +#define KREPEL 50.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 15.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 5.0e5 /* initial velocity range */ + +#define INCREASE_KREPEL 1 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e18 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 4 December 21 - A lighthouse beam in a Tokarsky room ### + +**Program:** `particle_trajectory.c` + +**Initial condition in function `animation()`:** + +``` + time = (double)i/(double)(NSTEPS-1); + x = - 0.95; + y = 0.0; + alpha = PID*(0.5 + time); + compute_trajectories_xy(x, y, alpha, alpha + DPI, configs, trajectory, traj_length); +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ + +/* Choice of the billiard table, see global_particles.c */ + +#define B_DOMAIN 30 /* choice of domain shape */ + +#define CIRCLE_PATTERN 5 /* pattern of circles */ +#define POLYLINE_PATTERN 1 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 10000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 10000 /* total number of sides of polygonal line */ +#define NCX 9 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 4 /* Sierpinski gastket depth */ + +#define LAMBDA 1.0 /* parameter controlling shape of domain */ +#define MU 0.005 /* 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 TRAJ_LENGTH 256 /* length of trajectory */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 1 /* set to 1 to show zoom on specific area */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ +#define PRINT_TRAJECTORY_LENGTH 1 /* set to 1 to print length of trajectory 0 */ + +#define NSTEPS 13300 /* number of frames of movie */ +#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.00001 /* integration step */ +#define NVID 150 /* number of iterations between images displayed on screen */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 32 /* number of colors */ +#define COLORSHIFT 0 /* hue of initial color */ +#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */ +#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ +#define NSEG 100 /* number of segments of boundary */ +#define LENGTH 0.03 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 2 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1000 /* final sleeping time */ + +``` + +### 3 December 21 - Crystalline defect propagation in a system of particles with Lennard-Jones interaction ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 0 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 640 /* number of grid points on x axis */ +#define NY 360 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#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 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.02 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 X_SHIFT -0.9 /* x range on which to apply OSCILLATE_TOPBOT */ + +#define OMEGA 0.00133333333 /* frequency of periodic excitation */ +#define K_BC 3.0 /* spatial period of periodic excitation in y direction */ +#define KX_BC 10.0 /* spatial period of periodic excitation in x direction */ +#define KY_BC 3.3333 /* 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 3.0e-6 /* damping factor in wave equation */ +#define GAMMAB 5.0e-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 2000 /* number of frames of movie */ +#define NVID 150 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.2 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ + +#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 */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e9 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-10 /* time step for particle displacement */ +#define KREPEL 2.5e3 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 15.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 2.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 0.0e2 /* initial velocity range */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e18 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 2 December 21 - Wave protection comparison 10: Triangles pointing right vs triangles pointing left ### + +**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 40 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN_B 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 0 /* pattern of circles, see list in global_pdes.c */ +#define CIRCLE_PATTERN_B 0 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.04665361 /* parameter controlling the dimensions of domain */ +#define MUB 0.04665361 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define APOLY_B 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 20 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 0.0 /* 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 3750 /* 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 150 /* 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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define 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 */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 60.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + + +/* 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 */ + +``` + +### 1 December 21 - Crystal formation: particles interacting with a Lennard-Jones potential ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 640 /* number of grid points on x axis */ +#define NY 360 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#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 340 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 X_SHIFT -0.9 /* x range on which to apply OSCILLATE_TOPBOT */ + +#define OMEGA 0.00133333333 /* frequency of periodic excitation */ +#define K_BC 3.0 /* spatial period of periodic excitation in y direction */ +#define KX_BC 10.0 /* spatial period of periodic excitation in x direction */ +#define KY_BC 3.3333 /* 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 3.0e-6 /* damping factor in wave equation */ +#define GAMMAB 5.0e-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 1000 /* number of frames of movie */ +#define NVID 50 /* 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 END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.2 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* Color palette, see list in global_pdes.c */ + +#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 */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 180.0 /* color of original particle */ +#define PARTICLE_HUE_MAX -50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e12 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 0.0000000002 /* time step for particle displacement */ +#define KSPRING 0.05 /* spring constant of particles */ +#define KWAVE 4.0 /* constant in force due to wave gradient */ +#define KREPEL 1.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 2.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 4.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DXMAX 1000.0 /* max displacement of particle in one time step */ +#define FMAX 1.0e12 /* maximal force */ +#define L_DETACH 0.25 /* spring length beyond which particles detach */ +#define DAMPING 0.00000 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ + +#define HASHX 16 /* size of hashgrid in x direction */ +#define HASHY 9 /* size of hashgrid in y direction */ +#define HASHMAX 10 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + diff --git a/Parameters_January22.md b/Parameters_January22.md new file mode 100644 index 0000000..5f2fa77 --- /dev/null +++ b/Parameters_January22.md @@ -0,0 +1,5082 @@ +### Parameter values for YouTube simulations ### + +Created by **Nils Berglund** and optimized by **Marco Mancini** + +C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund + +Below are parameter values used for different simulations, as well as initial conditions used in +function animation. Some simulations use variants of the published code. The list is going to be +updated gradually. + + + +### 31 January 22 - Evaporation/sublimation of Lennard-Jones crystal under gravity ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 0.0 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 1.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.018 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 54 /* number of grid point for grid of disks */ +#define NGRIDY 15 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2700 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 50 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 5.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 1.0 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 5.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 200.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 7.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 5.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.001 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 200 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 500 /* time at which to add first particle */ +#define ADD_PERIOD 100 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e10 /* maximal force */ + +#define HASHX 20 /* size of hashgrid in x direction */ +#define HASHY 12 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 30 January 22 - Shock wave in a Lennard-Jones gas, seen from a moving frame of reference ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.014 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 350 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 500 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 4 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 6 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 3.0e3 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 5.0e-7 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.0005 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 5.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 3.5 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 7.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 5.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ +#define FINAL_CONSTANT_PHASE 300 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 1 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 1 /* set to 1 to center display on moving obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 500 /* time at which to add first particle */ +#define ADD_PERIOD 100 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e10 /* maximal force */ + +#define HASHX 20 /* size of hashgrid in x direction */ +#define HASHY 12 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 29 January 22 - Waves escaping a ring of randomly rotated triangles ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.037 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.03 /* Courant number */ +#define COURANTB 0.01 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-4 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2100 /* number of frames of movie */ +#define NVID 35 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 50 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 + +#define PLOT_B 0 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.4 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 2.0 /* shift of colors on log scale */ +#define RESCALE_COLOR_IN_CENTER 1 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 1.5 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* 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 */ + +``` + +### 28 January 22 - Colliding vortices for interacting pentagons on a torus ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 3 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 2.25 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1600 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 50 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 3 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 1.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 2.0e-3 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 3.5 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 7.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 5.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ +#define FINAL_CONSTANT_PHASE 300 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 500 /* time at which to add first particle */ +#define ADD_PERIOD 100 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 24 /* size of hashgrid in x direction */ +#define HASHY 14 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 27 January 22 - Wave protection comparison 15: left vs right-pointing triangles in a triangular grid ### + +**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 TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ +#define TIME_LAPSE_FACTOR 4 /* factor of time-lapse movie */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ +#define YMID 500 /* mid point of display */ +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN_B 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_pdes.c */ +#define CIRCLE_PATTERN_B 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 RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ +#define RANDOM_POLY_ANGLE_B 0 /* set to 1 to randomize angle of polygons */ + +#define XDEP_POLY_ANGLE 0 /* set to 1 to rotate polygons depending on x coordinate */ +#define XDEP_POLY_ANGLE_B 0 /* set to 1 to rotate polygons depending on x coordinate */ +#define POLY_ROTATION_ANGLE -0.645 /* rotation angle for |x|=1 in units of Pi/2 */ +#define HEX_NONUNIF_COMPRESSSION 0.2 /* compression factor for */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling the dimensions of domain */ +#define MUB 0.04 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define APOLY_B 2.0 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 0.0 /* 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 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 150 /* 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 100 /* 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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 4 + +/* Color schemes */ + +#define COLOR_PALETTE 18 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ +#define BLACK_TEXT 1 /* set to 1 to write text in black instead of white */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.25 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 2000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ + +#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 */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 30.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + + +/* 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 */ + +``` + +### 26 January 22 - Interacting dipoles on a torus ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 5 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 2.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 2.25 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 50 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +// #define BOUNDARY_COND 0 +#define BOUNDARY_COND 3 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 1.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 2.0e-3 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 3.5 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 7.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 5.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 500 /* time at which to add first particle */ +#define ADD_PERIOD 100 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 24 /* size of hashgrid in x direction */ +#define HASHY 14 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 25 January 22 - Spinodal decomposition in the Allen-Cahn equation without and with noise ### + +**Program:** `allencahn.c` + +**Initial condition in function `animation()`:** `init_random(0.0, 1.0, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 15 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.000004 +#define VISCOSITY 20.0 +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 2 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 1.0 /* noise intentisity */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3800 /* number of frames of movie */ +#define NVID 15 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 4.0 /* factor by which to increase NVID in course of simulation */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 25 /* initial still time */ + +/* 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 */ + +/* Field representation */ + +#define FIELD_REP 0 + +#define F_INTENSITY 0 /* color represents intensity */ +#define F_GRADIENT 1 /* color represents norm of gradient */ + +#define PRINT_TIME 1 /* set to 1 to print running time */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 2 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.99 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 1 /* set to 1 to draw color scheme horizontally */ + +``` + +### 24 January 22 - Interacting squares on a torus ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 2 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 4.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.25 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.02 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2200 /* number of frames of movie */ +#define NVID 50 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 3 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 1.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 6.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 1.0e-3 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 10.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 7.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e2 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 500 /* time at which to add first particle */ +#define ADD_PERIOD 100 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 24 /* size of hashgrid in x direction */ +#define HASHY 14 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 23 January 22 - Crystal formation with periodic boundary conditions ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.25 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.025 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 50 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 3 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 1.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 6.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 5.0 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 2.0e-3 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE -150.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 7.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 2.0e2 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 500 /* time at which to add first particle */ +#define ADD_PERIOD 100 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 24 /* size of hashgrid in x direction */ +#define HASHY 14 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 22 January 22 - Déjeuner en paix: an anechoic chamber ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(0.0, -0.5, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 44 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.1 /* parameter controlling the dimensions of domain */ +#define MU 0.3 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.03 /* Courant number */ +#define COURANTB 0.01 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-4 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1400 /* number of frames of movie */ +#define NVID 35 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 50 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 + +#define PLOT_B 5 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 2.0 /* shift of colors on log scale */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 4.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 2.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 21 January 22 - Two types of particles interacting with Lennard-Jones type potentials depending on the golden ratio ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.0 +#define INITYMAX 1.0 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 1 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 4 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 4.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2600 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 50 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 2.0 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.01 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.7 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE -150.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 7.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 500 /* time at which to add first particle */ +#define ADD_PERIOD 100 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 20 January 22 - Two Fresnel lenses facing each other ### + +**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 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 3840 /* number of grid points on x axis */ +#define NY 2000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 45 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.06 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.03 /* 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-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2200 /* number of frames of movie */ +#define NVID 35 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 50 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 1000.0 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 + +#define PLOT_B 0 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.15 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 2.0 /* shift of colors on log scale */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 19 January 22 - Symmetric pistons ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.8 +#define INITXMAX 1.8 /* x interval for initial condition */ +#define INITYMIN -1.05 +#define INITYMAX 0.95 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.666667 /* proportion of particles of first type */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 6 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#define MU_B 0.04472136 /* parameter controlling radius of particles of second type */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2800 /* number of frames of movie */ +#define NVID 350 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 1 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 3 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 20.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 4.2 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 2.0 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.025 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e8 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE -150.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 0 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 7.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e1 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.5 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 1 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 1 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 18 January 22 - Phase separation in the Allen-Cahn equation ### + +**Program:** `allencahn.c` + +**Initial condition in function `animation()`:** `init_random(0.0, 1.0, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 15 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.000004 +#define VISCOSITY 20.0 +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 25 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 3.0 /* factor by which to increase NVID in course of simulation */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 25 /* initial still time */ + +/* 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 */ + +/* Field representation */ + +#define FIELD_REP 0 + +#define F_INTENSITY 0 /* color represents intensity */ +#define F_GRADIENT 1 /* color represents norm of gradient */ + +#define PRINT_TIME 1 /* set to 1 to print running time */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.99 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 1 /* set to 1 to draw color scheme horizontally */ + +``` + +### 17 January 22 - Crunching a mixture of pentagons an lozenges ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 1 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.666667 /* proportion of particles of first type */ + +#define INTERACTION 3 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 6 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 2.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling radius of particles */ +#define MU_B 0.04472136 /* parameter controlling radius of particles of second type */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2600 /* number of frames of movie */ +#define NVID 50 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 1 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 5 +#define PLOT_B 4 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.2 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 4.2 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 200.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ +#define SIGMA 7.5 /* noise intensity in thermostat */ +#define BETA 0.01 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e10 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 3.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 0.5 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE -150.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 0 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 7.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e1 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.5 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 1 /* set to 1 to decrease size of container */ +#define COMPRESSION_RATIO 0.38 /* final size of container */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 16 January 22 - Waves escaping a sunflower spiral ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.037 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 2750 /* number of frames of movie */ +#define NVID 40 /* number of iterations between images displayed on screen */ +#define NSEG 200 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 50 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 2.0 /* shift of colors on log scale */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 15 January 22 - A mixture of pentagons and lozenges interacting with Lennard-Jones potentials ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 1 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.666667 /* proportion of particles of first type */ + +#define INTERACTION 3 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 6 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 1.7 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling radius of particles */ +#define MU_B 0.04472136 /* parameter controlling radius of particles of second type */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2250 /* number of frames of movie */ +#define NVID 50 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 5 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 1.0 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 1.0 /* moment of inertia of second type of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define SIGMA 7.5 /* noise intensity in thermostat */ +#define BETA 0.001 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 3.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define DIMENSION_FACTOR 0.5 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE -100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 10.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 0 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 10.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.8 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e2 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define COMPRESSION_RATIO 0.2 /* final size of container */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 14 January 22 - A von Koch snowflake fractal radiating heat ### + +**Program:** `heat.c` + +**Initial condition in function `animation()`:** `init_gaussian(-1.0, 0.0, 0.1, 0.0, 0.01, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* 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 */ + +/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */ +/* but will multiply run time by 4 */ + +#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 JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 27 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 0 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.1 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 6 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 15 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.000004 +#define VISCOSITY 10.0 +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1200 /* number of frames of movie */ +#define NVID 30 /* number of iterations between images displayed on screen */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define DRAW_BILLIARD 0 /* set to 1 to draw billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ + +/* 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 */ + +/* Field representation */ + +#define FIELD_REP 0 + +#define F_INTENSITY 0 /* color represents intensity */ +#define F_GRADIENT 1 /* color represents norm of gradient */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 1 /* choice of color scheme */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.2 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 1 /* set to 1 to draw color scheme horizontally */ + +``` + +### 13 January 22 - A mixture of two types of particles interacting with Lennard-Jones potentials ### + +**Program:** `lennardjones.c` + +**Initial condition in function `animation()`:** `` + +``` +#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 XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 1 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.5 /* proportion of particles of first type */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 5.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.25 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.02 /* parameter controlling radius of particles */ +#define MU_B 0.017 /* parameter controlling radius of particles of second type */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3200 /* number of frames of movie */ +#define NVID 50 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 5 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.854101967 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 1.0 /* moment of inertia of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define SIGMA 7.5 /* noise intensity in thermostat */ +#define BETA 0.002 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.5 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define DIMENSION_FACTOR 0.5 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 50.0 /* constant in angular dynamics */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define COMPRESSION_RATIO 0.2 /* final size of container */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 January 22 - Wave protection comparison 14: the effect of non-uniform horizontal spacing ### + +**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 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ +#define YMID 500 /* mid point of display */ +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN_B 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_pdes.c */ +#define CIRCLE_PATTERN_B 13 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ +#define RANDOM_POLY_ANGLE_B 0 /* set to 1 to randomize angle of polygons */ + +#define XDEP_POLY_ANGLE 0 /* set to 1 to rotate polygons depending on x coordinate */ +#define XDEP_POLY_ANGLE_B 0 /* set to 1 to rotate polygons depending on x coordinate */ +#define POLY_ROTATION_ANGLE -0.645 /* rotation angle for |x|=1 in units of Pi/2 */ +#define HEX_NONUNIF_COMPRESSSION 0.2 /* compression factor for */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling the dimensions of domain */ +#define MUB 0.04 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define APOLY_B 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 20 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 0.0 /* 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 3300 /* 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 150 /* 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 100 /* 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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 4 + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.75 /* 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 LOG_SCALE 1.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ + +#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 */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 100.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + + +/* 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 */ + +``` + + +### 11 January 22 - Particles with spin interacting with a potential with pentagonal symmetry ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 3 /* particle interaction, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.25 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.025 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2800 /* number of frames of movie */ +#define NVID 100 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 50.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 1.0 /* moment of inertia of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define SIGMA 7.5 /* noise intensity in thermostat */ +#define BETA 0.002 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define DIMENSION_FACTOR 0.5 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 50.0 /* constant in angular dynamics */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define COMPRESSION_RATIO 0.2 /* final size of container */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 10 January 22 - A molecular chessboard: particles with spin interacting with a square-symmetric potential ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 2 /* particle interaction, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 4.0 /* angular frequency of spin-spin interaction */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 2.5 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.025 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +// #define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 100 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 50.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 1.0 /* moment of inertia of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define SIGMA 7.5 /* noise intensity in thermostat */ +#define BETA 0.002 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define DIMENSION_FACTOR 0.5 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 50.0 /* constant in angular dynamics */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e2 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define COMPRESSION_RATIO 0.2 /* final size of container */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 January 22 - Waves escaping rings of staggered triangular obstacles ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.037 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 2650 /* number of frames of movie */ +#define NVID 40 /* number of iterations between images displayed on screen */ +#define NSEG 200 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 20 /* 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 4 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 2.0 /* shift of colors on log scale */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 2.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 8 January 22 - Interacting particles with spins ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.25 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.025 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +// #define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3000 /* number of frames of movie */ +#define NVID 100 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 5.0e-6 /* time step for particle displacement */ +#define KREPEL 50.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 1.0 /* moment of inertia of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define SIGMA 7.5 /* noise intensity in thermostat */ +#define BETA 0.002 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define DIMENSION_FACTOR 0.5 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 50.0 /* constant in angular dynamics */ +#define DRAW_SPIN 1 /* set to 1 to draw spin vectors of particles */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e2 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define COMPRESSION_RATIO 0.2 /* final size of container */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 7 January 22 - Noise reflecting panels ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(-1.5, -0.5, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 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 44 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 20 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.1 /* parameter controlling the dimensions of domain */ +#define MU 0.1 /* parameter controlling the dimensions of domain */ +#define NPOLY 18 /* number of sides of polygon */ +#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 0 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1600 /* number of frames of movie */ +#define NVID 40 /* number of iterations between images displayed on screen */ +#define NSEG 200 /* 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 4 + +#define PLOT_B 5 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.2 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 2.0 /* shift of colors on log scale */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 4.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 4.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 6 January 22 - Shock waves in a Lennard-Jones gas ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2700 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 100 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 2 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define COMPRESSION_RATIO 0.2 /* final size of container */ + +#define MOVE_OBSTACLE 1 /* set to 1 to have a moving obstacle */ +#define OBSTACLE_RADIUS 0.3 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN -2.8 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 5 January 22 - Not quite a quasicrystal: Particles interacing with a potential based on the golden mean ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -2.0 +#define INITXMAX 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 4 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.5 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 350 /* 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 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 */ +#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_ljones.c */ + +#define PLOT 3 +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 20.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 2.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.01 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* number of temperature oscillations in BETA schedule */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 4 January 22 - A Fresnel lens ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(-1.0, 0.0, phi, psi, xy_in);` + +``` + if (i%300 == 299) + { + add_circular_wave(1.0, -1.0, 0.0, phi, psi, xy_in); + } +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 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 -1.125 +#define XMAX 1.125 /* 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 43 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 20 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.1 /* parameter controlling the dimensions of domain */ +#define NPOLY 18 /* number of sides of polygon */ +#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.002 /* 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-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 1200 /* number of frames of movie */ +#define NVID 40 /* number of iterations between images displayed on screen */ +#define NSEG 200 /* 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 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.2 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 2.5 /* scaling factor for energy log 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 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 16.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 24.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 3 January 22 - Under pressure: particles with a Lennard-Jones Interaction in a piston ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.8 +#define INITXMAX 1.8 /* x interval for initial condition */ +#define INITYMIN -1.05 +#define INITYMAX 0.95 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +// #define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 350 /* 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 1 /* width of particle boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 1 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 20.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 2.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.025 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e8 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e3 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.25 /* number of temperature oscillations in BETA schedule */ + +#define DECREASE_CONTAINER_SIZE 1 /* set to 1 to decrease size of container */ +#define COMPRESSION_RATIO 0.2 /* final size of container */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +``` + +### 2 January 22 - Wave protection comparison 13: Triangles pointing right vs gradually rotated triangles ### + +**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 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ +#define YMID 500 /* mid point of display */ +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN_B 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_pdes.c */ +#define CIRCLE_PATTERN_B 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 RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ +#define RANDOM_POLY_ANGLE_B 0 /* set to 1 to randomize angle of polygons */ + +#define XDEP_POLY_ANGLE 0 /* set to 1 to rotate polygons depending on x coordinate */ +#define XDEP_POLY_ANGLE_B 1 /* set to 1 to rotate polygons depending on x coordinate */ +#define POLY_ROTATION_ANGLE -0.645 /* rotation angle for |x|=1 in units of Pi/2 */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.04 /* parameter controlling the dimensions of domain */ +#define MUB 0.04 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define APOLY_B 0.335 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard 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 0.0 /* 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 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 150 /* 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 */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 4 + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.75 /* 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 LOG_SCALE 1.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ + +#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 */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 100.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + + +/* 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 */ + +``` + +### 1 January 22 - Molecular pool: Schooting atoms at a crystal ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.0 +#define INITXMAX 1.0 /* x interval for initial condition */ +#define INITYMIN -0.75 +#define INITYMAX 0.75 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_ljones.c */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#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 32 /* number of grid point for grid of disks */ +#define NGRIDY 20 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 350 /* 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 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 */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 +#define PLOT_B 3 /* plot type for second movie */ + + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.1 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.75 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e5 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 6.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 1.0e1 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.25 /* number of temperature oscillations in BETA schedule */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 1 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 200 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 0 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* 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 */ + +```