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Parameters.md
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Parameters.md
@ -1059,6 +1059,721 @@ updated gradually.
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```
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### 12 July 21 - Expanding perfect wave front on a genus 2 surface, generic initial point ###
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**Program:** `drop_billiard.c`
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**Initial condition in function `animation()`:** `init_drop_config(-1.0 + 0.3*sqrt(2.0), -1.0 + 0.5*sqrt(2.0), 0.0, DPI, configs);`
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```
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#define MOVIE 0 /* 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 13 /* choice of domain shape */
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#define CIRCLE_PATTERN 0 /* pattern of circles */
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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 15 /* number of circles in x direction */
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#define NCY 20 /* number of circles in y direction */
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#define LAMBDA 1.124950941 /* sin(36°)/sin(31.5°) for 5-star shape with 45° angles */
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#define MU 0.1 /* 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 5 /* 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 DRAW_BILLIARD 1 /* set to 1 to draw billiard */
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#define DRAW_CONSTRUCTION_LINES 1 /* 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 NPART 50000 /* number of particles */
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#define NPARTMAX 100000 /* maximal number of particles after resampling */
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#define NSTEPS 5500 /* number of frames of movie */
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#define TIME 40 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.0001 /* integration step */
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#define NVID 20 /* 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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/* For a good quality movie, take for instance TIME = 50, DPHI = 0.0002 */
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/* simulation parameters */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define LPERIODIC 0.1 /* lines longer than this are not drawn (useful for Sinai billiard) */
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#define LCUT 2.0 /* controls the max size of segments not considered as being cut */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
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#define ORDER_COLORS 1 /* set to 1 if colors should be drawn in order */
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/* color and other graphical parameters */
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#define NCOLORS 16 /* number of colors */
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#define COLORSHIFT 200 /* 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 NSEG 100 /* number of segments of boundary */
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#define BILLIARD_WIDTH 4 /* width of billiard */
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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 300.0 /* color outside billiard */
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#define PAINT_INT 1 /* set to 1 to paint interior in other color (for polygon) */
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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 100 /* final sleeping time */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 11 July 21 - Wave crashing into a percolation-style random arrangement of obstacles ###
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**Program:** Variant of `wave_billiard.c`
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**Initial condition in function `animation()`:** `init_wave(-1.5, 0.0, phi, psi, phi_tmp, psi_tmp, xy_in);`
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```
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#define MOVIE 1 /* set to 1 to generate movie */
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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 1.1 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 14 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define D_FLAT 6 /* flat interface */
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#define D_ANNULUS 7 /* annulus */
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#define D_POLYGON 8 /* polygon */
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#define D_YOUNG 9 /* Young diffraction slits */
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#define D_GRATING 10 /* diffraction grating */
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#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
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#define D_DISK_GRID 12 /* grid of disks */
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#define D_DISK_RANDOM 13 /* grid of randomly displaces disks */
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#define D_DISK_PERCOL 14 /* random grid of percolation type */
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#define D_MENGER 15 /* Menger-Sierpinski carpet */
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#define D_JULIA_INT 16 /* interior of Julia set */
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/* Billiard tables for heat equation */
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#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
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#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
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#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
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#define D_MANDELBROT 24 /* Mandelbrot set */
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#define D_JULIA 25 /* Julia set */
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#define D_MANDELBROT_CIRCLE 26 /* Mandelbrot set with circular conductor */
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#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
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#define MU 0.02 /* parameter controlling the dimensions of domain */
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#define NPOLY 8 /* 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 30 /* number of grid point for grid of disks */
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#define NGRIDY 40 /* 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 OMEGA 0.9 /* frequency of periodic excitation */
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#define COURANT 0.01 /* Courant number */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
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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 */
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#define B_COND 2
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#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
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#define BC_PERIODIC 1 /* periodic boundary conditions */
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#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
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#define BC_VPER_HABS 3 /* vertically periodic and horizontally absorbing boundary conditions */
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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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/* Parameters for length and speed of simulation */
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#define NSTEPS 3800 /* number of frames of movie */
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#define NVID 40 /* 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 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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/* Plot type */
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#define PLOT 2
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#define P_AMPLITUDE 0 /* plot amplitude of wave */
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#define P_ENERGY 1 /* plot energy of wave */
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#define P_MIXED 2 /* plot amplitude in upper half, energy in lower half */
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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 */
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#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
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#define C_HUE 1 /* color scheme modifies hue */
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#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 1.0 /* 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 1000.0 /* 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 240.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -240.0 /* amplitude of variation of hue for color scheme C_HUE */
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/* Basic math */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 10 July 21 - Doors and corners, kid - Billiard in a 30 degrees angle ###
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**Program:** Variant of `particle_billiard.c`
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**Initial condition in function `animation()`:** `init_drop_config(-1.2, 0.4, -0.35*PID, -0.15*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 720 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define XMIN -1.25
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#define XMAX 1.25 /* x interval */
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#define YMIN -1.25
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#define YMAX 1.25 /* 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 */
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#define B_DOMAIN 12 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define D_ANNULUS 7 /* annulus */
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#define D_POLYGON 8 /* polygon */
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#define D_REULEAUX 9 /* Reuleaux and star shapes */
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#define D_FLOWER 10 /* Bunimovich flower */
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#define D_ALT_REU 11 /* alternating between star and Reuleaux */
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#define D_ANGLE 12 /* angular sector */
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#define D_LSHAPE 13 /* L-shaped billiard for conical singularity */
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#define LAMBDA 0.166666666666 /* parameter controlling shape of billiard */
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#define MU 0.1 /* 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 6 /* number of sides of polygon */
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#define APOLY 2.0 /* 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 1 /* 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 500 /* 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 NSTEPS 500 /* number of frames of movie */
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#define TIME 1000 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.000006 /* 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 6 /* number of colors */
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#define COLORSHIFT 0 /* hue of initial 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 0.04 /* length of velocity vectors */
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#define BILLIARD_WIDTH 3 /* 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 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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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 9 July 21 - Soft obstacles: a wave encountering a grid of refracting circles ###
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**Program:** Variant of `wave_billiard.c`
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**Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.02, 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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/* 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 1.1 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 13 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define D_FLAT 6 /* flat interface */
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#define D_ANNULUS 7 /* annulus */
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#define D_POLYGON 8 /* polygon */
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#define D_YOUNG 9 /* Young diffraction slits */
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#define D_GRATING 10 /* diffraction grating */
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#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
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#define D_DISK_GRID 12 /* grid of disks */
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#define D_DISK_HEX 13 /* haxagonl grid of disks */
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#define D_MENGER 15 /* Menger-Sierpinski carpet */
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#define D_JULIA_INT 16 /* interior of Julia set */
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/* Billiard tables for heat equation */
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#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
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#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
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#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
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#define D_MANDELBROT 24 /* Mandelbrot set */
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#define D_JULIA 25 /* Julia set */
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#define D_MANDELBROT_CIRCLE 26 /* Mandelbrot set with circular conductor */
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#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
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#define MU 0.025 /* parameter controlling the dimensions of domain */
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#define NPOLY 8 /* 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 15 /* 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 OMEGA 0.9 /* frequency of periodic excitation */
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#define COURANTA 0.01 /* Courant number in medium A */
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#define COURANTB 0.005 /* Courant number in medium B */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
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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 */
|
||||
|
||||
#define B_COND 3
|
||||
|
||||
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
||||
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
||||
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
||||
#define BC_VPER_HABS 3 /* vertically periodic and horizontally absorbing boundary conditions */
|
||||
|
||||
/* 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 */
|
||||
|
||||
/* Parameters for length and speed of simulation */
|
||||
|
||||
#define NSTEPS 5500 /* 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 PAUSE 1000 /* number of frames after which to pause */
|
||||
#define PSLEEP 1 /* sleep time during pause */
|
||||
#define SLEEP1 1 /* initial sleeping time */
|
||||
#define SLEEP2 1 /* final sleeping time */
|
||||
|
||||
/* Plot type */
|
||||
|
||||
#define PLOT 2
|
||||
|
||||
#define P_AMPLITUDE 0 /* plot amplitude of wave */
|
||||
#define P_ENERGY 1 /* plot energy of wave */
|
||||
#define P_MIXED 2 /* plot amplitude in upper half, energy in lower half */
|
||||
|
||||
|
||||
/* Color schemes */
|
||||
|
||||
#define BLACK 1 /* background */
|
||||
|
||||
#define COLOR_SCHEME 1 /* choice of color scheme */
|
||||
|
||||
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
||||
#define C_HUE 1 /* color scheme modifies hue */
|
||||
|
||||
#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 1000.0 /* 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 */
|
||||
|
||||
/* Basic math */
|
||||
|
||||
#define PI 3.141592654
|
||||
#define DPI 6.283185307
|
||||
#define PID 1.570796327
|
||||
|
||||
```
|
||||
|
||||
### 8 July 21 - Expanding perfect wave front on a genus 2 surface ###
|
||||
|
||||
**Program:** `drop_billiard.c`
|
||||
|
||||
**Initial condition in function `animation()`:** `init_drop_config(-0.5, -0.5, 0.0, DPI, configs);`
|
||||
|
||||
```
|
||||
#define MOVIE 1 /* set to 1 to generate movie */
|
||||
|
||||
#define WINWIDTH 1280 /* window width */
|
||||
#define WINHEIGHT 720 /* window height */
|
||||
|
||||
#define XMIN -2.0
|
||||
#define XMAX 2.0 /* x interval */
|
||||
#define YMIN -1.125
|
||||
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
||||
|
||||
#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
|
||||
|
||||
/* Choice of the billiard table */
|
||||
|
||||
#define B_DOMAIN 13 /* choice of domain shape */
|
||||
|
||||
#define D_RECTANGLE 0 /* rectangular domain */
|
||||
#define D_ELLIPSE 1 /* elliptical domain */
|
||||
#define D_STADIUM 2 /* stadium-shaped domain */
|
||||
#define D_SINAI 3 /* Sinai billiard */
|
||||
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
||||
#define D_TRIANGLE 5 /* triangular billiard */
|
||||
#define D_ANNULUS 7 /* annulus */
|
||||
#define D_POLYGON 8 /* polygon */
|
||||
#define D_REULEAUX 9 /* Reuleaux and star shapes */
|
||||
#define D_FLOWER 10 /* Bunimovich flower */
|
||||
#define D_ALT_REU 11 /* alternating between star and Reuleaux */
|
||||
#define D_ANGLE 12 /* angular sector */
|
||||
#define D_LSHAPE 13 /* L-shaped billiard for conical singularity */
|
||||
|
||||
#define LAMBDA 1.124950941 /* sin(36°)/sin(31.5°) for 5-star shape with 45° angles */
|
||||
#define MU 0.1 /* second parameter controlling shape of billiard */
|
||||
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
||||
#define NPOLY 5 /* number of sides of polygon */
|
||||
#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
||||
#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */
|
||||
#define DRAW_CONSTRUCTION_LINES 1 /* set to 1 to draw additional construction lines for billiard */
|
||||
#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
|
||||
|
||||
#define 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 5000 /* number of frames of movie */
|
||||
#define TIME 40 /* time between movie frames, for fluidity of real-time simulation */
|
||||
#define DPHI 0.0001 /* integration step */
|
||||
#define NVID 20 /* 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 16 /* number of colors */
|
||||
#define COLORSHIFT 200 /* hue of initial color */
|
||||
#define RAINBOW_COLOR 1 /* 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 PI 3.141592654
|
||||
#define DPI 6.283185307
|
||||
#define PID 1.570796327
|
||||
|
||||
```
|
||||
|
||||
### 7 July 21 - Planar wave encountering a hexagonal grid (amplitude and energy) ###
|
||||
|
||||
**Program:** `wave_billiard.c`
|
||||
|
||||
**Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.02, 0.0, phi, psi, xy_in);`
|
||||
|
||||
```
|
||||
#define MOVIE 1 /* set to 1 to generate movie */
|
||||
|
||||
/* General geometrical parameters */
|
||||
|
||||
#define WINWIDTH 1280 /* window width */
|
||||
#define WINHEIGHT 720 /* window height */
|
||||
|
||||
#define NX 1280 /* number of grid points on x axis */
|
||||
#define NY 720 /* number of grid points on y axis */
|
||||
|
||||
#define XMIN -2.0
|
||||
#define XMAX 2.0 /* x interval */
|
||||
#define YMIN -1.125
|
||||
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
||||
|
||||
#define JULIA_SCALE 1.1 /* scaling for Julia sets */
|
||||
|
||||
/* Choice of the billiard table */
|
||||
|
||||
#define B_DOMAIN 13 /* choice of domain shape */
|
||||
|
||||
#define D_RECTANGLE 0 /* rectangular domain */
|
||||
#define D_ELLIPSE 1 /* elliptical domain */
|
||||
#define D_STADIUM 2 /* stadium-shaped domain */
|
||||
#define D_SINAI 3 /* Sinai billiard */
|
||||
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
||||
#define D_TRIANGLE 5 /* triangular billiard */
|
||||
#define D_FLAT 6 /* flat interface */
|
||||
#define D_ANNULUS 7 /* annulus */
|
||||
#define D_POLYGON 8 /* polygon */
|
||||
#define D_YOUNG 9 /* Young diffraction slits */
|
||||
#define D_GRATING 10 /* diffraction grating */
|
||||
#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
|
||||
#define D_DISK_GRID 12 /* grid of disks */
|
||||
#define D_DISK_HEX 13 /* haxagonl grid of disks */
|
||||
|
||||
#define D_MENGER 15 /* Menger-Sierpinski carpet */
|
||||
#define D_JULIA_INT 16 /* interior of Julia set */
|
||||
|
||||
/* Billiard tables for heat equation */
|
||||
|
||||
#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
|
||||
#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
|
||||
#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
|
||||
#define D_MANDELBROT 24 /* Mandelbrot set */
|
||||
#define D_JULIA 25 /* Julia set */
|
||||
#define D_MANDELBROT_CIRCLE 26 /* Mandelbrot set with circular conductor */
|
||||
|
||||
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
||||
#define MU 0.025 /* parameter controlling the dimensions of domain */
|
||||
#define NPOLY 8 /* number of sides of polygon */
|
||||
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
||||
#define MDEPTH 4 /* depth of computation of Menger gasket */
|
||||
#define MRATIO 3 /* ratio defining Menger gasket */
|
||||
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
|
||||
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
|
||||
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
||||
#define NGRIDX 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 OMEGA 0.9 /* frequency of periodic excitation */
|
||||
#define COURANTA 0.01 /* Courant number in medium A */
|
||||
#define COURANTB 0.005 /* Courant number in medium B */
|
||||
#define GAMMA 0.0 /* damping factor in wave equation */
|
||||
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
|
||||
/* 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 */
|
||||
|
||||
#define B_COND 3
|
||||
|
||||
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
||||
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
||||
#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
|
||||
#define BC_VPER_HABS 3 /* vertically periodic and horizontally absorbing boundary conditions */
|
||||
|
||||
/* 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 */
|
||||
|
||||
/* Parameters for length and speed of simulation */
|
||||
|
||||
#define NSTEPS 5500 /* 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 PAUSE 1000 /* number of frames after which to pause */
|
||||
#define PSLEEP 1 /* sleep time during pause */
|
||||
#define SLEEP1 1 /* initial sleeping time */
|
||||
#define SLEEP2 1 /* final sleeping time */
|
||||
|
||||
/* Plot type */
|
||||
|
||||
#define PLOT 2
|
||||
|
||||
#define P_AMPLITUDE 0 /* plot amplitude of wave */
|
||||
#define P_ENERGY 1 /* plot energy of wave */
|
||||
#define P_MIXED 2 /* plot amplitude in upper half, energy in lower half */
|
||||
|
||||
|
||||
/* Color schemes */
|
||||
|
||||
#define BLACK 1 /* background */
|
||||
|
||||
#define COLOR_SCHEME 1 /* choice of color scheme */
|
||||
|
||||
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
||||
#define C_HUE 1 /* color scheme modifies hue */
|
||||
|
||||
#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 1000.0 /* 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 */
|
||||
|
||||
/* Basic math */
|
||||
|
||||
#define PI 3.141592654
|
||||
#define DPI 6.283185307
|
||||
#define PID 1.570796327
|
||||
|
||||
```
|
||||
|
||||
|
||||
### xx July 21 - ###
|
||||
|
||||
**Program:** `x.c`
|
||||
|
||||
Loading…
Reference in New Issue
Block a user