From 3a22a5a48eddcb57dbb2ee1aedc6d907922623bf Mon Sep 17 00:00:00 2001 From: Nils Berglund <83530463+nilsberglund-orleans@users.noreply.github.com> Date: Mon, 1 Aug 2022 22:34:51 +0200 Subject: [PATCH] Add files via upload --- Parameters_July22.md | 8216 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 8216 insertions(+) create mode 100644 Parameters_July22.md diff --git a/Parameters_July22.md b/Parameters_July22.md new file mode 100644 index 0000000..4b20394 --- /dev/null +++ b/Parameters_July22.md @@ -0,0 +1,8216 @@ +### Parameter values for YouTube simulations ### + +Created by **Nils Berglund** and optimized by **Marco Mancini** + +C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund + +Below are parameter values used for different simulations, as well as initial conditions used in +function animation. Some simulations use variants of the published code. The list is going to be +updated gradually. + + +### 31 July 22 - Energy of a sonic boom ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** + +``` + init_wave_flat(phi, psi, xy_in); + if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == OSCILLATING_SOURCE_PERIOD - 1)) + { + sign = -sign; + period++; + yshift = (double)period*a + (double)(period*period)*b; + add_circular_wave(sign, -1.5 + yshift, 0.0, phi, psi, xy_in); + speed = (a + 2.0*(double)(period)*b)/((double)(3*NVID*OSCILLATING_SOURCE_PERIOD)); + printf("v = %.3lg, c = %.3lg\n", speed, c); + speed = speed/c; + } +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 3840 /* number of grid points on x axis */ +#define NY 2000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 1 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.4 /* parameter controlling the dimensions of domain */ +#define MU 0.2 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 6 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ +#define OSCILLATION_SCHEDULE 2 /* oscillation schedule, see list in global_pdes.c */ + +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define DAMPING 0.0 /* damping of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.015 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 0.0 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 6 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1250 /* number of frames of movie */ +#define NVID 20 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define PRINT_SPEED 1 /* print speed of moving source */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.004 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 +// #define PLOT 1 + +#define PLOT_B 4 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 50.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 1.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 30 July 22 - Bernoulli site percolation on a lattice of triangles ### + +**Program:** `percolation.c` (Constants not yet cleaned up) + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 992 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 20 + +/* Color schemes */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define HUE_CLOSED 330.0 /* color hue of closed cells */ +#define HUE_OPEN 180.0 /* color hue of open (dry) cells */ +#define HUE_FLOODED 30.0 /* color hue of open flooded cells */ +#define HUE_GRAPH 300.0 /* color hue in graph of cluster size */ + +#define PLOT_CLUSTER_SIZE 1 /* set to 1 to add a plot for the size of the percolation cluster */ + +#define NSTEPS 1100 /* number of frames of movie */ + +#define TEST_GRAPH 0 /* set to 1 to test graph connectivity matrix */ + + +/* Choice of the billiard table */ + +#define B_DOMAIN 49 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.5 /* parameter controlling the dimensions of domain */ +#define MU 0.2 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 6 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.001 /* frequency of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.015 /* Courant number in medium B */ + +/* Parameters for length and speed of simulation */ + +#define NVID 25 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define PRINT_SPEED 0 /* print speed of moving source */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.004 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 250.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.5 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 29 July 22 - Simulating a dam break with Lennard-Jones particles 3: Number of neighbors ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#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 INITXMIN -2.0 +#define INITXMAX -0.07 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 0.65 /* y interval for initial condition */ + +#define BCXMIN -2.05 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.25 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 12 /* pattern of repelling segments, see list in global_ljones.c */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 2 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 2.5 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.0075 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* number of sides of polygon */ +#define APOLY 0.666666666 /* 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 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ +#define TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ +#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3000 /* number of frames of movie */ +#define NVID 60 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 20 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 10 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 1 +#define PLOT_B 0 /* plot type for second movie */ + +#define DRAW_BONDS 1 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 5.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.0 /* radius in which to count neighbours */ +#define GRAVITY 2000.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.01 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define MIDDLE_CONSTANT_PHASE 370 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 350 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE 1180 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 1 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 0 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 1000 /* time at which to deactivate last segment */ +#define RELEASE_ROCKET_AT_DEACTIVATION 0 /* set to 1 to limit segments velocity before segment release */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 1.5 /* initial position of segments */ +#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ +#define SEGMENTS_VY0 -4.0 /* initial velocity of segments */ +#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 140 /* size of hashgrid in x direction */ +#define HASHY 70 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 28 July 22 - A Fabry-Pérot interferometer ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_wave_flat(phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 3840 /* number of grid points on x axis */ +#define NY 2000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 1 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 49 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.5 /* parameter controlling the dimensions of domain */ +#define MU 0.2 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 6 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define DAMPING 2.5e-5 /* damping of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.025 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 0.0 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 6 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1350 /* number of frames of movie */ +#define NVID 25 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 400 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define PRINT_SPEED 0 /* print speed of moving source */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.004 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 250.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.5 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 27 July 22 - Simulating a dam break with Lennard-Jones particles 2: Direction of velocities ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#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 INITXMIN -2.0 +#define INITXMAX -0.07 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 0.75 /* y interval for initial condition */ + +#define BCXMIN -2.05 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.25 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 12 /* pattern of repelling segments, see list in global_ljones.c */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 2 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.009 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* number of sides of polygon */ +#define APOLY 0.666666666 /* 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 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ +#define TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ +#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3000 /* number of frames of movie */ +#define NVID 60 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 20 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 10 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 8 +#define PLOT_B 0 /* plot type for second movie */ + +#define DRAW_BONDS 1 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 10.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.0 /* radius in which to count neighbours */ +#define GRAVITY 2000.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.01 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define MIDDLE_CONSTANT_PHASE 370 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 350 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE 1180 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 1 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 0 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 500 /* time at which to deactivate last segment */ +#define RELEASE_ROCKET_AT_DEACTIVATION 0 /* set to 1 to limit segments velocity before segment release */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 1.5 /* initial position of segments */ +#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ +#define SEGMENTS_VY0 -4.0 /* initial velocity of segments */ +#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 100 /* size of hashgrid in x direction */ +#define HASHY 50 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 26 July 22 - Waves on a topological surface of genus 2: Logarithm of the energy ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(-0.5, -0.5, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 50 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.1 /* Courant number */ +#define COURANTB 0.05 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 2.0e-3 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 12 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 10 + +#define PRECOMPUTE_BC 1 /* set to 1 to compute neighbours for Laplacian in advance */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1700 /* number of frames of movie */ +#define NVID 6 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ +#define PRINT_SPEED 0 /* set to 1 to print speed of moving source */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ +#define ROTATE_VIEW_WHILE_FADE 1 /* set to 1 to keep rotating viewpoint during fade */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.05 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 105 /* wave height */ +#define CPLOT 105 /* color scheme */ + +#define ZPLOT_B 109 +#define CPLOT_B 109 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 3.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.15 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 60.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 2000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT -1.5 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR 0.5 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 1.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#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 -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 500.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 500.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.03 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D -0.1 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 25 July 22 - Rocket nozzle comparison 2: Glas-shaped vs bell-shaped ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -3.0 +#define XMAX 3.0 /* x interval */ +#define YMIN -1.6875 +#define YMAX 1.6875 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.75 +#define INITXMAX 1.75 /* x interval for initial condition */ +#define INITYMIN -0.85 +#define INITYMAX 1.5 /* y interval for initial condition */ + +#define BCXMIN -3.1 +#define BCXMAX 3.1 /* x interval for boundary condition */ +#define BCYMIN -1.6875 +#define BCYMAX 4.5 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 102 /* pattern of repelling segments, see list in global_ljones.c */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 2 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.01 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* number of sides of polygon */ +#define APOLY 0.666666666 /* 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 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ +#define TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1800 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 50 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 21 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 20.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.0 /* radius in which to count neighbours */ +#define GRAVITY 15.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.025 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 1600 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 1 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 1 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 1 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ +#define SEGMENTS_X0 1.2 /* initial position of segments */ +#define SEGMENTS_Y0 0.0 /* initial position of segments */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 150 /* size of hashgrid in x direction */ +#define HASHY 150 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 24 July 22 - Bernoulli site percolation on a honeycomb lattice ### + +**Program:** `percolation.c` (Constants not yet cleaned up) + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 992 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 10 + +/* Color schemes */ + +#define COLOR_PALETTE 15 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define HUE_CLOSED 330.0 /* color hue of closed cells */ +#define HUE_OPEN 180.0 /* color hue of open (dry) cells */ +#define HUE_FLOODED 30.0 /* color hue of open flooded cells */ +#define HUE_GRAPH 300.0 /* color hue in graph of cluster size */ + +#define PLOT_CLUSTER_SIZE 1 /* set to 1 to add a plot for the size of the percolation cluster */ + +#define NSTEPS 1270 /* number of frames of movie */ + +#define TEST_GRAPH 0 /* set to 1 to test graph connectivity matrix */ + + +/* Choice of the billiard table */ + +#define B_DOMAIN 49 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.5 /* parameter controlling the dimensions of domain */ +#define MU 0.2 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 6 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.001 /* frequency of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.015 /* Courant number in medium B */ + +/* Parameters for length and speed of simulation */ + +#define NVID 25 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define PRINT_SPEED 0 /* print speed of moving source */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.004 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 250.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.5 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 23 July 22 - Simulating a dam break with Lennard-Jones particles ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#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 INITXMIN -2.0 +#define INITXMAX -0.07 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 0.75 /* y interval for initial condition */ + +#define BCXMIN -2.05 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.25 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 12 /* pattern of repelling segments, see list in global_ljones.c */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 2 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.009 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* number of sides of polygon */ +#define APOLY 0.666666666 /* 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 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ +#define TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ +#define DAM_WIDTH 0.05 /* width of dam for S_DAM segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3000 /* number of frames of movie */ +#define NVID 60 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 20 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 10 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 1 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 1 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 10.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.0 /* radius in which to count neighbours */ +#define GRAVITY 2000.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.01 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define MIDDLE_CONSTANT_PHASE 370 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 350 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE 1180 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 1 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 0 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 500 /* time at which to deactivate last segment */ +#define RELEASE_ROCKET_AT_DEACTIVATION 0 /* set to 1 to limit segments velocity before segment release */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 1.5 /* initial position of segments */ +#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ +#define SEGMENTS_VY0 -4.0 /* initial velocity of segments */ +#define DAMP_SEGS_AT_NEGATIVE_Y 0 /* set to 1 to dampen segments when y coordinate is negative */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 100 /* size of hashgrid in x direction */ +#define HASHY 50 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 22 July 22 - Colliding 1D fermions rendered in 3D ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_fermion_state(-0.5, 0.5, 5.0, -5.0, 0.1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ + +#define NX 500 /* number of grid points on x axis */ +#define NY 500 /* number of grid points on y axis */ + +#define XMIN -1.8 +#define XMAX 1.8 /* x interval */ +#define YMIN -1.8 +#define YMAX 1.8 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 6 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000002 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1200 /* number of frames of movie */ +#define NVID 500 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +/* Plot type - color scheme */ + +#define CPLOT 32 +#define CPLOT_B 30 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 32 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 1.0 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#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 VSCALE_AMPLITUDE 30.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#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 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 2.5 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {12.0, 0.0, 10.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 1.25 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 1.8 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.5 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 21 July 22 - Waves on a topological surface of genus 2, in 3D ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(-0.5, -0.5, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 50 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.1 /* Courant number */ +#define COURANTB 0.05 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 2.0e-3 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 12 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 10 + +#define PRECOMPUTE_BC 1 /* set to 1 to compute neighbours for Laplacian in advance */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2600 /* number of frames of movie */ +#define NVID 6 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ +#define PRINT_SPEED 0 /* set to 1 to print speed of moving source */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ +#define ROTATE_VIEW_WHILE_FADE 1 /* set to 1 to keep rotating viewpoint during fade */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.05 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 103 /* color scheme */ + +#define ZPLOT_B 104 +#define CPLOT_B 104 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 1 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 3.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 540.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.25 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 60.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 400.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 1.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#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 -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 10.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 30.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.03 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + + +### 20 July 22 - The Eagle has landed ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -3.0 +#define XMAX 3.0 /* x interval */ +#define YMIN -1.6875 +#define YMAX 1.6875 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -0.65 +#define INITXMAX 0.65 /* x interval for initial condition */ +#define INITYMIN 0.0 +#define INITYMAX 1.75 /* y interval for initial condition */ + +#define BCXMIN -3.1 +#define BCXMAX 3.1 /* x interval for boundary condition */ +#define BCYMIN -1.6875 +#define BCYMAX 4.5 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 101 /* pattern of repelling segments, see list in global_ljones.c */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 2 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +// #define MU 0.015 /* parameter controlling radius of particles */ +#define MU 0.01 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* number of sides of polygon */ +#define APOLY 0.666666666 /* 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 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ +#define TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* number of frames of movie */ +#define NVID 225 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 10 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 21 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 20.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.05 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.0 /* radius in which to count neighbours */ +#define GRAVITY 18.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.01 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define MIDDLE_CONSTANT_PHASE 370 /* final phase in which temperature is constant */ +#define FINAL_DECREASE_PHASE 350 /* final phase in which temperature decreases */ +#define FINAL_CONSTANT_PHASE 1180 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 1 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 1 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 1 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 100 /* time at which to deactivate last segment */ +#define RELEASE_ROCKET_AT_DEACTIVATION 0 /* set to 1 to limit segments velocity before segment release */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 1.5 /* initial position of segments */ +#define SEGMENTS_VX0 0.0 /* initial velocity of segments */ +#define SEGMENTS_VY0 -4.0 /* initial velocity of segments */ +#define DAMP_SEGS_AT_NEGATIVE_Y 1 /* set to 1 to dampen segments when y coordinate is negative */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 150 /* size of hashgrid in x direction */ +#define HASHY 150 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 19 July 22 - Colliding 1D fermions ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_fermion_state2(-0.5, 0.5, 5.0, -5.0, 0.1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 900 /* window width */ +#define WINHEIGHT 900 /* window height */ + +#define NX 450 /* number of grid points on x axis */ +#define NY 450 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -2.0 +#define YMAX 2.0 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 5 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000005 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 650 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 0 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +/* Plot type - color scheme */ + +#define CPLOT 30 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 1.0 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 0 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 5.0 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 50.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#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 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 18 July 22 - Bernoulli bond percolation on a square lattice ### + +**Program:** `percolation.c` (Constants not yet cleaned up) + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 992 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Boundary conditions, see list in global_pdes.c */ + +// #define B_COND 0 +#define B_COND 2 + +/* Color schemes */ + +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define HUE_CLOSED 30.0 /* color hue of closed cells */ +#define HUE_OPEN 180.0 /* color hue of open (dry) cells */ +#define HUE_FLOODED 330.0 /* color hue of open flooded cells */ + +#define PLOT_CLUSTER_SIZE 1 /* set to 1 to add a plot for the size of the percolation cluster */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 49 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.5 /* parameter controlling the dimensions of domain */ +#define MU 0.2 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 6 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.001 /* frequency of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.015 /* Courant number in medium B */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 800 /* number of frames of movie */ +#define NVID 25 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define PRINT_SPEED 0 /* print speed of moving source */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.004 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 250.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.5 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 17 July 22 - 3D representation of a sonic boom ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** + +``` + init_wave_flat_mod(phi, psi, xy_in); + if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == 1)) + { + yshift = (double)period*a + (double)(period*period)*b; + add_circular_wave_mod(sign, -1.5 + yshift, 0.0, phi, psi, xy_in); + speed = 0.55*(a + 2.0*(double)(period)*b)/((double)(NVID*OSCILLATING_SOURCE_PERIOD)); + printf("v = %.3lg, c = %.3lg\n", speed, c); + speed = speed/c; + sign = -sign; + period++; + } +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.1 /* Courant number */ +#define COURANTB 0.05 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 2.0e-3 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 12 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1200 /* number of frames of movie */ +#define NVID 6 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define PRINT_SPEED 1 /* set to 1 to print speed of moving source */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ +#define ROTATE_VIEW_WHILE_FADE 1 /* set to 1 to keep rotating viewpoint during fade */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.05 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 103 /* color scheme */ + +#define ZPLOT_B 109 +#define CPLOT_B 109 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 3.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 540.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.15 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 100.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 5000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 1.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#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 -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 13.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 1000.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.01 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 16 July 22 - A very energetic quantum particle starting in a well of a periodic egg carton potential ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 14.0, 0.0, 0.1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 600 /* number of grid points on x axis */ +#define NY 300 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 3 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.000000011 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1300 /* number of frames of movie */ +#define NVID 1100 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +/* Plot type - color scheme */ + +#define CPLOT 32 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 32 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 1.0 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#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 VSCALE_AMPLITUDE 5.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 15.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.1 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#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 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 15 July 22 - Rocket nozzle comparison: Straight vs bell-shaped ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -3.0 +#define XMAX 3.0 /* x interval */ +#define YMIN -1.6875 +#define YMAX 1.6875 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.75 +#define INITXMAX 1.75 /* x interval for initial condition */ +#define INITYMIN -0.85 +#define INITYMAX 1.5 /* y interval for initial condition */ + +#define BCXMIN -3.1 +#define BCXMAX 3.1 /* x interval for boundary condition */ +#define BCYMIN -1.6875 +#define BCYMAX 4.5 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 102 /* pattern of repelling segments, see list in global_ljones.c */ +#define NOZZLE_SHAPE 1 /* shape of nozzle, see list in global_ljones.c */ +#define NOZZLE_SHAPE_B 0 /* shape of nozzle for second rocket, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.01 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* number of sides of polygon */ +#define APOLY 0.666666666 /* 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 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ +#define TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1800 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 50 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 21 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 20.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.0 /* radius in which to count neighbours */ +#define GRAVITY 15.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.025 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 1600 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 1 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 1 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 1 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 40.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 200 /* time at which to deactivate last segment */ +#define SEGMENTS_X0 1.2 /* initial position of segments */ +#define SEGMENTS_Y0 0.0 /* initial position of segments */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 150 /* size of hashgrid in x direction */ +#define HASHY 150 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 14 July 22 - A sonic boom ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** + +``` + init_circular_wave(-1.5, 0.0, phi, psi, xy_in); + if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == OSCILLATING_SOURCE_PERIOD - 1)) + { + sign = -sign; + period++; + yshift = (double)period*a + (double)(period*period)*b; + add_circular_wave(sign, -1.5 + yshift, 0.0, phi, psi, xy_in); + speed = 0.5*(a + 2.0*(double)(period)*b)/((double)(NVID*OSCILLATING_SOURCE_PERIOD)); + printf("v = %.3lg, c = %.3lg\n", speed, c); + speed = speed/c; + } +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 3840 /* number of grid points on x axis */ +#define NY 2000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 1 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.4 /* parameter controlling the dimensions of domain */ +#define MU 0.2 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 6 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define DAMPING 2.5e-5 /* damping of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.0375 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 0.0 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 6 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1200 /* number of frames of movie */ +#define NVID 30 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define PRINT_SPEED 1 /* print speed of moving source */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.004 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 5 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 1.5 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 13 July 22 - A quite energetic quantum particle starting in a well of a periodic egg carton potential ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 7.0, -7.0, 0.1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 600 /* number of grid points on x axis */ +#define NY 300 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 3 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.000000011 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1400 /* number of frames of movie */ +#define NVID 1100 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +/* Plot type - color scheme */ + +#define CPLOT 32 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 32 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 1.0 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 18 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#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 VSCALE_AMPLITUDE 5.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 15.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.1 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#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 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 12 July 22 - The Eagle has wings ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -3.0 +#define XMAX 3.0 /* x interval */ +#define YMIN -1.6875 +#define YMAX 1.6875 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -0.5 +#define INITXMAX 0.5 /* x interval for initial condition */ +#define INITYMIN -0.85 +#define INITYMAX 1.5 /* y interval for initial condition */ + +#define BCXMIN -3.1 +#define BCXMAX 3.1 /* x interval for boundary condition */ +#define BCYMIN -1.6875 +#define BCYMAX 4.5 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 101 /* pattern of repelling segments, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.009 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* number of sides of polygon */ +#define APOLY 0.666666666 /* 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 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ +#define TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* number of frames of movie */ +#define NVID 300 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 50 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 21 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 20.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.02 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e7 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.0 /* radius in which to count neighbours */ +#define GRAVITY 15.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 1 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.025 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 1750 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 1 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 1 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 1 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 75.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 1 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 250 /* time at which to deactivate last segment */ +#define SEGMENTS_X0 0.0 /* initial position of segments */ +#define SEGMENTS_Y0 0.0 /* initial position of segments */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 150 /* size of hashgrid in x direction */ +#define HASHY 150 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 11 July 22 - Percolation, on the occasion of Hugo Duminil-Copin’s Fields Medal ### + +**Program:** `percolation.c` (the list of constant has not been cleaned up) + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 992 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 49 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.5 /* parameter controlling the dimensions of domain */ +#define MU 0.2 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 6 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.001 /* frequency of periodic excitation */ +#define COURANT 0.05 /* Courant number */ +#define COURANTB 0.015 /* Courant number in medium B */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 0 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1000 /* number of frames of movie */ +#define NVID 25 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 120 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define PRINT_SPEED 0 /* print speed of moving source */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00005 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.004 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 250.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 1.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.5 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 10 July 22 - A more energetic quantum particle starting in a well of a periodic egg carton potential ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 3.5, -3.5, 0.1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 600 /* number of grid points on x axis */ +#define NY 300 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 3 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000001 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ +// #define NOISE_INTENSITY 0.1 /* noise intensity */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1300 /* number of frames of movie */ +#define NVID 1200 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +/* Plot type - color scheme */ + +#define CPLOT 32 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 32 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 1.0 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 0 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#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 VSCALE_AMPLITUDE 5.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 15.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.1 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#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 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 9 July 22 - Rotating view of waves radiating from a von Koch snowflake fractal ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1400 /* number of grid points on x axis */ +#define NY 1400 /* number of grid points on y axis */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define XMIN -1.5 +#define XMAX 1.5 /* x interval */ +#define YMIN -1.5 +#define YMAX 1.5 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 41 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.1 /* Courant number */ +#define COURANTB 0.05 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 2.0e-3 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2600 /* number of frames of movie */ +#define NVID 4 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ +#define ROTATE_VIEW_WHILE_FADE 1 /* set to 1 to keep rotating viewpoint during fade */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.05 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 104 /* color scheme */ + +#define ZPLOT_B 109 +#define CPLOT_B 109 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 540.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.25 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 3.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 100.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 5000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 1.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#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 -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 350.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 350.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 15.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.15 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 8 July 22 - Trajectory length on log scale in approximate von Koch snowflake fractals ### + +**Program:** `particle_trajectory_vonKoch.c` (variant of `particle_trajectory.c`) + +**Initial condition in function `animation()`:** +``` + time = (double)i/(double)(NSTEPS-1); + x = 0.0; + y = 0.0; + alpha = time*DPI*MAX_ANGLE/360.0; + period = compute_trajectories_xy(x, y, alpha, alpha + DPI, configs, trajectory, traj_length); +``` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -1.0 +#define XMAX 3.0 /* 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 30 /* choice of domain shape */ + +#define CIRCLE_PATTERN 6 /* pattern of circles */ +#define POLYLINE_PATTERN 4 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 50000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 50000 /* total number of sides of polygonal line */ +#define NCX 9 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 7 /* Sierpinski gastket depth */ + +#define LAMBDA 0.8 /* parameter controlling shape of domain */ +#define MU 0.00001 /* 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 DRAW_BILLIARD 1 /* set to 1 to draw billiard */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ +#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ + +#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ +#define DEBUG 0 /* draw trajectories, for debugging purposes */ + +/* Simulation parameters */ + +#define NPART 1 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define TRAJ_LENGTH 8000 /* length of trajectory */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 1 /* set to 1 to show zoom on specific area */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ +#define PRINT_TRAJECTORY_LENGTH 1 /* set to 1 to print length of trajectory 0 */ +#define PRINT_TRAJECTORY_PERIOD 0 /* set to 1 to print period of trajectory 0 */ +#define DRAW_LENGTHS_PLOT 1 /* set to 1 to plot trajectory lengths */ +#define LENGTHS_LOG_SCALE 1 /* set to 1 to use log scale for plot of lengths */ +#define MAX_ANGLE 90.0 /* range of angles of trajectory */ + +#define NSTEPS 1200 /* number of frames of movie */ +#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.00001 /* integration step */ +#define NVID 150 /* number of iterations between images displayed on screen */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 64 /* 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 0.03 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 2 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define END_FRAMES 100 /* number of frames at end of movie */ + +``` + +### 7 July 22 - A quantum particle stating in a well of a periodic egg carton potential ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 1.5, 0.0, 0.1, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 600 /* number of grid points on x axis */ +#define NY 300 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 3 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 1.0 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000001 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1200 /* number of frames of movie */ +#define NVID 1250 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +/* Plot type - color scheme */ + +#define CPLOT 32 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 32 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 1.0 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#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 VSCALE_AMPLITUDE 5.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 15.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.1 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#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 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 6 July 22 - Waves escaping concentric rings of randomly rotated triangles ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1400 /* number of grid points on x axis */ +#define NY 1400 /* number of grid points on y axis */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define XMIN -1.5 +#define XMAX 1.5 /* x interval */ +#define YMIN -1.5 +#define YMAX 1.5 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.025 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.1 /* Courant number */ +#define COURANTB 0.04 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-2 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2200 /* number of frames of movie */ +#define NVID 4 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ +#define ROTATE_VIEW_WHILE_FADE 1 /* set to 1 to keep rotating viewpoint during fade */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.05 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 104 /* color scheme */ + +#define ZPLOT_B 109 +#define CPLOT_B 109 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 540.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.25 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 3.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 1000.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 5000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 1.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#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 -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 350.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 350.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 15.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.2 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 5 July 22 - Convection at constant temperature ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#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 INITXMIN -1.9 +#define INITXMAX 1.9 /* x interval for initial condition */ +#define INITYMIN -1.0 +#define INITYMAX 0.95 /* y interval for initial condition */ + +#define BCXMIN -2.0 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.125 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 0 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 11 /* pattern of repelling segments, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.0 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.2 /* parameter controlling the dimensions of domain */ +#define MU 0.01 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* number of sides of polygon */ +#define APOLY 0.666666666 /* 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 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ +#define TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3000 /* number of frames of movie */ +#define NVID 60 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 50 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 50 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 8 +#define PLOT_B 0 /* plot type for second movie */ + +#define DRAW_BONDS 1 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 20.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.006 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 7.0 /* radius in which to count neighbours */ +#define GRAVITY 1000.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 0 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.002 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 1 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 2 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.2 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 0 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 0 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 5.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 0 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 1000 /* time at which to deactivate last segment */ +#define SEGMENTS_X0 1.0 /* initial position of segments */ +#define SEGMENTS_Y0 -0.75 /* initial position of segments */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 100 /* size of hashgrid in x direction */ +#define HASHY 50 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 4 July 22 - Schrödinger’s equation in an ellipse (3D rotating view) ### + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, -7.5, 0.0, 0.15, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 600 /* number of grid points on x axis */ +#define NY 300 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 2 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 1 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.3 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.000000015 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2400 /* number of frames of movie */ +#define NVID 1200 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 720.0 /* total angle of rotation during simulation */ + +/* Plot type - color scheme */ + +#define CPLOT 30 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 0 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 0.5 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 12 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#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 VSCALE_AMPLITUDE 20.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 15.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.01 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#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 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.45 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.1 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +### 3 July 22 - Waves escaping a grid of triangles on concentric rigs ### + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1500 /* number of grid points on x axis */ +#define NY 1500 /* number of grid points on y axis */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define XMIN -1.5 +#define XMAX 1.5 /* x interval */ +#define YMIN -1.5 +#define YMAX 1.5 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */ +#define MU 0.025 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.1 /* Courant number */ +#define COURANTB 0.04 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-2 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2160 /* number of frames of movie */ +#define NVID 7 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.05 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 103 /* color scheme */ + +#define ZPLOT_B 109 +#define CPLOT_B 109 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 3.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 540.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 12 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.25 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 3.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 100.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 500.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 1.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#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 -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 10.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 40.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 15.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.12 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.2 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +### 2 July 22 - Archimedes' principle with two different bodies ### + +**Program:** `lennardjones.c` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ + /* so far incompatible with double movie */ +#define TIME_LAPSE_FACTOR 3 /* factor of time-lapse movie */ + + +/* General geometrical parameters */ + +#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 INITXMIN -1.9 +#define INITXMAX 1.9 /* x interval for initial condition */ +#define INITYMIN -1.0 +#define INITYMAX 0.95 /* y interval for initial condition */ + +#define BCXMIN -2.0 +#define BCXMAX 2.0 /* x interval for boundary condition */ +#define BCYMIN -1.125 +#define BCYMAX 1.125 /* y interval for boundary condition */ + +#define OBSXMIN -2.0 +#define OBSXMAX 2.0 /* x interval for motion of obstacle */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 0 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 3 /* pattern of obstacles, see list in global_ljones.c */ + +#define ADD_FIXED_SEGMENTS 1 /* set to 1 to add fixed segments as obstacles */ +#define SEGMENT_PATTERN 11 /* pattern of repelling segments, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.7 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ +#define CENTER_PX 0 /* set to 1 to center horizontal momentum */ +#define CENTER_PY 0 /* set to 1 to center vertical momentum */ +#define CENTER_PANGLE 0 /* set to 1 to center angular momentum */ + +#define INTERACTION 1 /* particle interaction, see list in global_ljones.c */ +#define INTERACTION_B 1 /* particle interaction for second type of particle, see list in global_ljones.c */ +#define SPIN_INTER_FREQUENCY 5.0 /* angular frequency of spin-spin interaction */ +#define SPIN_INTER_FREQUENCY_B 2.0 /* angular frequency of spin-spin interaction for second particle type */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 100 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define PDISC_DISTANCE 3.75 /* minimal distance in Poisson disc process, controls density of particles */ +#define PDISC_CANDIDATES 100 /* number of candidates in construction of Poisson disc process */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 0.2 /* parameter controlling the dimensions of domain */ +#define MU 0.012 /* parameter controlling radius of particles */ +#define MU_B 0.018 /* parameter controlling radius of particles of second type */ +#define NPOLY 25 /* number of sides of polygon */ +#define APOLY 0.666666666 /* 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 46 /* number of grid point for grid of disks */ +#define NGRIDY 24 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.035 /* width of tube for Ehrenfest urn configuration */ +#define TWO_CIRCLES_RADIUS_RATIO 0.8 /* ratio of radii for S_TWO_CIRCLES_EXT segment configuration */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3600 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 250 /* number of segments of boundary */ +#define INITIAL_TIME 150 /* time after which to start saving frames */ +#define OBSTACLE_INITIAL_TIME 50 /* time after which to start moving obstacle */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#define LINK_WIDTH 2 /* width of links between particles */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 0 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 8 /* plot type for second movie */ + +#define DRAW_BONDS 0 /* set to 1 to draw bonds between neighbours */ +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ +#define FILL_TRIANGLES 0 /* set to 1 to fill triangles between neighbours */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_ljones.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define ENERGY_HUE_MIN 330.0 /* color of original particle */ +#define ENERGY_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* energy of particle with hottest color */ +#define HUE_TYPE0 280.0 /* hue of particles of type 0 */ +#define HUE_TYPE1 70.0 /* hue of particles of type 1 */ +#define HUE_TYPE2 70.0 /* hue of particles of type 2 */ +#define HUE_TYPE3 210.0 /* hue of particles of type 3 */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.5 /* Lennard-Jones equilibrium distance */ +#define EQUILIBRIUM_DIST_B 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 20.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 1.0 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.2 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define VARY_THERMOSTAT 0 /* set to 1 for time-dependent thermostat schedule */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.01 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e11 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e11 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 6.0 /* radius in which to count neighbours */ +#define GRAVITY 500.0 /* gravity acting on all particles */ +#define INCREASE_GRAVITY 1 /* set to 1 to increase gravity during the simulation */ +#define GRAVITY_SCHEDULE 2 /* type of gravity schedule, see list in global_ljones.c */ +#define GRAVITY_FACTOR 100.0 /* factor by which to increase gravity */ +#define GRAVITY_INITIAL_TIME 200 /* time at start of simulation with constant gravity */ +#define GRAVITY_RESTORE_TIME 700 /* time at end of simulation with gravity restored to initial value */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 0 /* set to 1 to couple angular degrees of freedom to thermostat */ +#define DIMENSION_FACTOR 1.0 /* scaling factor taking into account number of degrees of freedom */ +#define KTORQUE 100.0 /* force constant in angular dynamics */ +#define KTORQUE_B 10.0 /* force constant in angular dynamics */ +#define KTORQUE_DIFF 150.0 /* force constant in angular dynamics for different particles */ +#define DRAW_SPIN 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_SPIN_B 0 /* set to 1 to draw spin vectors of particles */ +#define DRAW_CROSS 1 /* set to 1 to draw cross on particles of second type */ +#define SPIN_RANGE 7.0 /* range of spin-spin interaction */ +#define SPIN_RANGE_B 5.0 /* range of spin-spin interaction for second type of particle */ +#define QUADRUPOLE_RATIO 0.6 /* anisotropy in quadrupole potential */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 0.002 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 0 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 0 /* set to 1 to decrease size of container */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define COMPRESSION_RATIO 0.3 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 1 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 700 /* time before end of sim at which to restore size */ + +#define MOVE_OBSTACLE 0 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 0 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.12 /* radius of obstacle for circle boundary conditions */ +#define FUNNEL_WIDTH 0.25 /* funnel width for funnel boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ +#define RECORD_PRESSURES 0 /* set to 1 to record pressures on obstacle */ +#define N_PRESSURES 100 /* number of intervals to record pressure */ +#define N_P_AVERAGE 100 /* size of pressure averaging window */ +#define N_T_AVERAGE 50 /* size of temperature averaging window */ +#define MAX_PRESSURE 3.0e10 /* pressure shown in "hottest" color */ +#define PARTIAL_THERMO_COUPLING 0 /* set to 1 to couple only particles to the right of obstacle to thermostat */ +#define PARTIAL_THERMO_REGION 1 /* region for partial thermostat coupling (see list in global_ljones.c) */ +#define PARTIAL_THERMO_SHIFT 0.5 /* distance from obstacle at the right of which particles are coupled to thermostat */ +#define PARTIAL_THERMO_WIDTH 0.5 /* vertical size of partial thermostat coupling */ +#define PARTIAL_THERMO_HEIGHT 0.2 /* vertical size of partial thermostat coupling */ + +#define INCREASE_KREPEL 0 /* set to 1 to increase KREPEL during simulation */ +#define KREPEL_FACTOR 1000.0 /* factor by which to change KREPEL during simulation */ + +#define PART_AT_BOTTOM 0 /* set to 1 to include "seed" particles at bottom */ +#define MASS_PART_BOTTOM 10000.0 /* mass of particles at bottom */ +#define NPART_BOTTOM 100 /* number of particles at the bottom */ + +#define ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 0 /* time at which to add first particle */ +#define ADD_PERIOD 10000 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 200 /* final period where no particles are added */ +#define SAFETY_FACTOR 2.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define TRACER_PARTICLE 0 /* set to 1 to have a tracer particle */ +#define N_TRACER_PARTICLES 3 /* number of tracer particles */ +#define TRAJECTORY_LENGTH 8000 /* length of recorded trajectory */ +#define TRACER_PARTICLE_MASS 4.0 /* relative mass of tracer particle */ +#define TRAJECTORY_WIDTH 3 /* width of tracer particle trajectory */ + +#define ROTATE_BOUNDARY 0 /* set to 1 to rotate the repelling segments */ +#define SMOOTH_ROTATION 1 /* set to 1 to update segments at each time step (rather than at each movie frame) */ +#define PERIOD_ROTATE_BOUNDARY 1000 /* period of rotating boundary */ +#define ROTATE_INITIAL_TIME 0 /* initial time without rotation */ +#define ROTATE_FINAL_TIME 100 /* final time without rotation */ +#define ROTATE_CHANGE_TIME 0.33 /* relative duration of acceleration/deceleration phases */ +#define OMEGAMAX 100.0 /* maximal rotation speed */ +#define PRINT_OMEGA 0 /* set to 1 to print angular speed */ +#define PRINT_PARTICLE_SPEEDS 0 /* set to 1 to print average speeds/momenta of particles */ +#define PRINT_SEGMENTS_SPEEDS 1 /* set to 1 to print velocity of moving segments */ + +#define MOVE_BOUNDARY 1 /* set to 1 to move repelling segments, due to force from particles */ +#define SEGMENTS_MASS 5.0 /* mass of collection of segments */ +#define DEACTIVATE_SEGMENT 0 /* set to 1 to deactivate last segment after a certain time */ +#define SEGMENT_DEACTIVATION_TIME 1000 /* time at which to deactivate last segment */ +#define SEGMENTS_X0 1.0 /* initial position of segments */ +#define SEGMENTS_Y0 -0.75 /* initial position of segments */ + +#define POSITION_DEPENDENT_TYPE 0 /* set to 1 to make particle type depend on initial position */ +#define POSITION_Y_DEPENDENCE 0 /* set to 1 for the separation between particles to be vertical */ +#define PRINT_ENTROPY 0 /* set to 1 to compute entropy */ + +#define REACTION_DIFFUSION 0 /* set to 1 to simulate a chemical reaction (particles may change type) */ +#define RD_TYPES 3 /* number of types in reaction-diffusion equation */ +#define REACTION_PROB 0.0045 /* probability controlling reaction term */ + +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ +#define PRINT_LEFT 1 /* set to 1 to print certain parameters at the top left instead of right */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define LID_MASS 1000.0 /* mass of lid for BC_RECTANGLE_LID b.c. */ +#define LID_WIDTH 0.1 /* width of lid for BC_RECTANGLE_LID b.c. */ +#define WALL_MASS 2000.0 /* mass of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_FRICTION 0.0 /* friction on wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_WIDTH 0.1 /* width of wall for BC_RECTANGLE_WALL b.c. */ +#define WALL_VMAX 100.0 /* max speed of wall */ +#define WALL_TIME 500 /* time during which to keep wall */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e12 /* maximal force */ +#define FLOOR_OMEGA 0 /* set to 1 to limit particle momentum to PMAX */ +#define PMAX 1000.0 /* maximal force */ + +#define HASHX 80 /* size of hashgrid in x direction */ +#define HASHY 40 /* size of hashgrid in y direction */ +#define HASHMAX 100 /* maximal number of particles per hashgrid cell */ +#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */ + +#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 1 July 22 - Video #500 : An elliptical retrospective with Beethoven ### + +**Part 1** + +**Program:** `particle_billiard.c` + +**Initial condition in function `animation()`:** `init_drop_config(-0.5, 0.0, 0.2, 0.4, configs);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ + +/* Choice of the billiard table, see global_particles.c */ + +#define B_DOMAIN 1 /* choice of domain shape */ + +#define CIRCLE_PATTERN 1 /* pattern of circles */ +#define POLYLINE_PATTERN 8 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 100000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 100000 /* total number of sides of polygonal line */ +#define NCX 30 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 1 /* Sierpinski gastket depth */ + +#define LAMBDA 1.4 /* parameter controlling shape of domain */ +#define MU 0.01 /* second parameter controlling shape of billiard */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ +#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ + +#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ +#define DEBUG 0 /* draw trajectories, for debugging purposes */ + +/* Simulation parameters */ + +#define NPART 2000 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */ +#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ + +#define NSTEPS 3850 /* number of frames of movie */ +#define TIME 2500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.00001 /* integration step */ +#define NVID 100 /* number of iterations between images displayed on screen */ +#define END_FRAMES 25 /* number of still frames at the end of the movie */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 16 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 16 /* 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 0.01 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 3 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ + +``` + +**Part 2** + +**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 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + + +#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ + +/* Choice of the billiard table, see global_particles.c */ + +#define B_DOMAIN 1 /* choice of domain shape */ + +#define CIRCLE_PATTERN 1 /* pattern of circles */ +#define POLYLINE_PATTERN 8 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 100000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 100000 /* total number of sides of polygonal line */ +#define NCX 30 /* number of circles in x direction */ +#define NCY 20 /* number of circles in y direction */ +#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */ +#define SDEPTH 1 /* Sierpinski gastket depth */ + +#define LAMBDA 1.4 /* parameter controlling shape of domain */ +#define MU 0.01 /* second parameter controlling shape of billiard */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */ +#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */ + +#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */ +#define DEBUG 0 /* draw trajectories, for debugging purposes */ + +/* Simulation parameters */ + +#define NPART 40000 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 0 /* set to 1 to show zoom on specific area */ +#define PRINT_PARTICLE_NUMBER 0 /* set to 1 to print number of particles */ +#define PRINT_COLLISION_NUMBER 0 /* set to 1 to print number of collisions */ +#define TEST_ACTIVE 1 /* set to 1 to test whether particle is in billiard */ + +#define NSTEPS 5250 /* 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 25 /* number of iterations between images displayed on screen */ +#define END_FRAMES 25 /* number of still frames at the end of the movie */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 16 /* 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 0.005 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 3 /* width of particles */ +#define FRONT_WIDTH 3 /* width of wave front */ + +#define BLACK 1 /* set to 1 for black background */ +#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */ +#define OUTER_COLOR 270.0 /* color outside billiard */ +#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */ +#define PAINT_EXT 1 /* set to 1 to paint exterior */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ + +``` + +**Part 3** + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1920 /* number of grid points on x axis */ +#define NY 1000 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 1 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.4 /* parameter controlling the dimensions of domain */ +#define MU 0.2 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 6 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define AMPLITUDE 0.8 /* amplitude of periodic excitation */ +#define DAMPING 2.5e-5 /* damping of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.0375 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 0.0 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 100 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2740 /* number of frames of movie */ +#define NVID 30 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 200 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 0 + +#define PLOT_B 1 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.0 /* sensitivity of color on wave amplitude */ +#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 300.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 1.0 /* shift of colors on log scale */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 180.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 2.5 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 5.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +**Part 4** + +**Program:** `` + +**Initial condition in function `animation()`:** `` + +``` + +``` + +**Part 5** + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1800 /* number of grid points on x axis */ +#define NY 900 /* number of grid points on y axis */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 1 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.4 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.025 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2275 /* number of frames of movie */ +#define NVID 10 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.01 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 103 /* color scheme */ + +#define ZPLOT_B 104 +#define CPLOT_B 104 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 1.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 540.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 14 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.15 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 5.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 250.0 /* scaling factor for energy representation */ +#define LOG_SCALE 0.2 /* scaling factor for energy log representation */ +#define LOG_SHIFT -0.5 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 5.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#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 -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 15.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 40.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.5}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.01 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.5 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +**Part 6** + +**Program:** `wave_3d.c` + +**Initial condition in function `animation()`:** `init_circular_wave_mod(0.0, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 1800 /* number of grid points on x axis */ +#define NY 900 /* number of grid points on y axis */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */ + +#define JULIA_SCALE 0.8 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 1 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 202 /* pattern of circles or polygons, see list in global_pdes.c */ + +#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */ +#define IOR 1 /* choice of index of refraction, see list in global_pdes.c */ +#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.4 /* parameter controlling the dimensions of domain */ +#define MU 0.5 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 2.0 /* 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 36 /* number of grid point for grid of disks */ +#define NGRIDY 6 /* number of grid point for grid of disks */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -2.9 +#define ISO_XSHIFT_RIGHT 1.4 +#define ISO_YSHIFT_LEFT -0.15 +#define ISO_YSHIFT_RIGHT -0.15 +#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */ + + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.017 /* frequency of periodic excitation */ +#define AMPLITUDE 0.9 /* amplitude of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.02 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-6 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */ +#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 2 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1862 /* number of frames of movie */ +#define NVID 10 /* number of iterations between images displayed on screen */ +#define NSEG 1000 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 100 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.01 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define ZPLOT 103 /* wave height */ +#define CPLOT 103 /* color scheme */ + +#define ZPLOT_B 109 +#define CPLOT_B 109 /* plot type for second movie */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define FLOOR_ZCOORD 0 /* set to 1 to draw only facets with z not too negative */ +#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */ +#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */ +#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */ + +#define PLOT_SCALE_ENERGY 0.025 /* vertical scaling in energy plot */ +#define PLOT_SCALE_LOG_ENERGY 3.0 /* vertical scaling in log energy plot */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +/* Color schemes */ + +#define COLOR_PALETTE 17 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.15 /* sensitivity of color on wave amplitude */ +#define VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define VSCALE_ENERGY 2.5 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 500.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 2.0 /* shift of colors on log scale */ +#define LOG_ENERGY_FLOOR -1000.0 /* floor value for log of (total) energy */ +#define LOG_MEAN_ENERGY_SHIFT 10.0 /* additional shift for log of mean energy */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ + +#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 -200.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 15.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 80.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Parameters controlling 3D projection */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.5}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.01 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */ + +``` + +**Part 7** + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, -7.5, 0.0, 0.15, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 600 /* number of grid points on x axis */ +#define NY 300 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 2 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 1 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.4 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.00000002 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1612 /* number of frames of movie */ +#define NVID 850 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 540.0 /* total angle of rotation during simulation */ + +/* Plot type - color scheme */ + +#define CPLOT 30 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 0 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 0.5 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 13 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 0 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#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 VSCALE_AMPLITUDE 10.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 15.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.075 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#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 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.45 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.1 /* overall y shift for REP_PROJ_3D representation */ + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +**Part 8** + +**Program:** `rde.c` + +**Initial condition in function `animation()`:** `init_coherent_state(0.0, 0.0, 4.5, -7.0, 0.15, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ +#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */ + +/* General geometrical parameters */ + +#define WINWIDTH 1920 /* window width */ +#define WINHEIGHT 1000 /* window height */ +#define NX 600 /* number of grid points on x axis */ +#define NY 300 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.041666667 +#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */ + +/* Choice of simulated equation */ + +#define RDE_EQUATION 5 /* choice of reaction term, see list in global_3d.c */ +#define NFIELDS 2 /* number of fields in reaction-diffusion equation */ +#define NLAPLACIANS 2 /* number of fields for which to compute Laplacian */ + +#define ADD_POTENTIAL 1 /* set to 1 to add a potential (for Schrodiner equation) */ +#define POTENTIAL 4 /* type of potential, see list in global_3d.c */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 1 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_pdes.c */ + +#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */ +#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */ +#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */ + +#define LAMBDA 1.4 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* parameter controlling the dimensions of domain */ +#define NPOLY 5 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 7 /* depth of computation of Menger gasket */ +#define MRATIO 5 /* 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 */ + +#define X_SHOOTER -0.2 +#define Y_SHOOTER -0.6 +#define X_TARGET 0.4 +#define Y_TARGET 0.7 /* shooter and target positions in laser fight */ + +#define ISO_XSHIFT_LEFT -1.65 +#define ISO_XSHIFT_RIGHT 0.4 +#define ISO_YSHIFT_LEFT -0.05 +#define ISO_YSHIFT_RIGHT -0.05 +#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */ + +/* You can add more billiard tables by adapting the functions */ +/* xy_in_billiard and draw_billiard in sub_wave.c */ + +/* Physical patameters of wave equation */ + +#define DT 0.000000013 + +#define VISCOSITY 2.0 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ +#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN equation */ +#define K_HARMONIC 0.2 /* spring constant of harmonic potential */ +#define K_COULOMB 0.5 /* constant in Coulomb potential */ +#define BZQ 0.0008 /* parameter in BZ equation */ +#define BZF 1.2 /* parameter in BZ equation */ + +#define T_OUT 2.0 /* outside temperature */ +#define T_IN 0.0 /* inside temperature */ +#define SPEED 0.0 /* speed of drift to the right */ + +#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.005 /* noise intensity */ +#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */ +#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */ +#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */ + +#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */ +#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */ +#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */ +#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */ +#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, + for numerical stability */ + +#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */ +#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */ +#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */ +#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */ + + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1150 /* number of frames of movie */ +#define NVID 1200 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */ +#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */ +#define MAX_DT 0.024 /* maximal value of integration step */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 5 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 2 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 0 /* initial still time */ +#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ +#define FADE 1 /* set to 1 to fade at end of movie */ + +/* Visualisation */ + +#define PLOT_3D 1 /* controls whether plot is 2D or 3D */ + +#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */ +#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */ + +/* Plot type - color scheme */ + +#define CPLOT 30 +#define CPLOT_B 31 + +/* Plot type - height of 3D plot */ + +#define ZPLOT 30 /* z coordinate in 3D plot */ +#define ZPLOT_B 30 /* z coordinate in second 3D plot */ + +#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */ +#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */ +#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */ +#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */ +#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */ +#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */ +#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */ +#define ADD_POT_CONSTANT 1.0 /* constant in front of added potential */ + +#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ +#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */ +#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */ +#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */ +#define PRINT_NOISE 0 /* set to 1 to print noise intensity */ + +#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */ +#define FIELD_LINE_WIDTH 1 /* width of field lines */ +#define N_FIELD_LINES 120 /* number of field lines */ +#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */ +#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */ +#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */ +#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */ + +/* 3D representation */ + +#define REPRESENTATION_3D 1 /* choice of 3D representation */ + +#define REP_AXO_3D 0 /* linear projection (axonometry) */ +#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ +#define COLOR_PALETTE_B 10 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */ + +#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 VSCALE_AMPLITUDE 20.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define CURL_SCALE 0.000015 /* scaling factor for curl representation */ +#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */ +#define SLOPE_SCHROD_LUM 15.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */ +#define MIN_SCHROD_LUM 0.075 /* minimal luminosity in color scheme Z_ARGUMENT*/ + +#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 359.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */ +#define E_SCALE 100.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 6.0 /* scale of color scheme bar */ +#define COLORBAR_RANGE_B 3.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +/* only for compatibility with wave_common.c */ +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OMEGA 0.005 /* frequency of periodic excitation */ +#define COURANT 0.08 /* Courant number */ +#define COURANTB 0.03 /* Courant number in medium B */ +#define INITIAL_AMP 0.5 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */ +#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */ +#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */ +#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */ +/* end of constants added only for compatibility with wave_common.c */ + + +double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */ +double v_3d[2] = {-0.75, -0.45}; +double w_3d[2] = {0.0, 0.015}; +double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */ +double observer[3] = {8.0, 8.0, 6.0}; /* location of observer for REP_PROJ_3D representation */ +int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */ + +#define Z_SCALING_FACTOR 0.75 /* overall scaling factor of z axis for REP_PROJ_3D representation */ +#define XY_SCALING_FACTOR 2.45 /* overall scaling factor for on-screen (x,y) coordinates after projection */ +#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */ +#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */ +#define YSHIFT_3D 0.5 /* overall y shift for REP_PROJ_3D representation */ + + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 2.0 /* max value of wave amplitude */ + +``` + +