3070 lines
143 KiB
Markdown
3070 lines
143 KiB
Markdown
### 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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### 27 September 21 - Statistics for a Sinai billiard with Poisson-distributed obstacles ###
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**Program:** `particle_pinball.c`
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**Initial condition in function `animation()`:** `init_drop_config(0.5, 0.1, -0.5*PID, 0.5*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 21 /* choice of domain shape */
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#define CIRCLE_PATTERN 6 /* 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 40 /* 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 500 /* 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 7700 /* 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 NCOLORS 32 /* number of colors */
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#define COLORSHIFT 0 /* 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 1000 /* 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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### 26 September 21 - A hyperbolic wave reflector ###
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**Program:** `wave_billiard.c`
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**Initial condition in function `animation()`:** `init_circular_wave(0.0, -LAMBDA, phi, psi, xy_in);`
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**Oscillating source:**
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```
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if (i%150 == 149)
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{
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add_circular_wave(1.0, 0.0, LAMBDA, phi, psi, xy_in);
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add_circular_wave(1.0, 0.0, -LAMBDA, phi, psi, xy_in);
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}
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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 34 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 8 /* 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 0.6 /* parameter controlling the dimensions of domain */
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#define MU 0.3 /* parameter controlling the dimensions of domain */
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#define NPOLY 3 /* number of sides of polygon */
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#define APOLY 0.0 /* 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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/* 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 0.01 /* Courant number in medium B */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define GAMMAB 1.0e-6 /* 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 4050 /* number of frames of movie */
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#define NVID 32 /* 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 0.2 /* amplitude of initial condition */
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#define INITIAL_VARIANCE 0.002 /* variance of initial condition */
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#define INITIAL_WAVELENGTH 0.1 /* 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 0 /* plot type for second movie */
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/* Color schemes */
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#define BLACK 1 /* background */
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#define COLOR_SCHEME 1 /* 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 0.08 /* 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 200.0 /* 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 220.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -230.0 /* amplitude of variation of hue for color scheme C_HUE */
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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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### 25 September 21 - A particle version of Penrose’s unilluminable room ###
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**Program:** `particle_billiard.c`
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**Initial condition in function `animation()`:** `init_drop_config(1.4, 0.1, 0.0, DPI, 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 -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 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 16 /* choice of domain shape */
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#define CIRCLE_PATTERN 2 /* 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 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
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#define NCX 30 /* number of circles in x direction */
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#define NCY 20 /* number of circles in y direction */
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#define NPOISSON 500 /* 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 1.5 /* parameter controlling shape of domain */
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#define MU 0.3 /* 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 0.0 /* 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 10000 /* 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 NSTEPS 3500 /* number of frames of movie */
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#define TIME 1200 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.00001 /* 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 NCOLORS 16 /* number of colors */
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#define COLORSHIFT 0 /* hue of initial color */
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#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */
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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 0.01 /* length of velocity vectors */
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#define BILLIARD_WIDTH 2 /* width of billiard */
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#define PARTICLE_WIDTH 2 /* width of particles */
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#define FRONT_WIDTH 3 /* width of wave front */
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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 1 /* set to 1 to paint exterior */
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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 1000 /* final sleeping time */
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```
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### 24 September 21 - A triangular parabolic resonator ###
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**Program:** `wave_billiard.c`
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**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, 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 1 /* 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 32 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 8 /* 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 0.0 /* parameter controlling the dimensions of domain */
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#define MU 0.9 /* parameter controlling the dimensions of domain */
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#define NPOLY 3 /* number of sides of polygon */
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#define APOLY 0.0 /* 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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||
/* You can add more billiard tables by adapting the functions */
|
||
/* xy_in_billiard and draw_billiard below */
|
||
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/* 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 */
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||
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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 0.01 /* Courant number in medium B */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define GAMMAB 1.0e-6 /* 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 */
|
||
#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 */
|
||
/* 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
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/* Parameters for length and speed of simulation */
|
||
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||
#define NSTEPS 4850 /* number of frames of movie */
|
||
#define NVID 30 /* 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 */
|
||
#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 */
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||
#define SLEEP1 1 /* initial sleeping time */
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||
#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 1
|
||
|
||
#define PLOT_B 0 /* plot type for second movie */
|
||
|
||
/* Color schemes */
|
||
|
||
#define BLACK 1 /* background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
||
|
||
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 0.08 /* 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 */
|
||
|
||
```
|
||
|
||
### 23 September 21 - Squaring the circle and circling the square: Wave front in a 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 1.0 /* second parameter controlling shape of billiard */
|
||
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
||
#define NPOLY 4 /* number of sides of polygon */
|
||
#define APOLY 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 50000 /* number of particles */
|
||
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
||
|
||
#define NSTEPS 1200 /* number of frames of movie */
|
||
#define TIME 100 /* time between movie frames, for fluidity of real-time simulation */
|
||
#define DPHI 0.0001 /* 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 */
|
||
/* 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 NCOLORS 12 /* 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 NSEG 100 /* number of segments of boundary */
|
||
#define BILLIARD_WIDTH 4 /* width of billiard */
|
||
#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 300.0 /* color outside billiard */
|
||
#define PAINT_INT 1 /* set to 1 to paint interior in other color (for polygon) */
|
||
|
||
|
||
#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 */
|
||
|
||
```
|
||
|
||
### 22 September 21 - Energy evolution in a Sierpinski carpet 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 -1.777777778
|
||
#define XMAX 1.777777778 /* x interval */
|
||
#define YMIN -1.0
|
||
#define YMAX 1.0 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
|
||
|
||
/* Choice of the billiard table */
|
||
|
||
#define B_DOMAIN 15 /* choice of domain shape, see list in global_pdes.c */
|
||
#define B_DOMAIN_B 15 /* choice of domain shape, see list in global_pdes.c */
|
||
|
||
#define CIRCLE_PATTERN 2 /* pattern of circles, see list in global_pdes.c */
|
||
#define CIRCLE_PATTERN_B 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 4500 /* number of frames of movie */
|
||
#define NVID 25 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 200 /* time after which to start saving frames */
|
||
#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */
|
||
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1 /* final sleeping time */
|
||
#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 */
|
||
|
||
```
|
||
|
||
### 21 September 21 - Statistics for a Sinai billiard with obstacles on a square lattice ###
|
||
|
||
**Program:** `particle_pinball.c`
|
||
|
||
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.5*PID, 0.5*PID, configs);`
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
|
||
#define WINWIDTH 1280 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define XMIN -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 1 /* 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 12300 /* number of frames of movie */
|
||
#define TIME 3000 /* 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 */
|
||
#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 ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
||
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 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 150 /* number of bins for path length histogramm */
|
||
#define PATHLMAX 1.23 /* max free path on graph */
|
||
|
||
```
|
||
|
||
### 20 September 21 - Adding inertia: Mangroves swaying in 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 0.002 /* frequency of periodic excitation */
|
||
#define K_BC 3.0 /* spatial period of periodic excitation in y direction */
|
||
#define KX_BC 30.0 /* spatial period of periodic excitation in x direction */
|
||
#define KY_BC 10.0 /* spatial period of periodic excitation in y direction */
|
||
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
||
#define COURANT 0.02 /* Courant number */
|
||
#define COURANTB 0.01 /* Courant number in medium B */
|
||
#define GAMMA 2.0e-6 /* damping factor in wave equation */
|
||
#define GAMMAB 2.5e-4 /* damping factor in wave equation */
|
||
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
||
#define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */
|
||
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
||
#define KAPPAB 1.0e-6 /* "elasticity" term enforcing oscillations */
|
||
#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
|
||
#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
|
||
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
|
||
/* The physical damping coefficient is given by GAMMA/(DT)^2 */
|
||
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
|
||
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
|
||
|
||
/* Boundary conditions, see list in global_pdes.c */
|
||
|
||
#define B_COND 3
|
||
|
||
/* Parameters for length and speed of simulation */
|
||
|
||
// #define NSTEPS 1000 /* number of frames of movie */
|
||
#define NSTEPS 4500 /* 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 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 1.1e-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 DT_MANGROVE 0.1 /* time step for mangrove displacement */
|
||
#define KSPRING 0.25 /* spring constant of mangroves */
|
||
#define KWAVE 2.0 /* constant in force due to wave gradient */
|
||
#define DXMAX 0.02 /* max displacement of mangrove in one time step */
|
||
#define L_DETACH 0.2 /* spring length beyond which mangroves detach */
|
||
#define DAMP_MANGROVE 0.2 /* damping coefficient of mangroves */
|
||
#define MANGROVE_MASS 1.5 /* mass of mangrove of radius MU */
|
||
|
||
/* For debugging purposes only */
|
||
#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */
|
||
#define VMAX 10.0 /* max value of wave amplitude */
|
||
|
||
```
|
||
|
||
### 19 September 21 - Penrose’s solution to the illumination problem, 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 0 /* 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 8000 /* number of frames of movie */
|
||
#define NVID 30 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define 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 1
|
||
|
||
#define PLOT_B 0 /* plot type for second movie */
|
||
|
||
/* Color schemes */
|
||
|
||
#define BLACK 1 /* background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
||
|
||
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 0.08 /* 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 */
|
||
|
||
```
|
||
|
||
### 18 September 21 - Let's see some statistics: Collisions and free paths in a Sinai billiard ###
|
||
|
||
**Program:** `particle_pinball.c`
|
||
|
||
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.5*PID, 0.5*PID, configs);`
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
|
||
#define WINWIDTH 1280 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define XMIN -4.0
|
||
#define XMAX 4.0 /* x interval */
|
||
#define YMIN -1.25
|
||
#define YMAX 3.25 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
||
|
||
/* Choice of the billiard table, see global_particles.c */
|
||
|
||
#define B_DOMAIN 21 /* choice of domain shape */
|
||
|
||
#define CIRCLE_PATTERN 21 /* pattern of circles */
|
||
|
||
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
||
|
||
#define NMAXCIRCLES 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 24 /* number of circles in y direction */
|
||
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
||
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
|
||
|
||
#define LAMBDA 3.3 /* 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 16150 /* number of frames of movie */
|
||
#define TIME 3000 /* 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 */
|
||
#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 0 /* hue for single color */
|
||
#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 ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
||
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 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 150 /* number of bins for path length histogramm */
|
||
#define PATHLMAX 1.23 /* max free path on graph */
|
||
|
||
```
|
||
|
||
### 17 September 21 - A hexogonal 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 6 /* number of sides of polygon */
|
||
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
|
||
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
||
#define MRATIO 3 /* ratio defining Menger gasket */
|
||
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
||
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
||
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
||
#define NGRIDX 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 3950 /* 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 1
|
||
|
||
#define PLOT_B 0 /* plot type for second movie */
|
||
|
||
/* Color schemes */
|
||
|
||
#define BLACK 1 /* background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
||
|
||
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 0.08 /* 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 -240.0 /* amplitude of variation of hue for color scheme C_HUE */
|
||
|
||
/* For debugging purposes only */
|
||
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
||
#define VMAX 10.0 /* max value of wave amplitude */
|
||
|
||
```
|
||
|
||
### 16 September 21 - Penrose’s solution to the illumination problem ###
|
||
|
||
**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 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 9800 /* number of frames of movie */
|
||
#define NVID 30 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 0 /* time after which to start saving frames */
|
||
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1 /* final sleeping time */
|
||
#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 1
|
||
|
||
#define PLOT_B 0 /* plot type for second movie */
|
||
|
||
/* Color schemes */
|
||
|
||
#define BLACK 1 /* background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
||
|
||
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 0.1 /* 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 */
|
||
|
||
```
|
||
|
||
### 15 September 21 - Comparing 7 pinball configurations with parallel incoming particles ###
|
||
|
||
**Program:** `particle_pinball.c`
|
||
|
||
**Initial condition in function `animation()`:** `init_line_config(-1.25, -0.75, -1.25, 0.75, 0.25, configs); `
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
|
||
#define WINWIDTH 1280 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define XMIN -2.0
|
||
#define XMAX 2.0 /* x interval */
|
||
#define YMIN -1.125
|
||
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
||
|
||
/* Choice of the billiard table, see global_particles.c */
|
||
|
||
#define B_DOMAIN 20 /* choice of domain shape */
|
||
|
||
#define CIRCLE_PATTERN 3 /* pattern of circles */
|
||
|
||
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
||
|
||
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
||
#define NCX 15 /* number of circles in x direction */
|
||
#define NCY 20 /* number of circles in y direction */
|
||
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
||
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
|
||
|
||
#define LAMBDA 0.8 /* parameter controlling shape of domain */
|
||
#define MU 0.03 /* second parameter controlling shape of billiard */
|
||
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
||
#define NPOLY 6 /* number of sides of polygon */
|
||
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
|
||
#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */
|
||
#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */
|
||
#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
|
||
|
||
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
||
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
||
|
||
/* Simulation parameters */
|
||
|
||
#define NPART 1000 /* number of particles */
|
||
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
||
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
||
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
||
#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
|
||
#define SHOWTRAILS 1 /* set to 1 to keep trails of the particles */
|
||
|
||
#define NSTEPS 1500 /* number of frames of movie */
|
||
#define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */
|
||
#define DPHI 0.00001 /* integration step */
|
||
#define NVID 150 /* number of iterations between images displayed on screen */
|
||
|
||
/* Decreasing TIME accelerates the animation and the movie */
|
||
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
||
/* However, increasing DPHI too much deterioriates quality of simulation */
|
||
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
||
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
||
|
||
/* Colors and other graphical parameters */
|
||
|
||
#define NCOLORS 10 /* number of colors */
|
||
#define COLORSHIFT 0 /* hue of initial color */
|
||
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
|
||
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define LENGTH 0.02 /* length of velocity vectors */
|
||
#define BILLIARD_WIDTH 2 /* width of billiard */
|
||
#define PARTICLE_WIDTH 2 /* width of particles */
|
||
#define FRONT_WIDTH 3 /* width of wave front */
|
||
|
||
#define BLACK 1 /* set to 1 for black background */
|
||
#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
|
||
#define OUTER_COLOR 270.0 /* color outside billiard */
|
||
#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
|
||
#define ERASE_OUTSIDE 0 /* set to 1 to erase outside of rectangular domain */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1000 /* final sleeping time */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
```
|
||
|
||
### 14 September 21 - A moving non-eroding mangrove ###
|
||
|
||
**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 0.002 /* frequency of periodic excitation */
|
||
#define K_BC 3.0 /* spatial period of periodic excitation in y direction */
|
||
#define KX_BC 30.0 /* spatial period of periodic excitation in x direction */
|
||
#define KY_BC 10.0 /* spatial period of periodic excitation in y direction */
|
||
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
||
#define COURANT 0.02 /* Courant number */
|
||
#define COURANTB 0.00666 /* Courant number in medium B */
|
||
#define GAMMA 2.0e-6 /* damping factor in wave equation */
|
||
#define GAMMAB 1.0e-4 /* damping factor in wave equation */
|
||
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
||
#define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */
|
||
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
||
#define KAPPAB 1.0e-6 /* "elasticity" term enforcing oscillations */
|
||
#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
|
||
#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
|
||
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
|
||
/* The physical damping coefficient is given by GAMMA/(DT)^2 */
|
||
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
|
||
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
|
||
|
||
/* Boundary conditions, see list in global_pdes.c */
|
||
|
||
#define B_COND 3
|
||
|
||
/* Parameters for length and speed of simulation */
|
||
|
||
#define NSTEPS 7000 /* 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 */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 0
|
||
|
||
/* Color schemes */
|
||
|
||
#define BLACK 1 /* background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
||
|
||
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
|
||
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
||
#define E_SCALE 2500.0 /* scaling factor for energy representation */
|
||
|
||
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
||
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
||
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
|
||
#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */
|
||
|
||
/* mangrove properties */
|
||
|
||
#define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */
|
||
#define MANGROVE_HUE_MAX -50.0 /* color of saturated mangrove */
|
||
#define MANGROVE_EMAX 1.1e-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 KSPRING 0.45 /* spring constant of mangroves */
|
||
#define KWAVE 1.5 /* constant in force due to wave gradient */
|
||
#define DXMAX 0.02 /* max displacement of mangrove in one time step */
|
||
#define L_DETACH 0.11 /* spring length beyond which mangroves detach */
|
||
|
||
/* 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 */
|
||
|
||
```
|
||
|
||
### 13 September 21 - 13/09/21 "Energy evolution in a “golden spiral” 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 11 /* 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 4200 /* number of frames of movie */
|
||
#define NVID 25 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 200 /* time after which to start saving frames */
|
||
#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */
|
||
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1 /* final sleeping time */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 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 */
|
||
|
||
```
|
||
|
||
### 12 September 21 - A sunflower pinball ###
|
||
|
||
**Program:** `particle_pinball.c`
|
||
|
||
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.5*PID, 0.5*PID, configs);`
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
|
||
#define WINWIDTH 1280 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define XMIN -2.0
|
||
#define XMAX 2.0 /* x interval */
|
||
#define YMIN -1.125
|
||
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
||
|
||
/* Choice of the billiard table, see global_particles.c */
|
||
|
||
#define B_DOMAIN 21 /* choice of domain shape */
|
||
|
||
#define CIRCLE_PATTERN 21 /* pattern of circles */
|
||
|
||
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
||
|
||
#define NMAXCIRCLES 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 24 /* number of circles in y direction */
|
||
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
||
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
|
||
|
||
#define LAMBDA 1.8 /* 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 0.5 /* 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 1 /* 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 14200 /* number of frames of movie */
|
||
#define TIME 3000 /* time between movie frames, for fluidity of real-time simulation */
|
||
#define DPHI 0.000035 /* 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 */
|
||
#define LENGTH 0.05 /* length of velocity vectors */
|
||
#define BILLIARD_WIDTH 2 /* width of billiard */
|
||
#define PARTICLE_WIDTH 2 /* width of particles */
|
||
#define FRONT_WIDTH 3 /* width of wave front */
|
||
#define COLOR_TRAJECTORY 18 /* 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 ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
||
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1000 /* final sleeping time */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
```
|
||
|
||
### 11 September 21 - A resonator made of four parabolas ###
|
||
|
||
**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 31 /* 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 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 5800 /* number of frames of movie */
|
||
#define NVID 30 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 0 /* time after which to start saving frames */
|
||
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1 /* final sleeping time */
|
||
#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 1
|
||
|
||
#define PLOT_B 0 /* plot type for second movie */
|
||
|
||
/* Color schemes */
|
||
|
||
#define BLACK 1 /* background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
||
|
||
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 0.05 /* 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 */
|
||
|
||
```
|
||
|
||
### 10 September 21 - Energy evolution in a randomized square 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 2 /* 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 3600 /* number of frames of movie */
|
||
#define NVID 25 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 200 /* time after which to start saving frames */
|
||
#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */
|
||
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1 /* final sleeping time */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 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 */
|
||
|
||
```
|
||
|
||
### 9 September 21 - A quantum parabolic resonator ###
|
||
|
||
**Program:** `schrodinger.c`
|
||
|
||
**Initial condition in function `animation()`:** `init_coherent_state(0.5, 0.0, 40.0, 0.0, 0.25, phi, psi, xy_in);`
|
||
|
||
**In function `init_wave()`:** `if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.005)*cos(-sqrt(dist2)/0.1);`
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
|
||
/* General geometrical parameters */
|
||
|
||
#define WINWIDTH 720 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define NX 720 /* number of grid points on x axis */
|
||
#define NY 720 /* number of grid points on y axis */
|
||
|
||
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
||
/* but will multiply run time by 4 */
|
||
|
||
#define XMIN -2.0
|
||
#define XMAX 2.0 /* x interval */
|
||
#define YMIN -2.0
|
||
#define YMAX 2.0 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
|
||
|
||
/* Choice of the billiard table, see list in global_pdes.c */
|
||
|
||
#define B_DOMAIN 19 /* choice of domain shape */
|
||
|
||
#define CIRCLE_PATTERN 0 /* pattern of circles, see list in global_pdes.c */
|
||
|
||
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
||
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
||
|
||
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
|
||
#define MU 1.75 /* parameter controlling the dimensions of domain */
|
||
#define NPOLY 6 /* number of sides of polygon */
|
||
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
||
#define MDEPTH 3 /* depth of computation of Menger gasket */
|
||
#define MRATIO 3 /* ratio defining Menger gasket */
|
||
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
||
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
||
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
||
#define NGRIDX 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 in sub_wave.c */
|
||
|
||
/* Physical patameters of wave equation */
|
||
|
||
#define DT 0.00000001
|
||
#define HBAR 1.0
|
||
|
||
/* Boundary conditions, see list in global_pdes.c */
|
||
|
||
#define B_COND 1
|
||
|
||
/* Parameters for length and speed of simulation */
|
||
|
||
#define NSTEPS 1400 /* number of frames of movie */
|
||
#define NVID 2000 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#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 */
|
||
|
||
/* 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 */
|
||
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 11
|
||
|
||
|
||
/* Color schemes, see list in global_pdes.c */
|
||
|
||
#define BLACK 1 /* black background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme */
|
||
|
||
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
|
||
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
||
|
||
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
||
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
||
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define HUEMEAN 150.0 /* mean value of hue for color scheme C_HUE */
|
||
#define HUEAMP -150.0 /* amplitude of variation of hue for color scheme C_HUE */
|
||
|
||
```
|
||
|
||
### 8 September 21 - Video #200: “It’s alive, it’s alive!” Now the mangroves are moving… ###
|
||
|
||
**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 0.002 /* frequency of periodic excitation */
|
||
#define K_BC 3.0 /* spatial period of periodic excitation in y direction */
|
||
#define KX_BC 30.0 /* spatial period of periodic excitation in x direction */
|
||
#define KY_BC 10.0 /* spatial period of periodic excitation in y direction */
|
||
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
|
||
#define COURANT 0.02 /* Courant number */
|
||
#define COURANTB 0.00666 /* Courant number in medium B */
|
||
#define GAMMA 2.0e-6 /* damping factor in wave equation */
|
||
#define GAMMAB 1.0e-4 /* damping factor in wave equation */
|
||
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
|
||
#define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */
|
||
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
||
#define KAPPAB 1.0e-6 /* "elasticity" term enforcing oscillations */
|
||
#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
|
||
#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
|
||
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
|
||
/* The physical damping coefficient is given by GAMMA/(DT)^2 */
|
||
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
|
||
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
|
||
|
||
/* Boundary conditions, see list in global_pdes.c */
|
||
|
||
#define B_COND 3
|
||
|
||
/* Parameters for length and speed of simulation */
|
||
|
||
// #define NSTEPS 500 /* number of frames of movie */
|
||
#define NSTEPS 6300 /* number of frames of movie */
|
||
#define NVID 35 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 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 */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 0
|
||
|
||
/* Color schemes */
|
||
|
||
#define BLACK 1 /* background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
||
|
||
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
|
||
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
||
#define E_SCALE 2500.0 /* scaling factor for energy representation */
|
||
|
||
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
||
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
||
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
|
||
#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */
|
||
|
||
/* mangrove properties */
|
||
|
||
#define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */
|
||
#define MANGROVE_HUE_MAX -50.0 /* color of saturated mangrove */
|
||
#define MANGROVE_EMAX 1.1e-3 /* max energy for mangrove to survive */
|
||
|
||
#define RANDOM_RADIUS 1 /* set to 1 for random circle radius */
|
||
#define MOVE_MANGROVES 1 /* set to 1 for mobile mangroves */
|
||
#define KSPRING 1.0 /* spring constant of mangroves */
|
||
#define KWAVE 1.2 /* constant in force due to wave gradient */
|
||
#define DXMAX 0.015 /* max displacement of mangrove in one time step */
|
||
|
||
/* For debugging purposes only */
|
||
#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */
|
||
#define VMAX 10.0 /* max value of wave amplitude */
|
||
|
||
```
|
||
|
||
### 7 September 21 - A photon bouncing in an amorphous material ###
|
||
|
||
**Program:** `particle_pinball.c`
|
||
|
||
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.5*PID, 0.5*PID, configs);`
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
|
||
#define WINWIDTH 1280 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define XMIN -2.0
|
||
#define XMAX 2.0 /* x interval */
|
||
#define YMIN -1.125
|
||
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
||
|
||
/* Choice of the billiard table, see global_particles.c */
|
||
|
||
#define B_DOMAIN 21 /* choice of domain shape */
|
||
|
||
#define CIRCLE_PATTERN 21 /* pattern of circles */
|
||
|
||
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
||
|
||
#define NMAXCIRCLES 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 24 /* number of circles in y direction */
|
||
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
||
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
|
||
|
||
#define LAMBDA 1.6 /* 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 0.5 /* 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 1 /* 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 16600 /* number of frames of movie */
|
||
#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */
|
||
#define DPHI 0.00004 /* integration step */
|
||
#define NVID 150 /* number of iterations between images displayed on screen */
|
||
|
||
/* Decreasing TIME accelerates the animation and the movie */
|
||
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
||
/* However, increasing DPHI too much deterioriates quality of simulation */
|
||
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
||
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
||
|
||
/* Colors and other graphical parameters */
|
||
|
||
#define NCOLORS 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 */
|
||
#define LENGTH 0.5 /* 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 COLOR_TRAJECTORY 24 /* 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 ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
||
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1000 /* final sleeping time */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
```
|
||
|
||
### 6 September 21 - Energy evolution in a Poisson disc 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 0 /* 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 8 /* pattern of circles, see list in global_pdes.c */
|
||
#define CIRCLE_PATTERN_B 8 /* pattern of circles, see list in global_pdes.c */
|
||
|
||
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
||
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
||
|
||
#define LAMBDA 0.75 /* 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 3200 /* number of frames of movie */
|
||
#define NVID 25 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 200 /* time after which to start saving frames */
|
||
#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */
|
||
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1 /* final sleeping time */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 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 September 21 - A Sinai pinball with finite horizon ###
|
||
|
||
**Program:** `particle_pinball.c`
|
||
|
||
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, -0.5*PID, 0.5*PID, configs); `
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
|
||
#define WINWIDTH 1280 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define XMIN -2.0
|
||
#define XMAX 2.0 /* x interval */
|
||
#define YMIN -1.125
|
||
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
||
|
||
/* Choice of the billiard table, see global_particles.c */
|
||
|
||
#define B_DOMAIN 21 /* choice of domain shape */
|
||
|
||
#define CIRCLE_PATTERN 21 /* pattern of circles */
|
||
|
||
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
||
|
||
#define NMAXCIRCLES 2000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
||
#define NCX 50 /* number of circles in x direction */
|
||
#define NCY 26 /* number of circles in y direction */
|
||
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
||
|
||
#define LAMBDA 1.68 /* parameter controlling shape of domain */
|
||
#define MU 0.036 /* 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 0.5 /* 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 1 /* 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 13000 /* number of frames of movie */
|
||
#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */
|
||
#define DPHI 0.00004 /* integration step */
|
||
#define NVID 150 /* number of iterations between images displayed on screen */
|
||
|
||
/* Decreasing TIME accelerates the animation and the movie */
|
||
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
||
/* However, increasing DPHI too much deterioriates quality of simulation */
|
||
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
||
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
||
|
||
/* Colors and other graphical parameters */
|
||
|
||
#define NCOLORS 128 /* 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 0.045 /* length of velocity vectors */
|
||
#define BILLIARD_WIDTH 2 /* width of billiard */
|
||
#define PARTICLE_WIDTH 2 /* width of particles */
|
||
#define FRONT_WIDTH 3 /* width of wave front */
|
||
#define COLOR_TRAJECTORY 90 /* 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 ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1000 /* final sleeping time */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
```
|
||
|
||
### 4 September 21 - Energy evolution in a square grid wave protection ###
|
||
|
||
**Program:** `wave_energy.c` (variant of `wave_comparison.c`)
|
||
|
||
**Initial condition in function `animation()`:** `int_planar_wave_comp(XMIN + 0.015, 0.0, phi, psi, xy_in);`
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
|
||
#define WINWIDTH 1280 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define NX 1280 /* number of grid points on x axis */
|
||
#define NY 720 /* number of grid points on y axis */
|
||
|
||
#define XMIN -2.0
|
||
#define XMAX 2.0 /* x interval */
|
||
#define YMIN -1.125
|
||
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
|
||
|
||
/* Choice of the billiard table */
|
||
|
||
#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */
|
||
#define B_DOMAIN_B 20 /* choice of domain shape, see list in global_pdes.c */
|
||
|
||
#define CIRCLE_PATTERN 0 /* pattern of circles, see list in global_pdes.c */
|
||
#define CIRCLE_PATTERN_B 0 /* pattern of circles, see list in global_pdes.c */
|
||
|
||
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
|
||
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
||
|
||
#define 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 2800 /* number of frames of movie */
|
||
#define NVID 25 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 200 /* time after which to start saving frames */
|
||
#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */
|
||
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1 /* final sleeping time */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 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 */
|
||
|
||
```
|
||
|
||
### 3 September 21 - Illustrating the butterfly effect with a laser, long version without pauses ###
|
||
|
||
**Program:** `particle_pinball_angles.c` (variant of `particle_billiard.c`)
|
||
|
||
**Initial condition in function `animation()`:** `angle0 = 0.2 + 2.4815e-6, x0 = -1.1, y0 = -0.5625;`
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
|
||
#define WINWIDTH 1280 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define XMIN -2.0
|
||
#define XMAX 2.0 /* x interval */
|
||
#define YMIN -1.125
|
||
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
||
|
||
/* Choice of the billiard table, see global_particles.c */
|
||
|
||
#define B_DOMAIN 20 /* choice of domain shape */
|
||
|
||
#define CIRCLE_PATTERN 3 /* pattern of circles */
|
||
|
||
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
|
||
|
||
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
||
#define NCX 3 /* number of circles in x direction */
|
||
#define NCY 8 /* number of circles in y direction */
|
||
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
|
||
|
||
#define LAMBDA 0.5 /* parameter controlling shape of domain */
|
||
#define MU 0.11 /* second parameter controlling shape of billiard */
|
||
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
||
#define NPOLY 6 /* number of sides of polygon */
|
||
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
|
||
#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */
|
||
#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */
|
||
#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
|
||
|
||
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
||
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
||
|
||
/* Simulation parameters */
|
||
|
||
#define NPART 1 /* number of particles */
|
||
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
||
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
||
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
||
#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
|
||
#define SHOWTRAILS 1 /* set to 1 to keep trails of the particles */
|
||
|
||
#define NSTEPS 6000 /* number of frames of movie */
|
||
#define TIME 4200 /* time between movie frames, for fluidity of real-time simulation */
|
||
#define DPHI 0.00001 /* integration step */
|
||
#define NVID 150 /* number of iterations between images displayed on screen */
|
||
|
||
/* Decreasing TIME accelerates the animation and the movie */
|
||
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
||
/* However, increasing DPHI too much deterioriates quality of simulation */
|
||
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
||
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
||
|
||
/* Colors and other graphical parameters */
|
||
|
||
#define NCOLORS 128 /* number of colors */
|
||
#define COLORSHIFT 0 /* hue of initial color */
|
||
#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */
|
||
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define LENGTH 0.02 /* length of velocity vectors */
|
||
#define BILLIARD_WIDTH 2 /* width of billiard */
|
||
#define PARTICLE_WIDTH 3 /* width of particles */
|
||
#define FRONT_WIDTH 3 /* width of wave front */
|
||
|
||
#define BLACK 1 /* set to 1 for black background */
|
||
#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
|
||
#define OUTER_COLOR 270.0 /* color outside billiard */
|
||
#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
|
||
#define ERASE_OUTSIDE 0 /* set to 1 to erase outside of rectangular domain */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1000 /* final sleeping time */
|
||
#define END_FRAMES 50 /* number of still frames at end of movie */
|
||
|
||
#define LUM_ATTENUATION 0.005 /* luminosity attenuation */
|
||
|
||
```
|
||
|
||
### 2 September 21 - An elliptical resonator ###
|
||
|
||
**Program:** `wave_billiard.c`
|
||
|
||
**Initial condition in function `animation()`:** ``
|
||
|
||
```
|
||
#define MOVIE 1 /* set to 1 to generate movie */
|
||
#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */
|
||
|
||
/* General geometrical parameters */
|
||
|
||
#define WINWIDTH 720 /* window width */
|
||
#define WINHEIGHT 720 /* window height */
|
||
|
||
#define NX 720 /* number of grid points on x axis */
|
||
#define NY 720 /* number of grid points on y axis */
|
||
|
||
#define XMIN -1.6
|
||
#define XMAX 1.6 /* x interval */
|
||
#define YMIN -1.6
|
||
#define YMAX 1.6 /* y interval for 9/16 aspect ratio */
|
||
|
||
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
|
||
|
||
/* Choice of the billiard table */
|
||
|
||
#define B_DOMAIN 1 /* choice of domain shape, see list in global_pdes.c */
|
||
|
||
#define CIRCLE_PATTERN 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 1.25 /* 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 1400 /* number of frames of movie */
|
||
#define NVID 45 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 0 /* time after which to start saving frames */
|
||
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1 /* final sleeping time */
|
||
#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 1
|
||
|
||
#define PLOT_B 0 /* plot type for second movie */
|
||
|
||
/* Color schemes */
|
||
|
||
#define BLACK 1 /* background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
||
|
||
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
|
||
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
||
#define E_SCALE 500.0 /* scaling factor for energy representation */
|
||
|
||
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
||
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
||
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
|
||
#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */
|
||
|
||
/* For debugging purposes only */
|
||
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
||
#define VMAX 10.0 /* max value of wave amplitude */
|
||
|
||
```
|
||
|
||
### 1 September 21 - A parabolic resonating cavity ###
|
||
|
||
**Program:** `wave_billiard.c`
|
||
|
||
**Initial condition in function `animation()`:** `init_wave(-LAMBDA, 0.0, phi, psi, xy_in);`
|
||
|
||
**In `init_wave()`:** `if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01)`
|
||
|
||
```
|
||
#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 */
|
||
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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 8 /* 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 0.0 /* parameter controlling the dimensions of domain */
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#define MU 1.25 /* parameter controlling the dimensions of domain */
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#define NPOLY 3 /* number of sides of polygon */
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#define APOLY 1.0 /* 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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/* 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 0.01 /* Courant number in medium B */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define GAMMAB 1.0e-6 /* 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 */
|
||
#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 25 /* number of iterations between images displayed on screen */
|
||
#define NSEG 100 /* number of segments of boundary */
|
||
#define INITIAL_TIME 0 /* time after which to start saving frames */
|
||
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
|
||
|
||
#define PAUSE 1000 /* number of frames after which to pause */
|
||
#define PSLEEP 1 /* sleep time during pause */
|
||
#define SLEEP1 1 /* initial sleeping time */
|
||
#define SLEEP2 1 /* final sleeping time */
|
||
#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
|
||
#define END_FRAMES 100 /* number of still frames at end of movie */
|
||
|
||
/* Plot type, see list in global_pdes.c */
|
||
|
||
#define PLOT 1
|
||
|
||
#define PLOT_B 0 /* plot type for second movie */
|
||
|
||
/* Color schemes */
|
||
|
||
#define BLACK 1 /* background */
|
||
|
||
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
|
||
|
||
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
|
||
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
|
||
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
||
#define E_SCALE 500.0 /* scaling factor for energy representation */
|
||
|
||
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
||
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
||
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
||
#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
|
||
#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */
|
||
|
||
/* For debugging purposes only */
|
||
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
||
#define VMAX 10.0 /* max value of wave amplitude */
|
||
|
||
```
|
||
|