2021-11-12 16:23:44 +01:00
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### Parameter values for YouTube simulations ###
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Created by **Nils Berglund** and optimized by **Marco Mancini**
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C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund
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Below are parameter values used for different simulations, as well as initial conditions used in
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function animation. Some simulations use variants of the published code. The list is going to be
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updated gradually.
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### 31 October 21 - Homophonic drums: Two drums that should sound the same ###
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**Program:** `wave_billiard.c`
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**Initial condition in function `animation()`:** `init_circular_wave_xplusminus(startleft[0], startleft[1], startright[0], startright[1], phi, psi, xy_in);`
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```
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#define MOVIE 1 /* set to 1 to generate movie */
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#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */
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/* General geometrical parameters */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define NX 1280 /* number of grid points on x axis */
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#define NY 720 /* number of grid points on y axis */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define JULIA_SCALE 1.0 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 38 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 7 /* pattern of circles, see list in global_pdes.c */
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#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
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#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
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#define LAMBDA 1.2 /* parameter controlling the dimensions of domain */
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#define MU 0.5 /* parameter controlling the dimensions of domain */
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#define NPOLY 4 /* number of sides of polygon */
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#define APOLY 0.5 /* angle by which to turn polygon, in units of Pi/2 */
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#define MDEPTH 4 /* depth of computation of Menger gasket */
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#define MRATIO 3 /* ratio defining Menger gasket */
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#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
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#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define NGRIDX 16 /* number of grid point for grid of disks */
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#define NGRIDY 20 /* number of grid point for grid of disks */
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#define X_SHOOTER -0.2
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#define Y_SHOOTER -0.6
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#define X_TARGET 0.4
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#define Y_TARGET 0.7 /* shooter and target positions in laser fight */
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#define ISO_XSHIFT_LEFT -2.9
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#define ISO_XSHIFT_RIGHT 1.4
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#define ISO_YSHIFT_LEFT -0.15
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#define ISO_YSHIFT_RIGHT -0.15
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#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard below */
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/* Physical parameters of wave equation */
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#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
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#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
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#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
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#define OMEGA 0.002 /* frequency of periodic excitation */
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#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
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#define COURANT 0.02 /* Courant number */
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#define COURANTB 0.02 /* Courant number in medium B */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define GAMMAB 5.0e-3 /* damping factor in wave equation */
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#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
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#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
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#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
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#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
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#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
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/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
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/* Boundary conditions, see list in global_pdes.c */
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#define B_COND 2
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/* Parameters for length and speed of simulation */
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#define NSTEPS 9800 /* number of frames of movie */
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#define NVID 50 /* number of iterations between images displayed on screen */
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#define NSEG 100 /* number of segments of boundary */
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#define INITIAL_TIME 0 /* time after which to start saving frames */
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#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
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#define PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
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#define END_FRAMES 100 /* number of still frames at end of movie */
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/* Parameters of initial condition */
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#define INITIAL_AMP 0.75 /* amplitude of initial condition */
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#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */
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#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */
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/* Plot type, see list in global_pdes.c */
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#define PLOT 1
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#define PLOT_B 1 /* plot type for second movie */
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/* Color schemes */
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#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */
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#define BLACK 1 /* background */
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#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */
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#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 0.15 /* sensitivity of color on wave amplitude */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define E_SCALE 100.0 /* scaling factor for energy representation */
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
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#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */
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#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */
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#define SAVE_TIME_SERIES 1 /* set to 1 to save wave time series at a point */
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/* For debugging purposes only */
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#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
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#define VMAX 10.0 /* max value of wave amplitude */
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```
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### 30 October 21 - Blue noise statistics: Sinai billiard on a torus with Poisson disc sampled obstaces ###
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**Program:** `particle_pinball.c`
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**Initial condition in function `animation()`:** `nit_drop_config(0.0, 0.0, -0.45*PID, 0.45*PID, configs);`
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```
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#define MOVIE 1 /* set to 1 to generate movie */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define XMIN -4.0
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#define XMAX 4.0 /* x interval */
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#define YMIN -1.25
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#define YMAX 3.25 /* y interval for 9/16 aspect ratio */
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#define BOXYMIN -1.0
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#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */
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#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
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/* Choice of the billiard table, see global_particles.c */
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#define B_DOMAIN 23 /* choice of domain shape */
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#define CIRCLE_PATTERN 7 /* pattern of circles */
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#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
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#define NMAXCIRCLES 5000 /* total number of circles (must be at least NCX*NCY for square grid) */
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#define NCX 44 /* number of circles in x direction */
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#define NCY 10 /* number of circles in y direction */
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#define NPOISSON 350 /* number of points for Poisson C_RAND_POISSON arrangement */
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#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
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#define LAMBDA 3.8 /* parameter controlling shape of domain */
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#define MU 0.05 /* second parameter controlling shape of billiard */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define NPOLY 4 /* number of sides of polygon */
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#define APOLY 0.5 /* angle by which to turn polygon, in units of Pi/2 */
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#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */
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#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */
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#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
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#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
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#define DEBUG 0 /* draw trajectories, for debugging purposes */
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/* Simulation parameters */
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#define NPART 1 /* number of particles */
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#define NPARTMAX 100000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
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#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */
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#define TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */
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#define NSTEPS 10400 /* number of frames of movie */
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#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.00007 /* integration step */
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#define NVID 150 /* number of iterations between images displayed on screen */
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/* Decreasing TIME accelerates the animation and the movie */
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/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
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/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
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/* Colors and other graphical parameters */
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#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */
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#define NCOLORS 48 /* number of colors */
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#define COLORSHIFT 2 /* hue of initial color */
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#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
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#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */
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#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
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#define NSEG 100 /* number of segments of boundary */
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#define LENGTH 0.1 /* length of velocity vectors */
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#define BILLIARD_WIDTH 2 /* width of billiard */
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#define PARTICLE_WIDTH 4 /* width of particles */
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#define FRONT_WIDTH 3 /* width of wave front */
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#define COLOR_TRAJECTORY 8 /* hue for single color */
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#define BLACK 1 /* set to 1 for black background */
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#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
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#define OUTER_COLOR 270.0 /* color outside billiard */
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#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
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#define PAINT_EXT 0 /* set to 1 to paint exterior in other color */
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#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
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#define PAUSE 500 /* number of frames after which to pause */
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#define PSLEEP 5 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1000 /* final sleeping time */
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#define END_FRAMES 100 /* number of still frames at end of movie */
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#define NPATHBINS 200 /* number of bins for path length histogramm */
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#define PATHLMAX 1.8 /* max free path on graph */
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```
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### 29 October 21 - Waves traveling between two parabolic antennae ###
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**Program:** `wave_billiard.c`
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**Initial condition in function `animation()`:** `init_circular_wave(-LAMBDA, 0.0, phi, psi, xy_in);`
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```
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```
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if (i%345 == 344)
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{
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add_circular_wave(1.0, -LAMBDA, 0.0, phi, psi, xy_in);
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}
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```
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#define MOVIE 1 /* set to 1 to generate movie */
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#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */
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/* General geometrical parameters */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define NX 1280 /* number of grid points on x axis */
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#define NY 720 /* number of grid points on y axis */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define JULIA_SCALE 1.0 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 19 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 7 /* pattern of circles, see list in global_pdes.c */
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|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 1.2 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.5 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 4 /* 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 16 /* 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 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.02 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 5.0e-3 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#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 100 /* number of frames of movie */
|
|
|
|
|
#define NSTEPS 4500 /* 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 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
|
|
|
|
|
|
|
|
|
|
#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 0.15 /* 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 0 /* set to 1 to plot the color scheme */
|
|
|
|
|
|
|
|
|
|
#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 October 21 - Shining a light through a random circle arrangement ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_trajectory.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:**
|
|
|
|
|
```
|
|
|
|
|
x = -1.3;
|
|
|
|
|
y = -1.0 + 2.0*time;
|
|
|
|
|
compute_trajectories_xy(x, y, -0.5*PID, 0.5*PID, configs, trajectory, traj_length);
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 720 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -1.4
|
|
|
|
|
#define XMAX 1.4 /* x interval */
|
|
|
|
|
#define YMIN -1.4
|
|
|
|
|
#define YMAX 1.4 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table, see global_particles.c */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 20 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 5 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 9 /* number of circles in x direction */
|
|
|
|
|
#define NCY 20 /* number of circles in y direction */
|
|
|
|
|
#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 10.0 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.04 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* 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 50000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
#define TRAJ_LENGTH 16 /* 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 TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 1200 /* 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 64 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.03 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 27 October 21 - A rotating triangular-parabolic resonator ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard_rotate.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 32 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 7 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.8 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 3 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
#define ROTATION 0.0025 /* rotation angle per frame */
|
|
|
|
|
|
|
|
|
|
#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 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.02 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 5.0e-3 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#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 4000 /* 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 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 */
|
|
|
|
|
// #define INITIAL_VARIANCE 0.001 /* variance of initial condition */
|
|
|
|
|
// #define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */
|
|
|
|
|
|
|
|
|
|
/* Plot type, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define PLOT 1
|
|
|
|
|
|
|
|
|
|
#define PLOT_B 3 /* 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 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 10.0 /* scale of color scheme bar */
|
|
|
|
|
|
|
|
|
|
#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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 26 October 21 - A study in pink: parabolic resonator with 4 different focal points ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:**
|
|
|
|
|
```
|
|
|
|
|
init_circular_wave(LAMBDA, 0.0, phi, psi, xy_in);
|
|
|
|
|
add_circular_wave(-1.0, 0.0, LAMBDA, phi, psi, xy_in);
|
|
|
|
|
add_circular_wave(1.0, -LAMBDA, 0.0, phi, psi, xy_in);
|
|
|
|
|
add_circular_wave(-1.0, 0.0, -LAMBDA, 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 32 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 7 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.3 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.7 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.5 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
#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 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.02 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 5.0e-3 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
|
|
|
|
|
#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
|
|
|
|
|
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
|
|
|
|
|
/* The physical damping coefficient is given by GAMMA/(DT)^2 */
|
|
|
|
|
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
|
|
|
|
|
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
|
|
|
|
|
|
|
|
|
|
/* Boundary conditions, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define B_COND 2
|
|
|
|
|
|
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 4500 /* number of frames of movie */
|
|
|
|
|
#define NVID 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 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 0.0005 /* variance of initial condition */
|
|
|
|
|
#define INITIAL_WAVELENGTH 0.02 /* 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 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 0.15 /* 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 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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 25 October 21 - Trajectories in an elliptical billiard ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_trajectory.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:**
|
|
|
|
|
```
|
|
|
|
|
c = sqrt(LAMBDA*LAMBDA - 1.0);
|
|
|
|
|
a = 0.999*LAMBDA;
|
|
|
|
|
b = sqrt(a*a - c*c);
|
|
|
|
|
x = a*sin(PI*time);
|
|
|
|
|
y = b*cos(PI*time);
|
|
|
|
|
alpha = argument(x - c, y);
|
|
|
|
|
compute_trajectories_ellipse(x, y, configs, trajectory, traj_length); ```
|
|
|
|
|
|
2022-03-13 18:29:22 +01:00
|
|
|
```
|
|
|
|
|
|
2021-11-12 16:23:44 +01:00
|
|
|
```
|
|
|
|
|
#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 1 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 5 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 10 /* 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 LAMBDA 1.5 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.025 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 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 12 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
#define TRAJ_LENGTH 64 /* 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 TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 3200 /* 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 64 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.03 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 24 October 21 - Dante's 7th circle: a heptagonal parabolic resonator ###
|
|
|
|
|
|
|
|
|
|
**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 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 32 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 7 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 1.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 7 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
#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 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.02 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 5.0e-3 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#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 5000 /* 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 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 0.0005 /* variance of initial condition */
|
|
|
|
|
#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */
|
|
|
|
|
|
|
|
|
|
/* Plot type, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define PLOT 1
|
|
|
|
|
|
|
|
|
|
#define PLOT_B 3 /* 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 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 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 October 21 - Avoiding a laser in a room of mirrors, with moving shooter and target ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_trajectory.c` (variant of `particle_billiard.c`)
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:**
|
|
|
|
|
```
|
|
|
|
|
time = (double)i/(double)NSTEPS;
|
|
|
|
|
x_shooter = -0.2 - 0.3*sin(DPI*time);
|
|
|
|
|
y_shooter = -0.6*cos(DPI*time);
|
|
|
|
|
x_target = 0.4 + 0.4*sin(DPI*time);
|
|
|
|
|
y_target = 0.7*cos(DPI*time);
|
|
|
|
|
init_circle_config();
|
|
|
|
|
alpha = argument(x_target - x_shooter, y_target - y_shooter);
|
|
|
|
|
compute_trajectories_xy(x_shooter, y_shooter, 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 21 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 11 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 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 LAMBDA 1.0 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.02 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */
|
|
|
|
|
#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */
|
|
|
|
|
#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
|
|
|
|
|
|
|
|
|
/* Simulation parameters */
|
|
|
|
|
|
|
|
|
|
#define NPART 5000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
#define TRAJ_LENGTH 25 /* 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 TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 3200 /* 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 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.03 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 22 October 21 - Moving widdershins: A rotating parabolic resonator ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard_rotate.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 32 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 7 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 1.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
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|
|
|
|
|
#define ROTATION 0.0025 /* rotation angle per frame */
|
|
|
|
|
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|
|
#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 */
|
|
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|
|
#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 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.02 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 5.0e-3 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#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 4400 /* 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 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 0.0005 /* variance of initial condition */
|
|
|
|
|
#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */
|
|
|
|
|
|
|
|
|
|
/* Plot type, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define PLOT 0
|
|
|
|
|
|
|
|
|
|
#define PLOT_B 3 /* 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 0.2 /* 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 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 October 21 - Statistics for a Sinai billiard on the torus with Poisson-distributed obstacles ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_pinball.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.45*PID, 0.45*PID, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -4.0
|
|
|
|
|
#define XMAX 4.0 /* x interval */
|
|
|
|
|
#define YMIN -1.25
|
|
|
|
|
#define YMAX 3.25 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define BOXYMIN -1.0
|
|
|
|
|
#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */
|
|
|
|
|
|
|
|
|
|
#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 23 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 6 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 44 /* number of circles in x direction */
|
|
|
|
|
#define NCY 10 /* number of circles in y direction */
|
|
|
|
|
|
|
|
|
|
#define NPOISSON 350 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 3.8105 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.05 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.5 /* 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 0 /* set to 1 to keep trails of the particles */
|
|
|
|
|
#define TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 11700 /* number of frames of movie */
|
|
|
|
|
#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00007 /* 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 1 /* Color palette, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 48 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 2 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */
|
|
|
|
|
#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 0.1 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 4 /* width of particles */
|
|
|
|
|
#define FRONT_WIDTH 3 /* width of wave front */
|
|
|
|
|
#define COLOR_TRAJECTORY 8 /* hue for single color */
|
|
|
|
|
|
|
|
|
|
#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 in other color */
|
|
|
|
|
#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#define PAUSE 500 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 5 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1000 /* final sleeping time */
|
|
|
|
|
#define END_FRAMES 100 /* number of still frames at end of movie */
|
|
|
|
|
|
|
|
|
|
#define NPATHBINS 200 /* number of bins for path length histogramm */
|
|
|
|
|
#define PATHLMAX 2.5 /* max free path on graph */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 20 October 21 - Octarine Dream: Two eccentric waves in an octagonal-parabolic resonator ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_circular_wave(0.5, 0.5, phi, psi, xy_in);
|
|
|
|
|
add_circular_wave(-1.0, -0.5, 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 32 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 7 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 1.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
#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 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.02 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 5.0e-3 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#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 2700 /* 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 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 0.0005 /* variance of initial condition */
|
|
|
|
|
#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */
|
|
|
|
|
|
|
|
|
|
/* Plot type, see list in global_pdes.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_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 0.15 /* 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 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 200.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -160.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
|
|
|
|
|
|
|
|
|
|
/* 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 October 21 - A moving light source in a Penrose unilluminable room ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_trajectory.c` (variant of `particle_billiard.c`)
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:**
|
|
|
|
|
```
|
|
|
|
|
time = DPI*(0.025 + 0.95*(double)i/(double)NSTEPS);
|
|
|
|
|
x = 0.6 + 0.6*cos(time);
|
|
|
|
|
y = 0.0 + 0.7*sin(time);
|
|
|
|
|
init_drop_config(x, y, 0.0, DPI, configs);
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 720 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -1.4
|
|
|
|
|
#define XMAX 1.4 /* x interval */
|
|
|
|
|
#define YMIN -1.4
|
|
|
|
|
#define YMAX 1.4 /* 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 16 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 2 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 30 /* number of circles in x direction */
|
|
|
|
|
#define NCY 20 /* number of circles in y direction */
|
|
|
|
|
#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 1.3 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.3 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 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 15 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
#define TRAJ_LENGTH 7 /* 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 TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 1250 /* 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 1 /* Color palette, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 64 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.03 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 18 October 21 - Wave amplitude in two isospectral domains ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_circular_wave_xplusminus(startleft[0], startleft[1], startright[0], startright[1], phi, psi, xy_in);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
#define DOUBLE_MOVIE 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 37 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 7 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.9 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.55 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
#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 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.02 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 5.0e-3 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#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 3000 /* 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 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 0.0005 /* variance of initial condition */
|
|
|
|
|
#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */
|
|
|
|
|
|
|
|
|
|
/* Plot type, see list in global_pdes.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_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 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 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 210.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -150.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
|
|
|
|
|
|
|
|
|
|
/* For debugging purposes only */
|
|
|
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
|
#define VMAX 10.0 /* max value of wave amplitude */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 17 October 21 - Statistics for an (almost) finite horizon Sinai billiard on the torus ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_pinball.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.45*PID, 0.45*PID, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -4.0
|
|
|
|
|
#define XMAX 4.0 /* x interval */
|
|
|
|
|
#define YMIN -1.25
|
|
|
|
|
#define YMAX 3.25 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define BOXYMIN -1.0
|
|
|
|
|
#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */
|
|
|
|
|
|
|
|
|
|
#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 23 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 21 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 44 /* number of circles in x direction */
|
|
|
|
|
#define NCY 10 /* 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 LAMBDA 3.8105 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.085 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.5 /* 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 0 /* set to 1 to keep trails of the particles */
|
|
|
|
|
#define TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 10700 /* number of frames of movie */
|
|
|
|
|
#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00007 /* 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 1 /* Color palette, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 256 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 2 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */
|
|
|
|
|
#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 0.1 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 4 /* width of particles */
|
|
|
|
|
#define FRONT_WIDTH 3 /* width of wave front */
|
|
|
|
|
#define COLOR_TRAJECTORY 8 /* hue for single color */
|
|
|
|
|
|
|
|
|
|
#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 in other color */
|
|
|
|
|
#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#define PAUSE 500 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 5 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1000 /* final sleeping time */
|
|
|
|
|
#define END_FRAMES 100 /* number of still frames at end of movie */
|
|
|
|
|
|
|
|
|
|
#define NPATHBINS 200 /* number of bins for path length histogramm */
|
|
|
|
|
#define PATHLMAX 0.3 /* max free path on graph */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 16 October 21 - Escaping a laser with finite wavelength in a room of mirrors ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_circular_wave(X_SHOOTER, Y_SHOOTER, 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 201 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 7 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.03 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
#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 */
|
|
|
|
|
|
|
|
|
|
/* 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 0.02 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 5.0e-3 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#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 1500 /* 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 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 0.015 /* wavelength of initial condition */
|
|
|
|
|
|
|
|
|
|
/* Plot type, see list in global_pdes.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_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 0.75 /* 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 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 190.0 /* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 October 21 - Average energy of a wave in a Tokarsky unilluminable room ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_circular_wave(-2.0*ratio, 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 35 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.6 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.6 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
|
|
|
|
|
#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
|
|
|
|
|
#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
|
|
|
|
|
|
|
|
|
|
#define OMEGA 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.01 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 1.0e-6 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-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 3000 /* number of frames of movie */
|
|
|
|
|
#define NVID 100 /* 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 */
|
|
|
|
|
|
|
|
|
|
#define INITIAL_AMP 0.75 /* amplitude of initial condition */
|
|
|
|
|
#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */
|
|
|
|
|
#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */
|
|
|
|
|
|
|
|
|
|
/* Plot type, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define PLOT 3
|
|
|
|
|
|
|
|
|
|
#define PLOT_B 0 /* plot type for second movie */
|
|
|
|
|
|
|
|
|
|
/* 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 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 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 200.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -190.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 14 October 21 - Sinai billiard on a torus with triangular lattice, collisions and free path statistics ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_pinball.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.45*PID, 0.45*PID, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -4.0
|
|
|
|
|
#define XMAX 4.0 /* x interval */
|
|
|
|
|
#define YMIN -1.25
|
|
|
|
|
#define YMAX 3.25 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define BOXYMIN -1.0
|
|
|
|
|
#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */
|
|
|
|
|
|
|
|
|
|
#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 23 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 21 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 44 /* number of circles in x direction */
|
|
|
|
|
#define NCY 10 /* 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 LAMBDA 3.8105 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.05 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.5 /* 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 0 /* set to 1 to keep trails of the particles */
|
|
|
|
|
#define TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 11000 /* number of frames of movie */
|
|
|
|
|
#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00007 /* 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 1 /* Color palette, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 48 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 2 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */
|
|
|
|
|
#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 0.1 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 4 /* width of particles */
|
|
|
|
|
#define FRONT_WIDTH 3 /* width of wave front */
|
|
|
|
|
#define COLOR_TRAJECTORY 8 /* hue for single color */
|
|
|
|
|
|
|
|
|
|
#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 in other color */
|
|
|
|
|
#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#define PAUSE 500 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 5 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1000 /* final sleeping time */
|
|
|
|
|
#define END_FRAMES 100 /* number of still frames at end of movie */
|
|
|
|
|
|
|
|
|
|
#define NPATHBINS 200 /* number of bins for path length histogramm */
|
|
|
|
|
#define PATHLMAX 1.5 /* max free path on graph */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 13 October 21 - One cannot (always) hear the shape of a drum ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_circular_wave_xplusminus(-0.9, 0.0, 0.81, 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 37 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.6 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.6 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
#define ISO_XSHIFT_LEFT -1.0
|
|
|
|
|
#define ISO_XSHIFT_RIGHT 0.9
|
|
|
|
|
#define ISO_YSHIFT_LEFT 0.05
|
|
|
|
|
#define ISO_YSHIFT_RIGHT 0.05
|
|
|
|
|
#define ISO_SCALE 0.9 /* 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 3000 /* number of frames of movie */
|
|
|
|
|
#define NVID 60 /* 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 */
|
|
|
|
|
|
|
|
|
|
#define INITIAL_AMP 0.75 /* amplitude of initial condition */
|
|
|
|
|
#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */
|
|
|
|
|
#define INITIAL_WAVELENGTH 0.02 /* 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 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 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 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 190.0 /* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 12 October 21 - Particles in a hexagonal-parabolic resonator ###
|
|
|
|
|
|
|
|
|
|
**Program:** `drop_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, 0.0, DPI, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 720 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -1.125
|
|
|
|
|
#define XMAX 1.125 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table, see global_particles.c */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 15 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 0 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 15 /* number of circles in x direction */
|
|
|
|
|
#define NCY 20 /* number of circles in y direction */
|
|
|
|
|
#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.0 /* parameter controlling shape of billiard */
|
|
|
|
|
#define MU 0.9 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 6 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */
|
|
|
|
|
#define DRAW_CONSTRUCTION_LINES 1 /* set to 1 to draw additional construction lines for billiard */
|
|
|
|
|
#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
|
|
|
|
|
#define NPART 10000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 1440 /* number of frames of movie */
|
|
|
|
|
#define TIME 150 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.0001 /* integration step */
|
|
|
|
|
#define NVID 75 /* 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 */
|
|
|
|
|
/* For a good quality movie, take for instance TIME = 50, DPHI = 0.0002 */
|
|
|
|
|
|
|
|
|
|
/* simulation parameters */
|
|
|
|
|
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define LPERIODIC 0.1 /* lines longer than this are not drawn (useful for Sinai billiard) */
|
|
|
|
|
#define LCUT 2.0 /* controls the max size of segments not considered as being cut */
|
|
|
|
|
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
|
|
|
|
#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
#define ORDER_COLORS 1 /* set to 1 if colors should be drawn in order */
|
|
|
|
|
|
|
|
|
|
/* color and other graphical parameters */
|
|
|
|
|
|
|
|
|
|
#define COLOR_PALETTE 1 /* Color palette, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 6 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 3 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define BILLIARD_WIDTH 4 /* width of billiard */
|
|
|
|
|
#define FRONT_WIDTH 4 /* 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 300.0 /* color outside billiard */
|
|
|
|
|
#define PAINT_INT 1 /* set to 1 to paint interior in other color (for polygon) */
|
|
|
|
|
#define PAINT_EXT 0 /* set to 1 to paint exterior of billiard */
|
|
|
|
|
|
|
|
|
|
#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 100 /* final sleeping time */
|
|
|
|
|
#define END_FRAMES 0 /* number of frames at end of movie */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 11 October 21 - The color of magic: An octagonal parabolic resonator ###
|
|
|
|
|
|
|
|
|
|
**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 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 32 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 1.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
|
|
|
|
|
#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
|
|
|
|
|
#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
|
|
|
|
|
|
|
|
|
|
#define OMEGA 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.01 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 1.0e-6 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-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 6350 /* number of frames of movie */
|
|
|
|
|
#define NVID 60 /* 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 */
|
|
|
|
|
|
|
|
|
|
#define INITIAL_AMP 0.75 /* amplitude of initial condition */
|
|
|
|
|
#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */
|
|
|
|
|
#define INITIAL_WAVELENGTH 0.02 /* 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 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 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 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 210.0 /* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 10 October 21 - Swaying and repelling mangroves destroyed by the surf ###
|
|
|
|
|
|
|
|
|
|
**Program:** `mangrove.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_wave_flat(phi, psi, xy_in);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
/* General geometrical parameters */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define NX 1280 /* number of grid points on x axis */
|
|
|
|
|
#define NY 720 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 340 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.85 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.03 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 3 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 15 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */
|
|
|
|
|
#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */
|
|
|
|
|
#define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */
|
|
|
|
|
#define X_SHIFT -0.9 /* 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 20.0 /* spatial period of periodic excitation in x direction */
|
|
|
|
|
#define KY_BC 6.66666 /* 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 60 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define INITIAL_TIME 100 /* time after which to start saving frames */
|
|
|
|
|
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
|
|
|
|
|
|
|
|
|
#define PAUSE 1000 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1 /* final sleeping time */
|
|
|
|
|
#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 */
|
|
|
|
|
|
|
|
|
|
/* mangrove properties */
|
|
|
|
|
|
|
|
|
|
#define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */
|
|
|
|
|
#define MANGROVE_HUE_MAX -50.0 /* color of saturated mangrove */
|
|
|
|
|
#define MANGROVE_EMAX 1.5e-3 /* max energy for mangrove to survive */
|
|
|
|
|
|
|
|
|
|
#define RANDOM_RADIUS 1 /* set to 1 for random circle radius */
|
|
|
|
|
#define ERODE_MANGROVES 0 /* set to 1 for mangroves to be eroded */
|
|
|
|
|
#define MOVE_MANGROVES 1 /* set to 1 for mobile mangroves */
|
|
|
|
|
#define DETACH_MANGROVES 1 /* set to 1 for mangroves to be able to detach */
|
|
|
|
|
#define INERTIA 1 /* set to 1 for taking inertia into account */
|
|
|
|
|
#define REPELL_MANGROVES 1 /* set to 1 for mangroves to repell each other */
|
|
|
|
|
#define DT_MANGROVE 0.1 /* time step for mangrove displacement */
|
|
|
|
|
#define KSPRING 0.05 /* spring constant of mangroves */
|
|
|
|
|
#define KWAVE 4.0 /* constant in force due to wave gradient */
|
|
|
|
|
#define KREPEL 5.0 /* constant in repelling force between mangroves */
|
|
|
|
|
#define REPEL_RADIUS 1.1 /* radius in which repelling force acts (in units of mangrove radius) */
|
|
|
|
|
#define DXMAX 0.02 /* max displacement of mangrove in one time step */
|
|
|
|
|
#define L_DETACH 0.25 /* spring length beyond which mangroves detach */
|
|
|
|
|
#define DAMP_MANGROVE 0.1 /* damping coefficient of mangroves */
|
|
|
|
|
#define MANGROVE_MASS 1.5 /* mass of mangrove of radius MU */
|
|
|
|
|
|
|
|
|
|
#define HASHX 25 /* size of hashgrid in x direction */
|
|
|
|
|
#define HASHY 15 /* size of hashgrid in y direction */
|
|
|
|
|
#define HASHMAX 10 /* maximal number of mangroves per hashgrid cell */
|
|
|
|
|
#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */
|
|
|
|
|
|
|
|
|
|
/* 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 October 21 - Sinai billiard on a torus with square lattice of obstacles: collision and free path statistics ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_pinball.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** ``
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -4.0
|
|
|
|
|
#define XMAX 4.0 /* x interval */
|
|
|
|
|
#define YMIN -1.25
|
|
|
|
|
#define YMAX 3.25 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define BOXYMIN -1.0
|
|
|
|
|
#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */
|
|
|
|
|
|
|
|
|
|
#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 23 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 1 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 40 /* number of circles in x direction */
|
|
|
|
|
#define NCY 10 /* 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 LAMBDA 3.8 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.05 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.5 /* 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 0 /* set to 1 to keep trails of the particles */
|
|
|
|
|
#define TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 8800 /* number of frames of movie */
|
|
|
|
|
#define TIME 5000 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00007 /* 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 1 /* Color palette, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 48 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 2 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */
|
|
|
|
|
#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 0.1 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 4 /* width of particles */
|
|
|
|
|
#define FRONT_WIDTH 3 /* width of wave front */
|
|
|
|
|
#define COLOR_TRAJECTORY 8 /* hue for single color */
|
|
|
|
|
|
|
|
|
|
#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 in other color */
|
|
|
|
|
#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#define PAUSE 500 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 5 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1000 /* final sleeping time */
|
|
|
|
|
#define END_FRAMES 100 /* number of still frames at end of movie */
|
|
|
|
|
|
|
|
|
|
#define NPATHBINS 200 /* number of bins for path length histogramm */
|
|
|
|
|
#define PATHLMAX 1.5 /* max free path on graph */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 8 October 21 - Waves in a Tokarsky unilluminable room ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_circular_wave(-2.0*ratio, 0.0, phi, psi, xy_in);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */
|
|
|
|
|
|
|
|
|
|
/* General geometrical parameters */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define NX 1280 /* number of grid points on x axis */
|
|
|
|
|
#define NY 720 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 35 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 1.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 5 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
|
|
|
|
|
#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
|
|
|
|
|
#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
|
|
|
|
|
|
|
|
|
|
#define OMEGA 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.01 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 1.0e-6 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
|
|
|
|
|
#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
|
|
|
|
|
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
|
|
|
|
|
/* The physical damping coefficient is given by GAMMA/(DT)^2 */
|
|
|
|
|
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
|
|
|
|
|
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
|
|
|
|
|
|
|
|
|
|
/* Boundary conditions, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define B_COND 2
|
|
|
|
|
|
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 3500 /* number of frames of movie */
|
|
|
|
|
#define NVID 60 /* 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 */
|
|
|
|
|
|
|
|
|
|
#define INITIAL_AMP 0.75 /* amplitude of initial condition */
|
|
|
|
|
#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */
|
|
|
|
|
#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */
|
|
|
|
|
|
|
|
|
|
/* Plot type, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define PLOT 1
|
|
|
|
|
|
|
|
|
|
#define PLOT_B 3 /* plot type for second movie */
|
|
|
|
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
|
|
|
|
|
|
#define COLOR_PALETTE 1 /* 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 0.15 /* sensitivity of color on wave amplitude */
|
|
|
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
|
|
|
|
#define E_SCALE 200.0 /* 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 260.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -250.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */
|
|
|
|
|
|
|
|
|
|
/* 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 October 21 - Collision statistics for a “sunflower” Sinai billiard ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_pinball.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.5, 0.1, -0.5*PID, 0.5*PID, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -4.0
|
|
|
|
|
#define XMAX 4.0 /* x interval */
|
|
|
|
|
#define YMIN -1.25
|
|
|
|
|
#define YMAX 3.25 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define BOXYMIN -1.0
|
|
|
|
|
#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */
|
|
|
|
|
|
|
|
|
|
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table, see global_particles.c */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 21 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
// #define CIRCLE_PATTERN 6 /* pattern of circles */
|
|
|
|
|
#define CIRCLE_PATTERN 4 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 5000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 40 /* number of circles in x direction */
|
|
|
|
|
#define NCY 10 /* 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 LAMBDA 3.8 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.05 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.5 /* 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 0 /* set to 1 to keep trails of the particles */
|
|
|
|
|
#define TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 10300 /* number of frames of movie */
|
|
|
|
|
#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00007 /* integration step */
|
|
|
|
|
#define NVID 150 /* number of iterations between images displayed on screen */
|
|
|
|
|
|
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
|
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
|
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
|
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
|
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
|
|
|
|
|
|
/* Colors and other graphical parameters */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 64 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */
|
|
|
|
|
#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 0.1 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 4 /* width of particles */
|
|
|
|
|
#define FRONT_WIDTH 3 /* width of wave front */
|
|
|
|
|
#define COLOR_TRAJECTORY 8 /* hue for single color */
|
|
|
|
|
|
|
|
|
|
#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 in other color */
|
|
|
|
|
#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#define PAUSE 500 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 5 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1000 /* final sleeping time */
|
|
|
|
|
#define END_FRAMES 100 /* number of still frames at end of movie */
|
|
|
|
|
|
|
|
|
|
#define NPATHBINS 200 /* number of bins for path length histogramm */
|
|
|
|
|
#define PATHLMAX 1.5 /* max free path on graph */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 6 October 21 - "Energy evolution in a triangular grid wave protection" ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_energy.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `int_planar_wave_comp(XMIN + 0.015, 0.0, phi, psi, xy_in);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define NX 1280 /* number of grid points on x axis */
|
|
|
|
|
#define NY 720 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
#define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
#define CIRCLE_PATTERN_B 11 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.75 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.03 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MUB 0.03 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 3 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 15 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
|
|
|
|
|
#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
|
|
|
|
|
#define 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 200 /* time after which to start saving frames */
|
|
|
|
|
#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */
|
|
|
|
|
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
|
|
|
|
|
|
|
|
|
#define PAUSE 1000 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1 /* final sleeping time */
|
|
|
|
|
#define END_FRAMES 100 /* number of still frames at end of movie */
|
|
|
|
|
|
|
|
|
|
/* 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 1
|
|
|
|
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* background */
|
|
|
|
|
|
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
|
#define SLOPE 50.0 /* sensitivity of color on wave amplitude */
|
|
|
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
|
|
|
|
#define E_SCALE 500.0 /* scaling factor for energy representation */
|
|
|
|
|
|
|
|
|
|
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
|
|
|
|
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
|
|
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* For debugging purposes only */
|
|
|
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
|
#define VMAX 5.0 /* max value of wave amplitude */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
### 5 October 21 - Particles with trails in a Penrose unilluminable room ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** ``
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
init_partial_drop_config(0.0, 0.0, 0.0, DPI, 0, 2*NPART/5, 0, configs, color, newcolor);
|
|
|
|
|
init_partial_drop_config(0.0, 0.8, 0.0, DPI, 2*NPART/5, 4*NPART/5, 10, configs, color, newcolor);
|
|
|
|
|
init_partial_drop_config(1.2, 0.1, 0.0, DPI, 4*NPART/5, NPART, 36, configs, color, newcolor);
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 720 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -1.4
|
|
|
|
|
#define XMAX 1.4 /* x interval */
|
|
|
|
|
#define YMIN -1.4
|
|
|
|
|
#define YMAX 1.4 /* 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 16 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 2 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 30 /* number of circles in x direction */
|
|
|
|
|
#define NCY 20 /* number of circles in y direction */
|
|
|
|
|
#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 1.3 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.3 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 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 100 /* 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 TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 1300 /* 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 NCOLORS 64 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.03 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 2 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 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 */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
### 4 October 21 - Mean energy in a Penrose unilluminable room, starting behind a mushroom ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_wave_plus(LAMBDA - 0.3*MU, 0.5*MU, 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 33 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 1.5 /* 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 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
|
|
|
|
|
#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
|
|
|
|
|
#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
|
|
|
|
|
|
|
|
|
|
#define OMEGA 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.01 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 1.0e-6 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
|
|
|
|
|
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
|
|
|
|
#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
|
|
|
|
|
#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
|
|
|
|
|
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
|
|
|
|
|
/* The physical damping coefficient is given by GAMMA/(DT)^2 */
|
|
|
|
|
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
|
|
|
|
|
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
|
|
|
|
|
|
|
|
|
|
/* Boundary conditions, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define B_COND 2
|
|
|
|
|
|
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 3500 /* number of frames of movie */
|
|
|
|
|
#define NVID 40 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define INITIAL_TIME 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 */
|
|
|
|
|
|
|
|
|
|
#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 3
|
|
|
|
|
|
|
|
|
|
#define PLOT_B 0 /* plot type for second movie */
|
|
|
|
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* background */
|
|
|
|
|
|
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
|
#define SLOPE 0.25 /* sensitivity of color on wave amplitude */
|
|
|
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
|
|
|
|
#define E_SCALE 200.0 /* 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 -230.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* For debugging purposes only */
|
|
|
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
|
#define VMAX 10.0 /* max value of wave amplitude */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
### 3 October 21 - Mystery billiard 9 ###
|
|
|
|
|
|
|
|
|
|
**Program:** `mystery_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_line_config(0.0, -0.2, 0.0, 0.2, 0.0, 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 */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 15 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 0 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 5000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 40 /* number of circles in x direction */
|
|
|
|
|
#define NCY 10 /* 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 LAMBDA 0.0 /* parameter controlling shape of billiard */
|
|
|
|
|
#define MU 0.8 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 3 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define DRAW_BILLIARD 0 /* set to 1 to draw billiard */
|
|
|
|
|
#define DRAW_CONSTRUCTION_LINES 1 /* set to 1 to draw additional construction lines for billiard */
|
|
|
|
|
#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
|
|
|
|
|
|
|
|
|
/* Simulation parameters */
|
|
|
|
|
|
|
|
|
|
#define NPART 4001 /* 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 NSTEPS 4000 /* number of frames of movie */
|
|
|
|
|
#define TIME 1000 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.000015 /* integration step */
|
|
|
|
|
#define NVID 50 /* number of iterations between images displayed on screen */
|
|
|
|
|
|
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
|
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
|
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
|
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
|
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
|
|
|
|
|
|
/* Colors and other graphical parameters */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 15 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.02 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 3 /* 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 in other color */
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#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 PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
### 2 October 21 - A pentagonal-parabolic resonator ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_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 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 32 /* choice of domain shape, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
|
|
|
|
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 1.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 5 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
|
|
|
|
#define MRATIO 3 /* ratio defining Menger gasket */
|
|
|
|
|
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
|
|
|
|
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NGRIDX 16 /* number of grid point for grid of disks */
|
|
|
|
|
#define NGRIDY 20 /* number of grid point for grid of disks */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical parameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
|
|
|
|
|
#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
|
|
|
|
|
#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
|
|
|
|
|
|
|
|
|
|
#define OMEGA 0.002 /* frequency of periodic excitation */
|
|
|
|
|
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
|
|
|
|
#define COURANT 0.02 /* Courant number */
|
|
|
|
|
#define COURANTB 0.01 /* Courant number in medium B */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMAB 1.0e-6 /* damping factor in wave equation */
|
|
|
|
|
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
|
|
|
|
#define GAMMA_TOPBOT 1.0e-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 5600 /* number of frames of movie */
|
|
|
|
|
#define NVID 60 /* 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 */
|
|
|
|
|
|
|
|
|
|
#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
|
|
|
|
|
|
|
|
|
|
#define PLOT_B 1 /* plot type for second movie */
|
|
|
|
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* background */
|
|
|
|
|
|
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
|
|
|
|
|
|
|
|
|
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
|
#define SLOPE 0.15 /* sensitivity of color on wave amplitude */
|
|
|
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
|
|
|
|
#define E_SCALE 200.0 /* 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 210.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -210.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
|
|
|
|
|
|
|
|
|
|
/* For debugging purposes only */
|
|
|
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
|
#define VMAX 10.0 /* max value of wave amplitude */
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
### 1 October 21 - Statistics for a Sinai billiard with Poisson disc obstacles ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_pinball.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.5, 0.1, -0.5*PID, 0.5*PID, configs); `
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -4.0
|
|
|
|
|
#define XMAX 4.0 /* x interval */
|
|
|
|
|
#define YMIN -1.25
|
|
|
|
|
#define YMAX 3.25 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
#define BOXYMIN -1.0
|
|
|
|
|
#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */
|
|
|
|
|
|
|
|
|
|
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table, see global_particles.c */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 21 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 7 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 5000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 40 /* number of circles in x direction */
|
|
|
|
|
#define NCY 10 /* 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 LAMBDA 3.8 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.05 /* second parameter controlling shape of billiard */
|
|
|
|
|
// #define MU 0.034 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 4 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.5 /* 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 0 /* set to 1 to keep trails of the particles */
|
|
|
|
|
#define TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 10900 /* number of frames of movie */
|
|
|
|
|
#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00007 /* integration step */
|
|
|
|
|
#define NVID 150 /* number of iterations between images displayed on screen */
|
|
|
|
|
|
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
|
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
|
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
|
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
|
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
|
|
|
|
|
|
/* Colors and other graphical parameters */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 32 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */
|
|
|
|
|
#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 */
|
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#define LENGTH 0.1 /* length of velocity vectors */
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#define BILLIARD_WIDTH 2 /* width of billiard */
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#define PARTICLE_WIDTH 4 /* width of particles */
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#define FRONT_WIDTH 3 /* width of wave front */
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#define COLOR_TRAJECTORY 8 /* hue for single color */
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#define BLACK 1 /* set to 1 for black background */
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#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
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#define OUTER_COLOR 270.0 /* color outside billiard */
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#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
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#define PAINT_EXT 0 /* set to 1 to paint exterior in other color */
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#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
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#define PAUSE 500 /* number of frames after which to pause */
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#define PSLEEP 5 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1000 /* final sleeping time */
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#define END_FRAMES 100 /* number of still frames at end of movie */
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#define NPATHBINS 200 /* number of bins for path length histogramm */
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#define PATHLMAX 2.5 /* max free path on graph */
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```
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