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2021-07-28 09:24:19 +02:00 · 2021-07-28 09:24:19 +02:00 · e68f0d2c28
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 #define PID 	1.570796327    

 ```
+
+### 14 July 21 - Young's double-slit experiment, evolution of the phase ###
+
+**Program:** `schrodinger.c`
+
+**Initial condition in function `animation()`:** `init_coherent_state(-0.8, 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 	720  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define NX 720          /* number of grid points on x axis */
+#define NY 720          /* number of grid points on y axis */
+
+#define XMIN -1.25
+#define XMAX 1.25	/* x interval */
+#define YMIN -1.25
+#define YMAX 1.25	/* y interval for 9/16 aspect ratio */
+
+#define JULIA_SCALE 1.0 /* scaling for Julia sets */
+
+/* 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 D_EHRENFEST 11  /* Ehrenfest urn type geometry */
+#define D_DISK_GRID 12  /* grid of disks */
+#define D_DISK_HEX 13   /* haxagonl grid of disks */
+#define D_DISK_PERCOL 14    /* random grid of percolation type */
+
+#define D_MENGER 15     /* Menger-Sierpinski carpet */ 
+#define D_JULIA_INT 16  /* interior of Julia set */ 
+#define D_MENGER_ROTATED 17  /* rotated Menger-Sierpinski carpet */
+
+/* Billiard tables for heat equation */
+
+#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
+#define D_MENGER_HEATED 22  /* Menger gasket with different temperatures */
+#define D_MENGER_H_OPEN 23  /* Menger gasket with different temperatures and larger domain */
+#define D_MANDELBROT 24     /* Mandelbrot set */
+#define D_JULIA 25          /* Julia set */
+#define D_MANDELBROT_CIRCLE 26     /* Mandelbrot set with circular conductor */
+
+#define LAMBDA 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 MDEPTH 3            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 15            /* number of grid point for grid of disks */
+#define NGRIDY 20           /* number of grid point for grid of disks */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard in sub_wave.c */
+
+/* Physical patameters of wave equation */
+
+#define DT 0.000000005
+#define HBAR 1.0
+
+/* Boundary conditions */
+
+#define B_COND 0
+
+#define BC_DIRICHLET 0   /* Dirichlet boundary conditions */
+#define BC_PERIODIC 1    /* periodic boundary conditions */
+#define BC_ABSORBING 2   /* absorbing boundary conditions (beta version) */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 1200      /* number of frames of movie */
+#define NVID 1200         /* 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 */
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+
+/* Plot type */
+
+#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          /* black 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 0.75        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 150.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -150.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* Basic math */
+
+#define PI 	3.141592654
+#define DPI 	6.283185307
+#define PID 	1.570796327
+```
+
+### 13 July 21 - Planar wave hitting a percolation-style random arrangement of obstacles ###
+
+**Program:** Variant of `wave_billiard.c`
+
+**Initial condition in function `animation()`:** `init_planar_wave(XMIN + 0.05, 0.0, phi, psi, xy_in);`
+
+```
+#define MOVIE 1         /* set to 1 to generate movie */
+
+/* General geometrical parameters */
+
+#define WINWIDTH 	1280  /* window width */
+#define WINHEIGHT 	720   /* window height */
+
+#define NX 1280          /* number of grid points on x axis */
+#define NY 720          /* number of grid points on y axis */
+
+/* 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 */
+
+#define JULIA_SCALE 1.1 /* scaling for Julia sets */
+
+/* Choice of the billiard table */
+
+#define B_DOMAIN 14      /* choice of domain shape */
+
+#define D_RECTANGLE 0   /* rectangular domain */
+#define D_ELLIPSE 1     /* elliptical domain */
+#define D_STADIUM 2     /* stadium-shaped domain */
+#define D_SINAI 3       /* Sinai billiard */
+#define D_DIAMOND 4     /* diamond-shaped billiard */
+#define D_TRIANGLE 5    /* triangular billiard */
+#define D_FLAT 6        /* flat interface */
+#define D_ANNULUS 7     /* annulus */
+#define D_POLYGON 8     /* polygon */
+#define D_YOUNG 9       /* Young diffraction slits */
+#define D_GRATING 10    /* diffraction grating */
+#define D_EHRENFEST 11  /* Ehrenfest urn type geometry */
+#define D_DISK_GRID 12  /* grid of disks */
+#define D_DISK_RANDOM 13    /* grid of randomly displaces disks */
+#define D_DISK_PERCOL 14    /* random grid of percolation type */
+
+#define D_MENGER 15     /* Menger-Sierpinski carpet */ 
+#define D_JULIA_INT 16  /* interior of Julia set */ 
+
+/* Billiard tables for heat equation */
+
+#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
+#define D_MENGER_HEATED 22  /* Menger gasket with different temperatures */
+#define D_MENGER_H_OPEN 23  /* Menger gasket with different temperatures and larger domain */
+#define D_MANDELBROT 24     /* Mandelbrot set */
+#define D_JULIA 25          /* Julia set */
+#define D_MANDELBROT_CIRCLE 26     /* Mandelbrot set with circular conductor */
+
+#define LAMBDA 1.0	    /* parameter controlling the dimensions of domain */
+#define MU 0.02 	    /* 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 MDEPTH 4            /* depth of computation of Menger gasket */
+#define MRATIO 3            /* ratio defining Menger gasket */
+#define MANDELLEVEL 1000      /* iteration level for Mandelbrot set */
+#define MANDELLIMIT 10.0     /* limit value for approximation of Mandelbrot set */
+#define FOCI 1              /* set to 1 to draw focal points of ellipse */
+#define NGRIDX 30            /* number of grid point for grid of disks */
+#define NGRIDY 40           /* number of grid point for grid of disks */
+
+/* You can add more billiard tables by adapting the functions */
+/* xy_in_billiard and draw_billiard below */
+
+/* Physical parameters of wave equation */
+
+#define OMEGA 0.9           /* frequency of periodic excitation */
+#define COURANT 0.01       /* Courant number */
+#define GAMMA 0.0      /* damping factor in wave equation */
+#define GAMMA_BC 1.0e-4      /* damping factor on boundary */
+#define KAPPA 0.0       /* "elasticity" term enforcing oscillations */
+#define KAPPA_BC 5.0e-4       /* "elasticity" term on absorbing boundary */
+/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
+/* The physical damping coefficient is given by GAMMA/(DT)^2 */
+/* Increasing COURANT speeds up the simulation, but decreases accuracy */
+/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
+
+/* Boundary conditions */
+
+#define B_COND 3
+
+#define BC_DIRICHLET 0   /* Dirichlet boundary conditions */
+#define BC_PERIODIC 1    /* periodic boundary conditions */
+#define BC_ABSORBING 2   /* absorbing boundary conditions (beta version) */
+#define BC_VPER_HABS 3   /* vertically periodic and horizontally absorbing boundary conditions */
+
+
+/* For debugging purposes only */
+#define FLOOR 0         /* set to 1 to limit wave amplitude to VMAX */
+#define VMAX 10.0       /* max value of wave amplitude */
+
+/* Parameters for length and speed of simulation */
+
+#define NSTEPS 6000      /* number of frames of movie */
+#define NVID 40          /* number of iterations between images displayed on screen */
+#define NSEG 100         /* number of segments of boundary */
+
+#define PAUSE 1000         /* number of frames after which to pause */
+#define PSLEEP 1         /* sleep time during pause */
+#define SLEEP1  1        /* initial sleeping time */
+#define SLEEP2  1   /* final sleeping time */
+
+/* Plot type */
+
+#define PLOT 2
+
+#define P_AMPLITUDE 0    /* plot amplitude of wave */
+#define P_ENERGY 1       /* plot energy of wave */
+#define P_MIXED 2        /* plot amplitude in upper half, energy in lower half */
+
+
+/* Color schemes */
+
+#define BLACK 1          /* background */
+
+#define COLOR_SCHEME 1   /* choice of color scheme */
+
+#define C_LUM 0          /* color scheme modifies luminosity (with slow drift of hue) */
+#define C_HUE 1          /* color scheme modifies hue */
+
+#define SCALE 0          /* set to 1 to adjust color scheme to variance of field */
+#define SLOPE 1.0        /* sensitivity of color on wave amplitude */
+#define ATTENUATION 0.0  /* exponential attenuation coefficient of contrast with time */
+#define E_SCALE 1000.0    /* scaling factor for energy representation */
+
+#define COLORHUE 260     /* initial hue of water color for scheme C_LUM */
+#define COLORDRIFT 0.0   /* how much the color hue drifts during the whole simulation */
+#define LUMMEAN 0.5      /* amplitude of luminosity variation for scheme C_LUM */
+#define LUMAMP 0.3       /* amplitude of luminosity variation for scheme C_LUM */
+#define HUEMEAN 240.0    /* mean value of hue for color scheme C_HUE */
+#define HUEAMP -240.0      /* amplitude of variation of hue for color scheme C_HUE */
+
+/* Basic math */
+
+#define PI 	3.141592654
+#define DPI 	6.283185307
+#define PID 	1.570796327
+
+```
+
+### xx July 21 -  ###
+
+**Program:** `x.c`
+
+**Initial condition in function `animation()`:** `xxx`
+
+```
+
+```