2021-07-29 14:43:56 +02:00
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### Parameter values for YouTube simulations ###
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Created by **Nils Berglund** and optimized by **Marco Mancini**
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C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund
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Below are parameter values used for different simulations, as well as initial conditions used in
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function animation. Some simulations use variants of the published code. The list is going to be
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updated gradually. Some constants have been moved to global files in later versions.
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### 31 May 21 - Video #100: 100 000 particles in a concave hectogon billiard ###
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**Program:** `particle_billiard.c`
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**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.5, 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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/* Choice of the billiard table */
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#define B_DOMAIN 9 /* 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 LAMBDA 0.04588546
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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 100 /* 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 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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#define NPART 100000 /* 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 4000 /* number of frames of movie */
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#define TIME 125 /* 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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#define NCOLORS -7 /* number of colors */
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#define COLORSHIFT 220 /* hue of initial color */
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#define NSEG 100 /* number of segments of boundary */
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#define LENGTH 0.003 /* length of velocity vectors */
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#define BILLIARD_WIDTH 4 /* 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 1 /* set to 1 to paint interior in other color (for polygon) */
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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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#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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### 30 May 21 - The quantum Ehrenfest model ###
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**Program:** `schrodinger.c`
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**Initial condition in function `animation()`:** `init_coherent_state(-1.2, 0.0, 8.0, 8.0, 0.08, 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 640 /* number of grid points on x axis */
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#define NY 360 /* number of grid points on y axis */
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/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
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/* but will multiply run time by 4 */
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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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/* Choice of the billiard table */
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#define B_DOMAIN 11 /* 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 LAMBDA 0.8 /* parameter controlling the dimensions of domain */
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#define MU 0.05 /* parameter controlling the dimensions of domain */
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#define NPOLY 6 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
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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 patameters of wave equation */
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#define DT 0.00000002
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#define HBAR 1.0
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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 5230 //7500 /* number of frames of movie */
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#define NVID 1000 /* 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 0
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#define P_MODULE 0 /* plot module of wave function squared */
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#define P_PHASE 1 /* plot phase of wave function */
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#define P_REAL 2 /* plot real part */
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#define P_IMAGINARY 3 /* plot imaginary part */
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/* Boundary conditions */
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#define B_COND 1
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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 */
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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 C_PHASE 2 /* color scheme shows phase */
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#define SCALE 1 /* 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 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 150.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -150.0 /* 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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### 29 May 21 - A quantum Sinai billiard: probability density ###
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**Program:** `schrodinger.c`
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**Initial condition in function `animation()`:** `init_coherent_state(-1.2, 0.0, 20.0, 0.0, 0.2, 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 640 /* number of grid points on x axis */
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#define NY 360 /* number of grid points on y axis */
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/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
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/* but will multiply run time by 4 */
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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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/* Choice of the billiard table */
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#define B_DOMAIN 3 /* 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 LAMBDA 0.2 /* parameter controlling the dimensions of domain */
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#define MU 0.05 /* parameter controlling the dimensions of domain */
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#define NPOLY 6 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
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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 patameters of wave equation */
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#define DT 0.00000002
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#define HBAR 1.0
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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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/* 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 3500 //7500 /* number of frames of movie */
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#define NVID 750 /* 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 1
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#define P_MODULE 0 /* plot module of wave function squared */
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#define P_PHASE 1 /* plot phase of wave function */
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#define P_REAL 2 /* plot real part */
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#define P_IMAGINARY 3 /* plot imaginary part */
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/* Boundary conditions */
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#define B_COND 1
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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 */
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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 C_PHASE 2 /* color scheme shows phase */
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#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 1.2 /* 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 COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
|
|
|
|
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
|
|
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define HUEMEAN 130.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -150.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 28 May 21 - The Vitruvian pond: wave front in a 5-pointed star ###
|
|
|
|
|
|
|
|
|
|
**Program:** `drop_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.1, 0.0, DPI, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -1.8
|
|
|
|
|
#define XMAX 1.8 /* x interval */
|
|
|
|
|
#define YMIN -0.91
|
|
|
|
|
#define YMAX 1.115 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 9 /* 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 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 RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
|
|
|
|
|
#define NPART 300000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 500000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define LPERIODIC 1.0 /* lines longer than this are not drawn (useful for Sinai billiard) */
|
|
|
|
|
#define LCUT 2000.0 /* 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 */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 4000 /* number of frames of movie */
|
|
|
|
|
#define TIME 15 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.0001 /* integration step */
|
|
|
|
|
#define NVID 10 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NCOLORS 10 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 200 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define BILLIARD_WIDTH 6 /* 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) */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#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
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 27 May 21 - A quantum Sinai billiard, phase evolution ###
|
|
|
|
|
|
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(-1.2, 0.0, 20.0, 0.0, 0.2, 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 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 3 /* 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 LAMBDA 0.2 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.05 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define DT 0.00000002
|
|
|
|
|
#define HBAR 1.0
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 3500 /* number of frames of movie */
|
|
|
|
|
#define NVID 750 /* 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 1
|
|
|
|
|
|
|
|
|
|
#define P_MODULE 0 /* plot module of wave function squared */
|
|
|
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
|
|
|
#define P_REAL 2 /* plot real part */
|
|
|
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
|
|
|
|
|
|
/* Boundary conditions */
|
|
|
|
|
|
|
|
|
|
#define B_COND 1
|
|
|
|
|
|
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
|
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
|
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions */
|
|
|
|
|
|
|
|
|
|
/* 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 C_PHASE 2 /* color scheme shows phase */
|
|
|
|
|
|
|
|
|
|
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
|
#define SLOPE 1.2 /* sensitivity of color on wave amplitude */
|
|
|
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
|
|
|
|
|
|
|
|
|
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
|
|
|
|
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
|
|
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define HUEMEAN 130.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -150.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 26 May 21 - 50 pence for your thoughts - Billiard in a 7-sided Reuleaux t̶r̶i̶a̶n̶g̶l̶e̶ polygon ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `alpha = 3.0*PI/7.0; init_sym_drop_config(-0.99, 0.0, -alpha, alpha, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 0 /* 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 */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 9 /* 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 LAMBDA -1.949855824 /* 7-sided Reuleaux triangle */
|
|
|
|
|
#define MU 0.1 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 7 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
|
|
|
|
|
|
|
|
|
/* Simulation parameters */
|
|
|
|
|
|
|
|
|
|
#define NPART 10000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
|
|
|
|
#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 9000 /* number of frames of movie */
|
|
|
|
|
#define TIME 125 /* 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 -7 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 220 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.01 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 4 /* 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 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 1000 /* final sleeping time */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 25 May 21 - Young's double-slit experiment for a quantum particle, phase representation ###
|
|
|
|
|
|
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(-1.2, 0.0, 20.0, 0.0, 0.25, 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 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 9 /* 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 LAMBDA 0.3 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.05 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define DT 0.00000002
|
|
|
|
|
#define HBAR 1.0
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 4000 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 750 /* 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 1
|
|
|
|
|
|
|
|
|
|
#define P_MODULE 0 /* plot module of wave function squared */
|
|
|
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
|
|
|
#define P_REAL 2 /* plot real part */
|
|
|
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
|
|
|
|
|
|
/* Boundary conditions */
|
|
|
|
|
|
|
|
|
|
#define B_COND 1
|
|
|
|
|
|
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
|
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
|
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions */
|
|
|
|
|
|
|
|
|
|
/* 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 C_PHASE 2 /* color scheme shows phase */
|
|
|
|
|
|
|
|
|
|
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
|
#define SLOPE 1.5 /* sensitivity of color on wave amplitude */
|
|
|
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
|
|
|
|
|
|
|
|
|
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
|
|
|
|
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
|
|
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define HUEMEAN 130.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -130.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 24 May 21 - The redemption of the pentagon ###
|
|
|
|
|
|
|
|
|
|
**Program:** `drop_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, PID, DPI+PID, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -1.8
|
|
|
|
|
#define XMAX 1.8 /* x interval */
|
|
|
|
|
#define YMIN -0.91
|
|
|
|
|
#define YMAX 1.115 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 9 /* 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 LAMBDA 3.75738973 /* sin(36°)/sin(9°) for 5-star shape with 90° 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 RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
|
|
|
|
|
#define NPART 100000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define LPERIODIC 1.0 /* lines longer than this are not drawn (useful for Sinai billiard) */
|
|
|
|
|
#define LCUT 1000.0 /* 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 NSTEPS 4500 /* number of frames of movie */
|
|
|
|
|
#define TIME 20 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.0001 /* integration step */
|
|
|
|
|
#define NVID 10 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NCOLORS 10 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 270 /* hue of initial color */
|
|
|
|
|
#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) */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#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
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 23 May 21 - Young's double-slit experiment for a quantum particle ###
|
|
|
|
|
|
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(-1.2, 0.0, 20.0, 0.0, 0.25, 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 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 9 /* 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 LAMBDA 0.3 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.05 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define DT 0.00000002
|
|
|
|
|
#define HBAR 1.0
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 4000 /* number of frames of movie */
|
|
|
|
|
#define NVID 750 /* 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 0
|
|
|
|
|
|
|
|
|
|
#define P_MODULE 0 /* plot module of wave function squared */
|
|
|
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
|
|
|
#define P_REAL 2 /* plot real part */
|
|
|
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
|
|
|
|
|
|
/* Boundary conditions */
|
|
|
|
|
|
|
|
|
|
#define B_COND 1
|
|
|
|
|
|
|
|
|
|
#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
|
|
|
|
|
#define BC_PERIODIC 1 /* periodic boundary conditions */
|
|
|
|
|
#define BC_ABSORBING 2 /* absorbing boundary conditions */
|
|
|
|
|
|
|
|
|
|
/* 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 C_PHASE 2 /* color scheme shows phase */
|
|
|
|
|
|
|
|
|
|
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
|
#define SLOPE 1.5 /* sensitivity of color on wave amplitude */
|
|
|
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
|
|
|
|
|
|
|
|
|
|
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
|
|
|
|
|
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
|
|
|
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
|
|
|
|
|
#define HUEMEAN 130.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -130.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 22 May 21 - Billiard in a Reuleaux triangle ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_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 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -1.8
|
|
|
|
|
#define XMAX 1.8 /* x interval */
|
|
|
|
|
#define YMIN -0.91
|
|
|
|
|
#define YMAX 1.115 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 9 /* 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 LAMBDA -1.73205080756888 /* -sqrt(3) for triangle tiling plane */
|
|
|
|
|
#define MU 0.1 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 3 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 0.3333333333333333333 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
|
|
|
|
|
|
|
|
|
#define NPART 10000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 50000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
|
|
|
|
#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 9000 /* number of frames of movie */
|
|
|
|
|
#define TIME 600 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00001 /* integration step */
|
|
|
|
|
#define NVID 75 /* number of iterations between images displayed on screen */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 14 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.007 /* length of velocity vectors */
|
|
|
|
|
|
|
|
|
|
#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 1 /* set to 1 to paint interior in other color (for polygon) */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#define PAUSE 1000 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1000 /* final sleeping time */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 21 May 21 - Phasers locked on target: Phase evolution in the quantum hexagonal billiard ###
|
|
|
|
|
|
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 0.0, 10.0, 0.1, 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 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 8 /* 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 LAMBDA 1.5 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define DT 0.00000002
|
|
|
|
|
#define HBAR 1.0
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 6000 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 750 /* 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 1
|
|
|
|
|
|
|
|
|
|
#define P_MODULE 0 /* plot module of wave function squared */
|
|
|
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
|
|
|
#define P_REAL 2 /* plot real part */
|
|
|
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
|
|
|
|
|
|
/* 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 C_PHASE 2 /* color scheme shows phase */
|
|
|
|
|
|
|
|
|
|
#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 200.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -120.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
2021-07-29 17:10:55 +02:00
|
|
|
### 20 May 21 - How to distinguish an icosikaipentagon from a circle ###
|
|
|
|
|
|
|
|
|
|
**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 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 8 /* 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 LAMBDA 1.0 /* parameter controlling shape of billiard */
|
|
|
|
|
#define MU 0.1 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 25 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
|
|
|
|
|
#define NPART 40000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define LPERIODIC 1.0 /* 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 NSTEPS 8000 /* number of frames of movie */
|
|
|
|
|
#define TIME 50 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.0001 /* integration step */
|
|
|
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NCOLORS -6 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 240 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
|
|
|
#define COLOR_OUTSIDE 1 /* 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) */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#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
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 19 May 21 - The hexagonal quantum billiard: probability density ###
|
|
|
|
|
|
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 10.0, 0.0, 0.1, phi, psi, xy_in);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
/* General geometrical parameters */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 8 /* 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 LAMBDA 1.5 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define DT 0.00000005
|
|
|
|
|
#define HBAR 1.0
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 6000 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 750 /* 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 0
|
|
|
|
|
|
|
|
|
|
#define P_MODULE 0 /* plot module of wave function squared */
|
|
|
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
|
|
|
#define P_REAL 2 /* plot real part */
|
|
|
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
|
|
|
|
|
|
/* 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 C_PHASE 2 /* color scheme shows phase */
|
|
|
|
|
|
|
|
|
|
#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 200.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -120.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 18 May 21 - Diamonds are a nerd's best friend - A finite horizon Sinai billiard ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_line_config(0.0, 0.1, 0.0, 0.3, 0.0, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 9 /* 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 LAMBDA 10.0 /* parameter controlling shape of billiard */
|
|
|
|
|
#define MU 0.1 /* 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 RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
|
|
|
|
|
|
|
|
|
#define NPART 5000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 50000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
|
|
|
|
#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 10000 /* number of frames of movie */
|
|
|
|
|
#define TIME 500 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00001 /* integration step */
|
|
|
|
|
#define NVID 75 /* number of iterations between images displayed on screen */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 14 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.007 /* length of velocity vectors */
|
|
|
|
|
|
|
|
|
|
#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 1 /* set to 1 to paint interior in other color (for polygon) */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#define PAUSE 1000 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1000 /* final sleeping time */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 17 May 21 - The hexagonal quantum billiard: real part of the wave function ###
|
|
|
|
|
|
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 0.0, 10.0, 0.1, 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 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 8 /* 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 LAMBDA 1.5 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define DT 0.00000002
|
|
|
|
|
#define HBAR 1.0
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 6000 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 750 /* 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_MODULE 0 /* plot module of wave function squared */
|
|
|
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
|
|
|
#define P_REAL 2 /* plot real part */
|
|
|
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
|
|
|
|
|
|
/* 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 C_PHASE 2 /* color scheme shows phase */
|
|
|
|
|
|
|
|
|
|
#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 200.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -120.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 16 May 21 - Hexing the circle: are hexagons really bestagons? ###
|
|
|
|
|
|
|
|
|
|
**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 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 8 /* 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 LAMBDA 1.0 /* parameter controlling shape of billiard */
|
|
|
|
|
#define MU 0.1 /* 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 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
|
|
|
|
|
#define NPART 40000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define LPERIODIC 1.0 /* 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 NSTEPS 5175 /* number of frames of movie */
|
|
|
|
|
#define TIME 50 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.0001 /* integration step */
|
|
|
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NCOLORS -12 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 240 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
|
|
|
#define COLOR_OUTSIDE 1 /* set to 1 for colored outside */
|
|
|
|
|
#define OUTER_COLOR 270.0 /* color outside billiard */
|
|
|
|
|
#define PAINT_INT 1 /* set to 1 to paint interior in other color (for polygon) */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#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
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 15 May 21 - Scarred for life, no compensation - Schrödinger's equation in a stadium ###
|
|
|
|
|
|
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 0.0, 5.0, 0.03, 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 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 2 /* 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 LAMBDA 1.5 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define DT 0.00000002
|
|
|
|
|
#define HBAR 1.0
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 6000 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 500 /* 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 0
|
|
|
|
|
|
|
|
|
|
#define P_MODULE 0 /* plot module of wave function squared */
|
|
|
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
|
|
|
#define P_REAL 2 /* plot real part */
|
|
|
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
|
|
|
|
|
|
/* 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 C_PHASE 2 /* color scheme shows phase */
|
|
|
|
|
|
|
|
|
|
#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 160.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -120.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 14 May 21 - What's going on with the pentagon? ###
|
|
|
|
|
|
|
|
|
|
**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 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 8 /* 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 LAMBDA 1.0 /* parameter controlling shape of billiard */
|
|
|
|
|
#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 RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
|
|
|
|
|
#define NPART 10000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 20000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define LPERIODIC 1.0 /* 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 NSTEPS 5000 /* number of frames of movie */
|
|
|
|
|
#define TIME 50 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.0001 /* integration step */
|
|
|
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NCOLORS 8 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 180 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
|
|
|
#define PAINT_INT 1 /* set to 1 to paint interior in other color (for polygon) */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#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
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 13 May 21 - Quantum of focus: Schrödinger's equation in an elliptical domain ###
|
|
|
|
|
|
|
|
|
|
**Program:** `schrodinger.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_coherent_state(-0.5, 0.0, 1.0, 1.0, 0.03, phi, psi, xy_in);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
/* General geometrical parameters */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 1 /* 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 LAMBDA 1.5 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define DT 0.00000002
|
|
|
|
|
#define HBAR 1.0
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
/* 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 4000 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 500 /* 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 0
|
|
|
|
|
|
|
|
|
|
#define P_MODULE 0 /* plot module of wave function squared */
|
|
|
|
|
#define P_PHASE 1 /* plot phase of wave function */
|
|
|
|
|
#define P_REAL 2 /* plot real part */
|
|
|
|
|
#define P_IMAGINARY 3 /* plot imaginary part */
|
|
|
|
|
|
|
|
|
|
/* 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 C_PHASE 2 /* color scheme shows phase */
|
|
|
|
|
|
|
|
|
|
#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 120.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP -120.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 12 May 21 - The eccentric annular billiard, or how to mix a Pan Galactic Gargle Blaster ###
|
|
|
|
|
|
|
|
|
|
**Program:** `particle_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_line_config(-0.7, 0.2, -0.7, 0.7, 0.0, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 0 /* 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 */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 7 /* 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 LAMBDA 0.5 /* parameter controlling shape of billiard */
|
|
|
|
|
// #define LAMBDA 1.73205080756888 /* sqrt(3) for triangle tiling plane */
|
|
|
|
|
#define MU 0.1 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
|
|
|
|
|
|
|
|
|
#define NPART 50 /* number of particles */
|
|
|
|
|
// #define NPART 50 /* number of particles */
|
|
|
|
|
#define NPARTMAX 50000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
|
|
|
|
#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 7500 /* number of frames of movie */
|
|
|
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
// #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 */
|
|
|
|
|
// #define NVID 500 /* number of iterations between images displayed on screen */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 5 /* number of colors */
|
|
|
|
|
// #define NCOLORS 14 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.05 /* length of velocity vectors */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#define PAUSE 1000 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1000 /* final sleeping time */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 11 May 21 - Diffraction of a wave on a grating ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(-1.0, 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 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 10 /* 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 LAMBDA 0.08 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.02 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define OMEGA 0.7 /* frequency of periodic excitation */
|
|
|
|
|
#define COURANT 0.01 /* Courant number */
|
|
|
|
|
#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 */
|
|
|
|
|
|
|
|
|
|
/* 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 4500 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 50 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define PAUSE 100 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1 /* final sleeping time */
|
|
|
|
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
|
|
|
|
|
|
#define COLOR_SCHEME 0 /* 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 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 270 /* 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 60.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 10 May 21 - A perfect wave front in the Bermuda triangle billiard ###
|
|
|
|
|
|
2021-07-29 17:40:51 +02:00
|
|
|
**Program:** `drop_billiard.c`
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 17:40:51 +02:00
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, 0.0, DPI, configs);`
|
2021-07-29 17:10:55 +02:00
|
|
|
|
|
|
|
|
```
|
2021-07-29 17:40:51 +02:00
|
|
|
#define MOVIE 0 /* 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 */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 8 /* 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 LAMBDA 1.0 /* parameter controlling shape of billiard */
|
|
|
|
|
#define MU 0.1 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 3 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
|
|
|
|
|
#define NPART 10000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 20000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define LPERIODIC 0.01 /* lines longer than this are not drawn (useful for Sinai billiard) */
|
|
|
|
|
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
|
|
|
|
#define MARGIN 0.02 /* distance above which points of curve are not drawn */
|
|
|
|
|
#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 5000 /* number of frames of movie */
|
|
|
|
|
#define TIME 150 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.0001 /* integration step */
|
|
|
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NCOLORS 10 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 60 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#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
|
2021-07-29 17:10:55 +02:00
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 9 May 21 - Waves around a conical singularity ###
|
|
|
|
|
|
2021-07-29 17:40:51 +02:00
|
|
|
**Program:** Special code `wave_conical.c`, not yet incorporated
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 17:40:51 +02:00
|
|
|
Main changes:
|
2021-07-29 17:10:55 +02:00
|
|
|
|
|
|
|
|
```
|
2021-07-29 17:40:51 +02:00
|
|
|
#define D_CONICAL 999 /* L-shape with conical singularity */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.3 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define COURANT 0.01 /* Courant number */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define KAPPA 5.0e-7 /* "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 */
|
|
|
|
|
|
|
|
|
|
/* 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 7500 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 50 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define 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 */
|
|
|
|
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
|
|
|
|
|
|
#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 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 120.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP 120.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
int xy_in_billiard(x, y)
|
|
|
|
|
/* returns 1 if (x,y) represents a point in the billiard */
|
|
|
|
|
double x, y;
|
|
|
|
|
{
|
|
|
|
|
double l2, r2, omega, c, angle;
|
|
|
|
|
int k, condition;
|
|
|
|
|
|
|
|
|
|
switch (B_DOMAIN) {
|
|
|
|
|
case D_CONICAL:
|
|
|
|
|
{
|
|
|
|
|
if ((vabs(x) < 1.0)&&(y > -1.0)&&(y < 0.0)) return(1);
|
|
|
|
|
else if ((vabs(y) < 1.0)&&(x > -1.0)&&(x < 0.0)) return(1);
|
|
|
|
|
else return(0);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
void draw_segment(x1, y1, x2, y2, h, s, l)
|
|
|
|
|
/* draw line segment (x1,y1)-(x2,y2) in color (h,s,l) */
|
|
|
|
|
double x1, y1, x2, y2, h, s, l;
|
|
|
|
|
{
|
|
|
|
|
double rgb[3], pos[2];
|
|
|
|
|
|
|
|
|
|
glBegin(GL_LINE_STRIP);
|
|
|
|
|
hsl_to_rgb(h, s, l, rgb);
|
|
|
|
|
glColor3f(rgb[0], rgb[1], rgb[2]);
|
|
|
|
|
xy_to_pos(x1, y1, pos);
|
|
|
|
|
glVertex2d(pos[0], pos[1]);
|
|
|
|
|
xy_to_pos(x2, y2, pos);
|
|
|
|
|
glVertex2d(pos[0], pos[1]);
|
|
|
|
|
glEnd();
|
|
|
|
|
}
|
|
|
|
|
|
2021-07-29 17:40:51 +02:00
|
|
|
void draw_billiard() /* draws the billiard boundary */
|
|
|
|
|
{
|
|
|
|
|
double x0, x, y, phi, r = 0.01, pos[2], pos1[2], alpha, dphi, omega, rgb[3];
|
|
|
|
|
int i;
|
|
|
|
|
|
|
|
|
|
glColor3f(0.0, 0.0, 0.0);
|
|
|
|
|
glLineWidth(5);
|
|
|
|
|
|
|
|
|
|
glEnable(GL_LINE_SMOOTH);
|
|
|
|
|
|
|
|
|
|
switch (B_DOMAIN) {
|
|
|
|
|
case (D_CONICAL):
|
|
|
|
|
{
|
|
|
|
|
draw_segment(-1.0, -1.0, 0.0, -1.0, 0.0, 1.0, 0.5);
|
|
|
|
|
draw_segment(-1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.5);
|
|
|
|
|
draw_segment(-1.0, -1.0, -1.0, 0.0, 220.0, 1.0, 0.5);
|
|
|
|
|
draw_segment(1.0, -1.0, 1.0, 0.0, 220.0, 1.0, 0.5);
|
|
|
|
|
draw_segment(0.0, -1.0, 1.0, -1.0, 60.0, 1.0, 0.5);
|
|
|
|
|
draw_segment(0.0, 0.0, 1.0, 0.0, 60.0, 1.0, 0.5);
|
|
|
|
|
draw_segment(-1.0, 0.0, -1.0, 1.0, 180.0, 1.0, 0.5);
|
|
|
|
|
draw_segment(0.0, 0.0, 0.0, 1.0, 180.0, 1.0, 0.5);
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
void evolve_wave(phi, psi, xy_in)
|
|
|
|
|
/* time step of field evolution */
|
|
|
|
|
/* phi is value of field at time t, psi at time t-1 */
|
|
|
|
|
double *phi[NX], *psi[NX]; short int *xy_in[NX];
|
|
|
|
|
{
|
|
|
|
|
int i, j, iplus, iminus, jplus, jminus, i1, i2, i3, j1, j2, j3, ij[2];
|
|
|
|
|
double delta, x, y;
|
|
|
|
|
|
|
|
|
|
/* boundaries */
|
|
|
|
|
xy_to_ij(-1.0, -1.0, ij);
|
|
|
|
|
i1 = ij[0]; j1 = ij[1];
|
|
|
|
|
xy_to_ij(0.0, 0.0, ij);
|
|
|
|
|
i2 = ij[0]; j2 = ij[1];
|
|
|
|
|
xy_to_ij(1.0, 1.0, ij);
|
|
|
|
|
i3 = ij[0]; j3 = ij[1];
|
|
|
|
|
|
|
|
|
|
#pragma omp parallel for private(i,j,iplus,iminus,delta,x,y)
|
|
|
|
|
for (i=0; i<NX; i++){
|
|
|
|
|
for (j=0; j<NY; j++){
|
|
|
|
|
if (xy_in[i][j]){
|
|
|
|
|
/* boundary conditions */
|
|
|
|
|
iplus = i+1;
|
|
|
|
|
if ((iplus == i2)&&(j > j2)) iplus = i1+1;
|
|
|
|
|
else if ((iplus == i3)&&(j <= j2)) iplus = i1+1;
|
|
|
|
|
|
|
|
|
|
iminus = i-1;
|
|
|
|
|
if ((iminus == i1)&&(j > j2)) iminus = i2-1;
|
|
|
|
|
else if ((iminus == i1)&&(j <= j2)) iminus = i3-1;
|
|
|
|
|
|
|
|
|
|
jplus = j+1;
|
|
|
|
|
if ((jplus == j2)&&(i > i2)) jplus = j1+1;
|
|
|
|
|
else if ((jplus == j3)&&(i <= i2)) jplus = j1+1;
|
|
|
|
|
|
|
|
|
|
jminus = j-1;
|
|
|
|
|
if ((jminus == j1)&&(i > i2)) jminus = j2-1;
|
|
|
|
|
else if ((jminus == j1)&&(i <= i2)) jminus = j3-1;
|
|
|
|
|
|
|
|
|
|
/* discretized Laplacian */
|
|
|
|
|
delta = phi[iplus][j] + phi[iminus][j] + phi[i][jplus] + phi[i][jminus] - 4.0*phi[i][j];
|
|
|
|
|
|
|
|
|
|
x = phi[i][j];
|
|
|
|
|
y = psi[i][j];
|
|
|
|
|
|
|
|
|
|
/* evolve phi */
|
|
|
|
|
phi[i][j] = -y + 2*x + courant2*delta - KAPPA*x - GAMMA*(x-y);
|
|
|
|
|
|
|
|
|
|
psi[i][j] = x;
|
|
|
|
|
|
|
|
|
|
if (FLOOR)
|
|
|
|
|
{
|
|
|
|
|
if (phi[i][j] > VMAX) phi[i][j] = VMAX;
|
|
|
|
|
if (phi[i][j] < -VMAX) phi[i][j] = -VMAX;
|
|
|
|
|
if (psi[i][j] > VMAX) psi[i][j] = VMAX;
|
|
|
|
|
if (psi[i][j] < -VMAX) psi[i][j] = -VMAX;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
2021-07-29 18:20:32 +02:00
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 8 May 21 - If life gives you a lemon billiard, use it to make lemonade! ###
|
2021-07-29 17:40:51 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
**Program:** `particle_billiard.c`
|
2021-07-29 17:40:51 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
**Initial condition in function `animation()`:** `init_line_config(0.0, -0.7, 0.0, 0.7, 0.0, configs);`
|
2021-07-29 17:10:55 +02:00
|
|
|
|
|
|
|
|
```
|
2021-07-29 18:20:32 +02:00
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#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 */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
/* Choice of the billiard table */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define B_DOMAIN 2 /* 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 LAMBDA -0.8 /* parameter controlling shape of billiard */
|
|
|
|
|
#define MU 0.1 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
|
|
|
|
|
|
|
|
|
#define NPART 10000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 50000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
|
|
|
|
#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 5000 /* number of frames of movie */
|
|
|
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00001 /* integration step */
|
|
|
|
|
#define NVID 750 /* number of iterations between images displayed on screen */
|
|
|
|
|
|
|
|
|
|
#define NCOLORS 10 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.05 /* length of velocity vectors */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#define PAUSE 1000 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1000 /* final sleeping time */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
2021-07-29 17:10:55 +02:00
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 7 May 21 - Diffraction - Young's double-slit experiment with waves ###
|
|
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
**Program:** `wave_billiard.c`
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
**Initial condition in function `animation()`:** `init_wave(-1.0, 0.0, phi, psi, xy_in);`
|
2021-07-29 17:10:55 +02:00
|
|
|
|
|
|
|
|
```
|
2021-07-29 18:20:32 +02:00
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
/* General geometrical parameters */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#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 */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
/* Choice of the billiard table */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define B_DOMAIN 9 /* choice of domain shape */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#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 */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define LAMBDA 0.5 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define MU 0.04 /* 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 FOCI 1 /* set to 1 to draw focal points of ellipse */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
/* Physical patameters of wave equation */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define OMEGA 0.7 /* frequency of periodic excitation */
|
|
|
|
|
#define COURANT 0.01 /* Courant number */
|
|
|
|
|
#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 */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
/* 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 */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
/* Parameters for length and speed of simulation */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define NSTEPS 4000 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 50 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define PAUSE 100 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1 /* final sleeping time */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
/* Color schemes */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
|
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
#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 220.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP 60.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
2021-07-29 17:10:55 +02:00
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
### 6 May 21 - Wave fronts in a square: Dr Jekyll shouting from Hyde Park Corner ###
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
**Program:** `drop_billiard.c`
|
2021-07-29 17:10:55 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(1.0, 1.0, PI, 3.0*DPI, configs);`
|
2021-07-29 17:10:55 +02:00
|
|
|
|
|
|
|
|
```
|
2021-07-29 18:20:32 +02:00
|
|
|
#define MOVIE 0 /* 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 */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 0 /* 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 LAMBDA 1.0 /* parameter controlling shape of billiard */
|
|
|
|
|
#define MU 0.1 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 8 /* number of sides of polygon */
|
|
|
|
|
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
|
|
|
|
|
#define NPART 20000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 20000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define LPERIODIC 2.0 /* lines longer than this are not drawn (useful for Sinai billiard) */
|
|
|
|
|
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
|
|
|
|
#define MARGIN 1.0 /* distance above which points of curve are not drawn */
|
|
|
|
|
#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 10000 /* 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 100 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NCOLORS 20 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 90 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#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
|
2021-07-29 17:10:55 +02:00
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
### 5 May 21 - Winter is coming ###
|
2021-07-29 14:43:56 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
**Program:** `wave_billiard.c`
|
2021-07-29 14:43:56 +02:00
|
|
|
|
2021-07-29 18:20:32 +02:00
|
|
|
**Initial condition in function `animation()`:** `init_wave(0.0, 0.0, phi, psi, xy_in);`
|
2021-07-29 14:43:56 +02:00
|
|
|
|
|
|
|
|
```
|
2021-07-29 18:20:32 +02:00
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
/* General geometrical parameters */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 8 /* 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 LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 6 /* number of sides of polygon */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define COURANT 0.01 /* Courant number */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define KAPPA 5.0e-7 /* "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 */
|
|
|
|
|
|
|
|
|
|
/* 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 4575 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 50 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define 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 */
|
|
|
|
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
|
|
|
|
|
|
#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 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 235.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP 60.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 4 May 21 - Why the Bunimovich stadium is chaotic ###
|
|
|
|
|
|
2021-08-01 15:26:37 +02:00
|
|
|
**Program:** `particle_billiard.c` (adapted to August 1 version)
|
2021-07-29 18:20:32 +02:00
|
|
|
|
2021-08-01 15:26:37 +02:00
|
|
|
**Initial condition in function `animation()`:** `init_line_config(0.0, -0.05, 0.0, 0.05, 0.0, configs);`
|
2021-07-29 18:20:32 +02:00
|
|
|
|
|
|
|
|
```
|
2021-08-01 15:26:37 +02:00
|
|
|
#define MOVIE 0 /* 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 2 /* choice of domain shape */
|
|
|
|
|
|
|
|
|
|
#define CIRCLE_PATTERN 2 /* pattern of circles */
|
|
|
|
|
|
|
|
|
|
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
|
|
|
|
|
#define NCX 15 /* number of circles in x direction */
|
|
|
|
|
#define NCY 20 /* number of circles in y direction */
|
|
|
|
|
|
|
|
|
|
#define LAMBDA 0.5 /* parameter controlling shape of domain */
|
|
|
|
|
#define MU 0.035 /* second parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
#define NPOLY 9 /* 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 0 /* set to 1 to draw additional construction lines for billiard */
|
|
|
|
|
#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
|
|
|
|
|
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
#define DEBUG 0 /* draw trajectories, for debugging purposes */
|
|
|
|
|
|
|
|
|
|
/* Simulation parameters */
|
|
|
|
|
|
|
|
|
|
#define NPART 5000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 100000 /* maximal number of particles after resampling */
|
|
|
|
|
#define LMAX 0.01 /* minimal segment length triggering resampling */
|
|
|
|
|
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
|
|
|
|
|
#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 3000 /* number of frames of movie */
|
|
|
|
|
#define TIME 750 /* time between movie frames, for fluidity of real-time simulation */
|
|
|
|
|
#define DPHI 0.00002 /* 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 0 /* set to 1 to use different colors for all particles */
|
|
|
|
|
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
#define LENGTH 0.05 /* length of velocity vectors */
|
|
|
|
|
#define BILLIARD_WIDTH 3 /* width of billiard */
|
|
|
|
|
#define PARTICLE_WIDTH 2 /* width of particles */
|
|
|
|
|
#define FRONT_WIDTH 3 /* width of wave front */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
|
|
|
#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
|
|
|
|
|
#define OUTER_COLOR 270.0 /* color outside billiard */
|
|
|
|
|
#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#define 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 */
|
2021-07-29 18:20:32 +02:00
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 3 May 21 - The Revelation of Sonmi 451 ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c`
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(0.0, 0.6, phi, psi, xy_in);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
/* General geometrical parameters */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 7 /* 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 LAMBDA 0.5 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define NPOLY 6 /* number of sides of polygon */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define COURANT 0.01 /* Courant number */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define KAPPA 1.0e-8 /* "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 */
|
|
|
|
|
|
|
|
|
|
/* 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 7900 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 75 /* 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 */
|
|
|
|
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
|
|
|
|
|
|
#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 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 310.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP 110.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 2 May 21 - Triangulating the circle ###
|
|
|
|
|
|
|
|
|
|
**Program:** `drop_billiard.c` (old version)
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(0.0, -0.5, 0.0, DPI, configs);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 5 /* 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 LAMBDA 1.73205080756888 /* parameter controlling shape of billiard */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
|
|
|
|
|
|
#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 NPART 10000 /* number of particles */
|
|
|
|
|
#define NPARTMAX 20000 /* 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 MARGIN 1.0 /* distance above which points of curve are not drawn */
|
|
|
|
|
#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
|
|
|
|
|
|
|
|
|
|
#define NSTEPS 5000 /* number of frames of movie */
|
|
|
|
|
#define TIME 75 /* 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 */
|
|
|
|
|
/* TIME shoud be a multiple of NVID */
|
|
|
|
|
#define NCOLORS 10 /* number of colors */
|
|
|
|
|
#define COLORSHIFT 200 /* hue of initial color */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define BLACK 1 /* set to 1 for black background */
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/* 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 */
|
|
|
|
|
|
|
|
|
|
#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
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
### 1 May 21 - Snell's law of refraction ###
|
|
|
|
|
|
|
|
|
|
**Program:** `wave_billiard.c` (old version, should be remade by using option `TWOSPEED 1`)
|
|
|
|
|
|
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(-1.0, 0.5, phi, psi, xy_in);`
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
|
|
|
|
|
|
|
|
/* General geometrical parameters */
|
|
|
|
|
|
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
|
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
|
|
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
|
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
|
|
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
|
|
|
/* but will multiply run time by 4 */
|
|
|
|
|
|
|
|
|
|
#define XMIN -2.0
|
|
|
|
|
#define XMAX 2.0 /* x interval */
|
|
|
|
|
#define YMIN -1.125
|
|
|
|
|
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
|
|
|
|
|
|
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
|
|
|
|
|
|
#define B_DOMAIN 6 /* 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 LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
|
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
|
|
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
|
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
|
|
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
|
|
|
|
|
|
#define COURANT 0.01 /* Courant number */
|
|
|
|
|
#define COURANT1 0.005 /* Courant number in second domain */
|
|
|
|
|
#define GAMMA 0.0 /* damping factor in wave equation */
|
|
|
|
|
#define KAPPA 5.0e-9 /* "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 */
|
|
|
|
|
|
|
|
|
|
/* 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 8000 //7500 /* number of frames of movie */
|
|
|
|
|
#define NVID 75 /* number of iterations between images displayed on screen */
|
|
|
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
|
|
|
|
|
|
#define PAUSE 100 /* number of frames after which to pause */
|
|
|
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
|
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
|
|
|
#define SLEEP2 1 /* final sleeping time */
|
|
|
|
|
|
|
|
|
|
/* Color schemes */
|
|
|
|
|
|
|
|
|
|
#define COLOR_SCHEME 0 /* 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 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 330.0 /* mean value of hue for color scheme C_HUE */
|
|
|
|
|
#define HUEAMP 90.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
|
|
|
|
|
|
/* Basic math */
|
|
|
|
|
|
|
|
|
|
#define PI 3.141592654
|
|
|
|
|
#define DPI 6.283185307
|
|
|
|
|
#define PID 1.570796327
|
2021-07-29 14:43:56 +02:00
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
