From d8fe4409e96ed34eeae6ff951e2f187d5c3530d5 Mon Sep 17 00:00:00 2001 From: nilsberglund-orleans <83530463+nilsberglund-orleans@users.noreply.github.com> Date: Sun, 13 Mar 2022 15:36:12 +0100 Subject: [PATCH] Add files via upload --- Parameters_February22.md | 4697 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 4697 insertions(+) create mode 100644 Parameters_February22.md diff --git a/Parameters_February22.md b/Parameters_February22.md new file mode 100644 index 0000000..16d6301 --- /dev/null +++ b/Parameters_February22.md @@ -0,0 +1,4697 @@ +### 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. + + +### 28 February 22 - Shock wave in a Lennard-Jones gas, with improved boundary conditions ### + +**Program:** `lennardjones.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 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 -2.9 +#define INITXMAX 2.9 /* x interval for initial condition */ +#define INITYMIN -1.0 +#define INITYMAX 1.0 /* y interval for initial condition */ + +#define BCXMIN -3.0 +#define BCXMAX 3.0 /* 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 0 /* pattern of obstacles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 0 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ + +#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 4.0 /* 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 5.0 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.012 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 10 /* number of grid point for grid of disks */ +#define NGRIDY 3 /* 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 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 2700 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 100 /* time after which to start saving frames */ +#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 4 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 6 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* Color schemes */ + +#define COLOR_PALETTE 10 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* 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 PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.5e3 /* energy of particle with hottest color */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 3.0e-7 /* time step for particle displacement */ +#define KREPEL 12.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 5.0e2 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.25 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.001 /* initial inverse temperature */ +#define MU_XI 0.01 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 5.0e8 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 5.0e7 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#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 5.0 /* 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 0.1 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* 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 1 /* set to 1 to have a moving obstacle */ +#define CENTER_VIEW_ON_OBSTACLE 1 /* set to 1 to center display on moving obstacle */ +#define RESAMPLE_Y 1 /* set to 1 to resample y coordinate of moved particles (for shock waves) */ +#define NTRIALS 2000 /* number of trials when resampling */ +#define OBSTACLE_RADIUS 0.25 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 25 /* time at which to add first particle */ +#define ADD_PERIOD 20 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 250 /* 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 PRINT_PARTICLE_NUMBER 0 /* set to 1 to print total number of particles */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e9 /* maximal force */ + +#define HASHX 25 /* size of hashgrid in x direction */ +#define HASHY 15 /* 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 */ + +``` + +### 27 February 22 - A Fresnel zone plate, higher resolution version ### + +**Program:** `wave_diffraction.c` (variant of `wave_billiard.c`) + +**Initial condition in function `animation()`:** `` + +``` +#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 20 /* choice of domain shape, see list in global_pdes.c */ + +/* Choice of wave speed distribution */ + +#define WS_EARTH 1 /* wave speed in the Earth */ +#define WS_FRESNEL_PLATE 2 /* Fresnel plate */ + +#define WAVE_SPEED 2 /* choice of wave speed */ + +#define CIRCLE_PATTERN 99 /* 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 1.2 /* parameter controlling the dimensions of domain */ +#define MU 0.05 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* 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 0.004 /* frequency of periodic excitation */ +#define AMPLITUDE 2.0 /* amplitude of periodic excitation */ +#define COURANT 0.03 /* Courant number */ +#define COURANTB 0.01 /* Courant number in medium B */ +#define GAMMA 2.0e-3 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1500 /* number of frames of movie */ +#define NVID 50 /* number of iterations between images displayed on screen */ +#define NSEG 100 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.01 /* 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 18 /* 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 0.75 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 100.0 /* 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 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 50.0 /* 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 */ + +``` + +### 26 February 22 - A molecular Galton board ### + +**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 */ + +/* 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 -0.05 +#define INITXMAX 0.05 /* x interval for initial condition */ +#define INITYMIN 1.1 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 99 /* pattern of circles, see list in global_ljones.c */ + +#define ADD_FIXED_OBSTACLES 1 /* set to 1 do add fixed circular obstacles */ +#define OBSTACLE_PATTERN 1 /* pattern of obstacles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 0 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ + +#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 4.0 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.017 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 10 /* number of grid point for grid of disks */ +#define NGRIDY 3 /* 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 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 5000 /* number of frames of movie */ +#define NVID 450 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#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 12 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 5 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* 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 PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.5e3 /* energy of particle with hottest color */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-7 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 1.5e3 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.25 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 20.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.001 /* initial inverse temperature */ +#define MU_XI 0.025 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e10 /* confining harmonic potential outside simulation region */ +#define KSPRING_OBSTACLE 1.0e10 /* harmonic potential of obstacles */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 500000.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 5.0 /* 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 250.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 0 /* 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 OBSTACLE_RADIUS 0.03 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 1 /* set to 1 to add particles */ +#define ADD_TIME 25 /* time at which to add first particle */ +#define ADD_PERIOD 20 /* time interval between adding further particles */ +#define FINAL_NOADD_PERIOD 250 /* final period where no particles are added */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define PRINT_PARTICLE_NUMBER 1 /* set to 1 to print total number of particles */ + +#define EHRENFEST_COPY 0 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e9 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* 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 */ + +``` + +### 25 February 22 - A Fresnel zone plate ### + +**Program:** `wave_diffraction.c` (variant of `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 */ + +#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 */ + + +/* General geometrical parameters */ + +#define JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +/* Choice of wave speed distribution */ + +#define WS_EARTH 1 /* wave speed in the Earth */ +#define WS_FRESNEL_PLATE 2 /* Fresnel plate */ + +#define WAVE_SPEED 2 /* choice of wave speed */ + +#define CIRCLE_PATTERN 99 /* 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 1.2 /* parameter controlling the dimensions of domain */ +#define MU 0.05 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 10 /* number of grid point for grid of disks */ +#define NGRIDY 12 /* 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 0.004 /* frequency of periodic excitation */ +#define AMPLITUDE 2.0 /* amplitude of periodic excitation */ +#define COURANT 0.02 /* Courant number */ +#define COURANTB 0.01 /* Courant number in medium B */ +#define GAMMA 2.0e-3 /* damping factor in wave equation */ +#define GAMMAB 1.0e-6 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1000 /* number of frames of movie */ +#define NVID 50 /* number of iterations between images displayed on screen */ +#define NSEG 100 /* number of segments of boundary */ +#define INITIAL_TIME 0 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0001 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.01 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 1 + +#define PLOT_B 5 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 15 /* 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 1.5 /* sensitivity of color on wave amplitude */ +#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 2.5 /* 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 0.25 /* 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 */ + +``` + +### 24 February 22 - Epidemics: a spatial SIR model with graphs ### + +**Program:** `sir.c` + +``` +#define MOVIE 1 /* set to 1 to generate 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 -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.075 +#define INITYMAX 0.1 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.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 PDISC_DISTANCE 5.0 /* minimal distance in Poisson disc process */ +#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 SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction, only needed if particles are not all the same */ + +#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.018 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 32 /* number of grid point for grid of disks */ +#define NGRIDY 26 /* 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 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 */ + +/* Boundary conditions, see list in global_ljones.c */ + +// #define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3000 /* number of frames of movie */ +#define NVID 300 /* number of iterations between images displayed on screen */ +#define NSEG 100 /* number of segments of boundary */ +#define INITIAL_TIME 50 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of billiard boundary */ +#define CONTAINER_WIDTH 4 /* width of container boundary */ + +#define PLOT_GRAPH 1 /* set to 1 to plot gaph of populations */ + +#define PAUSE 1000 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +/* Boundary conditions, see list in global_ljones.c */ + +#define BOUNDARY_COND 1 + + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 2 + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* Color palette, see list in global_ljones.c */ + +#define BLACK 1 /* background */ + +#define COLOR_SCHEME 1 /* 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 1.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */ + +/* particle properties */ + +#define PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 30.0 /* color of saturated particle */ +#define PARTICLE_EMAX 5.0e1 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define MOVE_PARTICLES 1 /* set to 1 for mobile particles */ +#define INERTIA 1 /* set to 1 for taking inertia into account */ +#define DT_PARTICLE 4.0e-7 /* time step for particle displacement */ +#define KREPEL 30.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 3.5 /* Lennard-Jones equilibrium distance */ +#define REPEL_RADIUS 20.0 /* radius in which repelling force acts (in units of particle radius) */ +#define DAMPING 1.5e5 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define V_INITIAL 20.0 /* initial velocity range */ +#define SIGMA 10.0 /* noise intensity in thermostat */ +#define BETA 1.0e-3 /* initial inverse temperature */ +#define MU_XI 0.1 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 1.0e8 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ + +#define INCREASE_BETA 0 /* set to 1 to increase BETA during simulation */ +#define BETA_FACTOR 5.0e2 /* factor by which to change BETA during simulation */ + +#define CENTER_VIEW_ON_OBSTACLE 0 /* set to 1 to center display on moving obstacle */ +#define SYMMETRIC_DECREASE 0 /* set tp 1 to decrease container symmetrically */ +#define OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ + +#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 ADD_PARTICLES 0 /* set to 1 to add particles */ +#define ADD_TIME 300 /* time at which to add first particle */ +#define ADD_PERIOD 2000 /* time interval between adding further particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 2.0e10 /* maximal force */ + +#define P_PROTECTED 0.5 /* probability of being protected */ +#define CONTAMINATION_RADIUS 3.25 /* radius in which people can contiminate others */ +#define P_INFECTION 0.05 /* probability of getting infected */ +#define P_INFECTION_PROTECTED 0.005 /* probability of getting infected if protected */ +#define INFECTION_CHANGE 0.2 /* time change of infection */ +#define RECOVER_THRESHOLD 100.0 /* threshold for getting recovered */ + +#define HASHX 20 /* size of hashgrid in x direction */ +#define HASHY 12 /* 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 */ + +/* For debugging purposes only */ +#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +``` + +### 23 February 22 - A reaction-diffusion equation based on the Rock-Paper-Scissors automaton (longer version) ### + +**Program:** `bz.c` + +**Initial condition in function `animation()`:** `init_random(0.5, 0.5, phi, psi, chi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* 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 JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 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 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 0.000001 + +#define VISCOSITY 0.5 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#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 0.1 /* noise intensity */ +// #define NOISE_INTENSITY 0.05 /* noise intensity */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3500 /* number of frames of movie */ +#define NVID 5 /* 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 2 /* 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 25 /* initial still time */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Plot type */ + +#define PLOT 0 + +/* Field representation */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ + +#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 */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 18 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 4 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 1.0 /* 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 2.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 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 0.55 /* scale of color scheme bar */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + + +### 22 February 22 - Periodic trajectories in a Tokarsky room ### + +**Program:** `particle_trajectory.c` + +**Initial condition in function `animation()`:** + +``` + time = (double)i/(double)(NSTEPS-1); + x = 0.0; + if (time < 0.5) y = 0.999 - 0.798*2.0*time; + else y = 0.999 - 0.798 + 0.798*2.0*(time - 0.5); + alpha = 0.0; + 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 -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */ + +/* Choice of the billiard table, see global_particles.c */ + +#define B_DOMAIN 30 /* choice of domain shape */ + +#define CIRCLE_PATTERN 6 /* pattern of circles */ +#define POLYLINE_PATTERN 6 /* pattern of polyline */ + +#define ABSORBING_CIRCLES 1 /* set to 1 for circular scatterers to be absorbing */ + +#define NMAXCIRCLES 10000 /* total number of circles (must be at least NCX*NCY for square grid) */ +#define NMAXPOLY 10000 /* 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 4 /* Sierpinski gastket depth */ + +#define LAMBDA 0.8 /* 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 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 256 /* 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 0 /* set to 1 to print length of trajectory 0 */ +#define PRINT_TRAJECTORY_PERIOD 1 /* set to 1 to print period of trajectory 0 */ + +#define NSTEPS 2000 /* 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 14 /* 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 1000 /* final sleeping time */ +#define END_FRAMES 100 /* number of frames at end of movie */ + +``` + +### 21 February 22 - A reaction-diffusion equation based on the Rock-Paper-Scissors automaton ### + +**Program:** `bz.c` + +**Initial condition in function `animation()`:** `init_random(0.5, 0.5, phi, psi, chi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* General geometrical parameters */ + +#define WINWIDTH 720 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define NX 720 /* number of grid points on x axis */ +#define NY 720 /* number of grid points on y axis */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 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 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 0.0000005 + +#define VISCOSITY 2.5 + +#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */ + +#define EPSILON 0.8 /* time scale separation */ +#define DELTA 0.1 /* time scale separation */ +#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 0.1 /* noise intensity */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1250 /* number of frames of movie */ +#define NVID 15 /* 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 2 /* 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 5 /* initial still time */ +#define END_FRAMES 50 /* number of still frames at end of movie */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Plot type */ + +#define PLOT 0 + +#define PRINT_TIME 0 /* set to 1 to print running time */ + +#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 */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 18 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 4 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 1.0 /* 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 4.0 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 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 0.55 /* scale of color scheme bar */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 20 February 22 - Osmosis ### + +**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 */ + +/* 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 -1.6 +#define INITXMAX -0.4 /* x interval for initial condition */ +#define INITYMIN -0.6 +#define INITYMAX 0.6 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ +#define SYMMETRIZE_FORCE 1 /* set to 1 to symmetrize two-particle interaction */ + +#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 4.0 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.017 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 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 5500 /* number of frames of movie */ +#define NVID 750 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#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 5 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 5 +#define PLOT_B 3 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* 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 PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.5e3 /* energy of particle with hottest color */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 0.5e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 7.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.25 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 20.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.001 /* initial inverse temperature */ +#define MU_XI 0.025 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e8 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 5.0 /* 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 250.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 0 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define EHRENFEST_COPY 1 /* set to 1 to add equal number of larger particles (for Ehrenfest model) */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e9 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* 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 February 22 - A quadratic resonance diffuser ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** `init_circular_wave(-0.5, 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 -1.7 +#define XMAX 2.3 /* 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 46 /* 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 0.1 /* 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 0.004 /* frequency of periodic excitation */ +#define AMPLITUDE 2.0 /* amplitude of periodic excitation */ +#define COURANT 0.03 /* Courant number */ +#define COURANTB 0.017704918 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-4 /* 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 0 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1600 /* 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 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 */ + +/* 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 5 + +#define PLOT_B 0 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 18 /* 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* 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 1.5 /* 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 */ + +``` + +### 18 February 22 - Interacting particles in Ehrenfest-type urns ### + +**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 */ + +/* 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 -1.6 +#define INITXMAX -0.4 /* x interval for initial condition */ +#define INITYMIN -0.6 +#define INITYMAX 0.6 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#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 4.0 /* 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 3.2 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* number of grid point for grid of disks */ +#define EHRENFEST_RADIUS 0.9 /* radius of container for Ehrenfest urn configuration */ +#define EHRENFEST_WIDTH 0.075 /* width of tube for Ehrenfest urn 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 9000 /* number of frames of movie */ +#define NVID 450 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#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 5 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 3 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* 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 PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.5e3 /* energy of particle with hottest color */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 1.0e-6 /* time step for particle displacement */ +#define KREPEL 20.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.25 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.001 /* initial inverse temperature */ +#define MU_XI 0.025 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e8 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 5.0 /* 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 250.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 0 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e9 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* 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 */ + +``` + +### 17 February 22 - Interacting squares on a topological Klein bottle ### + +**Program:** `lennardjones.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 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 -1.1 +#define INITYMAX 1.1 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 2 /* 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 4.0 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.03 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2000 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#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 11 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* 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 PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.25 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.002 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 5.0 /* 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 250.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 0 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e9 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* 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 */ + +``` + +### 16 February 22 - Two Fresnel lenses facing away from each other ### + +**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 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 3840 /* number of grid points on x axis */ +#define NY 2000 /* number of grid points on y axis */ + +#define XMIN -1.7 +#define XMAX 2.3 /* 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 45 /* 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 -1.3 /* parameter controlling the dimensions of domain */ +#define MU 0.07 /* 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 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.004 /* frequency of periodic excitation */ +#define AMPLITUDE 2.0 /* amplitude of periodic excitation */ +#define COURANT 0.03 /* Courant number */ +#define COURANTB 0.017704918 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-4 /* 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 3825 /* 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 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 */ + +/* 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 4 + +#define PLOT_B 5 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.0 /* scaling factor for energy log representation */ +#define LOG_SHIFT 5.0 /* 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 0.05 /* 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 */ + +#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 */ + +``` + +### 15 February 22 - Interacting dipoles on a topological Klein bottle ### + +**Program:** `lennardjones.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 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 -1.8 +#define INITXMAX 1.8 /* x interval for initial condition */ +#define INITYMIN -1.0 +#define INITYMAX 1.0 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 5 /* 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 2.0 /* 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 1.8 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.045 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1800 /* number of frames of movie */ +#define NVID 120 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#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 11 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* 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 PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.1 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.001 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 3.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 5.0 /* 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 250.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 0 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e8 /* maximal force */ + +#define HASHX 24 /* size of hashgrid in x direction */ +#define HASHY 14 /* 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 February 22 - Crystal formation on a topological Klein bottle ### + +**Program:** `lennardjones.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 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 -1.8 +#define INITXMAX 1.8 /* x interval for initial condition */ +#define INITYMIN -1.0 +#define INITYMAX 1.0 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#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 2.0 /* 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 2.75 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.02 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1700 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 10 /* time after which to start saving frames */ +#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 11 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 3 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* 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 PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.0e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 5.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.1 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.002 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 4.5 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 5.0 /* 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 500.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 0 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e9 /* maximal force */ + +#define HASHX 32 /* size of hashgrid in x direction */ +#define HASHY 18 /* 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 */ + +``` + +### 13 February 22 - Wave protection comparison 16: nonuniformly spaced triangles with two opposed directions ### + +**Program:** `wave_comparison.c` + +**Initial condition in function `animation()`:** `int_planar_wave_comp(XMIN + 0.015, 0.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +#define TIME_LAPSE 1 /* set to 1 to add a time-lapse movie at the end */ +#define TIME_LAPSE_FACTOR 4 /* factor of time-lapse movie */ + +#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 YMID 500 /* mid point of display */ +#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 JULIA_SCALE 1.0 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 40 /* choice of domain shape, see list in global_pdes.c */ +#define B_DOMAIN_B 40 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 13 /* pattern of circles, see list in global_pdes.c */ +#define CIRCLE_PATTERN_B 13 /* 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 RANDOM_POLY_ANGLE_B 0 /* set to 1 to randomize angle of polygons */ + +#define XDEP_POLY_ANGLE 0 /* set to 1 to rotate polygons depending on x coordinate */ +#define XDEP_POLY_ANGLE_B 0 /* set to 1 to rotate polygons depending on x coordinate */ +#define POLY_ROTATION_ANGLE -0.645 /* rotation angle for |x|=1 in units of Pi/2 */ +#define HEX_NONUNIF_COMPRESSSION 0.15 /* compression factor for HEX_NONUNIF pattern */ +#define HEX_NONUNIF_COMPRESSSION_B -0.15 /* compression factor for HEX_NONUNIF pattern */ + +#define LAMBDA 0.8 /* parameter controlling the dimensions of domain */ +#define MU 0.035 /* parameter controlling the dimensions of domain */ +#define MUB 0.035 /* parameter controlling the dimensions of domain */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define APOLY_B 2.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 4 /* depth of computation of Menger gasket */ +#define MRATIO 3 /* ratio defining Menger gasket */ +#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */ +#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */ +#define FOCI 1 /* set to 1 to draw focal points of ellipse */ +#define NGRIDX 20 /* 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 below */ + +/* Physical parameters of wave equation */ + +#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */ +#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */ +#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */ + +#define OMEGA 0.0 /* frequency of periodic excitation */ +#define AMPLITUDE 0.025 /* amplitude of periodic excitation */ +#define COURANT 0.02 /* Courant number */ +#define COURANTB 0.004 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 1.0e-8 /* damping factor in wave equation */ +#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */ +#define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */ +#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */ +#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */ +#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */ +/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */ +/* The physical damping coefficient is given by GAMMA/(DT)^2 */ +/* Increasing COURANT speeds up the simulation, but decreases accuracy */ +/* For similar wave forms, COURANT^2*GAMMA should be kept constant */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 3 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3700 /* number of frames of movie */ +#define NVID 25 /* number of iterations between images displayed on screen */ +#define NSEG 100 /* number of segments of boundary */ +#define INITIAL_TIME 150 /* time after which to start saving frames */ +#define COMPUTE_ENERGIES 1 /* set to 1 to compute and print energies */ +#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 1 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* Parameters of initial condition */ + +#define INITIAL_AMP 0.75 /* amplitude of initial condition */ +#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */ +#define INITIAL_WAVELENGTH 0.02 /* wavelength of initial condition */ + +/* Plot type, see list in global_pdes.c */ + +#define PLOT 4 + +/* Color schemes */ + +#define COLOR_PALETTE 12 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* background */ +#define BLACK_TEXT 1 /* set to 1 to write text in black instead of white */ + +#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 ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 2000.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.5 /* 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 220.0 /* mean value of hue for color scheme C_HUE */ +#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */ + +#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */ +#define COLORBAR_RANGE 30.0 /* 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 */ + + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 5.0 /* max value of wave amplitude */ + +``` + +### 12 February 22 - Frustration in an antiferromagnetic material ### + +**Program:** `lennardjones.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 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 2.0 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 5 /* 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 2.0 /* 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 2.0 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.045 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2500 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#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 2 +#define BOUNDARY_COND 3 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* 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 PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 3.5 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.01 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.002 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 3.3 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 5.0 /* 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 500.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 2.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 100 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e10 /* maximal force */ + +#define HASHX 23 /* size of hashgrid in x direction */ +#define HASHY 14 /* 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 February 22 - Liquid crystals ### + +**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 */ + +/* General geometrical parameters */ + +#define WINWIDTH 720 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -1.125 +#define XMAX 1.125 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#define INITXMIN -1.125 +#define INITXMAX 1.125 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 1.125 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#define INTERACTION 6 /* 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 2.0 /* 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 2.25 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.045 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 1350 /* number of frames of movie */ +#define NVID 120 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 50 /* time after which to start saving frames */ +#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 3 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 4 +#define PLOT_B 3 /* plot type for second movie */ + +#define COLOR_BONDS 1 /* set to 1 to color bonds according to length */ + +/* Color schemes */ + +#define COLOR_PALETTE 0 /* 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 PARTICLE_HUE_MIN 359.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 0.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.001 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 10.0 /* initial velocity range */ +#define OMEGA_INITIAL 10.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.002 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 3.3 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 1 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 5.0 /* 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 500.0 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 1.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 0 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 100 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e10 /* maximal force */ + +#define HASHX 23 /* size of hashgrid in x direction */ +#define HASHY 14 /* 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 */ + +``` + +### 10 February 22 - Phase of spiral waves in the stochastic FitzHugh-Nagumo equation ### + +**Program:** `fhn.c` + +**Initial condition in function `animation()`:** `init_random(0.0, 1.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* 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 JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 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 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 0.00000015 + +#define VISCOSITY 5.0 +#define GAMMA_INVERSE 1.0 + +#define EPSILON 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN 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 1 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.04 /* noise intensity */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3700 /* number of frames of movie */ +#define NVID 10 /* 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 2 /* 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 25 /* initial still time */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Plot type */ + +#define PLOT 11 + +/* Field representation */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ + +#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 */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 18 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 4 /* choice of color scheme */ + +#define COLOR_PHASE_SHIFT 1.0 /* 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 1.5 /* 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 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 0.55 /* scale of color scheme bar */ +#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 9 February 22 - A Carnot cycle ### + +**Program:** `lennardjones_carnot.c` (variant of `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 */ + +/* 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 -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.05 +#define INITYMAX 0.0 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#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 1.0 /* 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 5.0 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.012 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3500 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 400 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#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 1 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 6 /* plot type for second movie */ + +/* 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 PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.5 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ + +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.002 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 7.0 /* 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 5.0 /* 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 0.001 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 400 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 1 /* 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 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 0 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e10 /* maximal force */ + +#define HASHX 23 /* size of hashgrid in x direction */ +#define HASHY 14 /* 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 */ + +``` + +### 8 February 22 - Spiral waves in the stochastic FitzHugh-Nagumo equation ### + +**Program:** `fhn.c` + +**Initial condition in function `animation()`:** `init_random(0.0, 1.0, phi, psi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* 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 JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 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 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 0.00000025 + +#define VISCOSITY 2.0 +#define GAMMA_INVERSE 1.0 + +#define EPSILON 0.1 /* time scale separation */ +#define FHNA 1.0 /* parameter in FHN equation */ +#define FHNC -0.01 /* parameter in FHN 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 1 /* set to 1 to add noise, set to 2 to add noise in right half */ +#define NOISE_INTENSITY 0.1 /* noise intensity */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 4500 /* number of frames of movie */ +#define NVID 5 /* 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 2 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 25 /* initial still time */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* For debugging purposes only */ +#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */ +#define VMAX 10.0 /* max value of wave amplitude */ + +/* Plot type */ + +#define PLOT 0 + +/* Field representation */ + +#define FIELD_REP 0 + +#define F_INTENSITY 0 /* color represents intensity */ +#define F_GRADIENT 1 /* color represents norm of gradient */ + +#define PRINT_TIME 0 /* set to 1 to print running time */ + +#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 */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 1.5 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ + +#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */ +#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */ +#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */ +#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */ +#define HUEMEAN 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 ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */ + +``` + +### 7 February 22 - Another property of the Tokarsky unilluminable room without right angles ### + +**Program:** `particle_billiard.c` + +**Initial condition in function `animation()`:** `init_line_config(0.0, 0.3, 0.0, 0.9, 0.0, configs);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +#define WINWIDTH 1280 /* window width */ +#define WINHEIGHT 720 /* window height */ + +#define XMIN -2.0 +#define XMAX 2.0 /* x interval */ +#define YMIN -1.125 +#define YMAX 1.125 /* y interval for 9/16 aspect ratio */ + +#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 1 /* pattern of circles */ +#define POLYLINE_PATTERN 6 /* 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 0.8 /* parameter controlling shape of domain */ +#define MU 0.015 /* 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 5000 /* number of particles */ +#define NPARTMAX 100000 /* maximal number of particles after resampling */ +#define LMAX 0.01 /* minimal segment length triggering resampling */ +#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */ +#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */ +#define SHOWTRAILS 1 /* set to 1 to keep trails of the particles */ +#define SHOWZOOM 1 /* set to 1 to show zoom on specific area */ +#define PRINT_PARTICLE_NUMBER 1 /* 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 5000 /* number of frames of movie */ +#define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */ +#define DPHI 0.00001 /* integration step */ +#define NVID 150 /* number of iterations between images displayed on screen */ + +/* Decreasing TIME accelerates the animation and the movie */ +/* For constant speed of movie, TIME*DPHI should be kept constant */ +/* However, increasing DPHI too much deterioriates quality of simulation */ +/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */ +/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */ + +/* Colors and other graphical parameters */ + +#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */ + +#define NCOLORS 32 /* number of colors */ +#define COLORSHIFT 0 /* hue of initial color */ +#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */ +#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */ +#define NSEG 100 /* number of segments of boundary */ +#define LENGTH 0.05 /* length of velocity vectors */ +#define BILLIARD_WIDTH 2 /* width of billiard */ +#define PARTICLE_WIDTH 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 1000 /* final sleeping time */ + +``` + +### 6 February 22 - Phase separation in the Cahn-Hilliard equation ### + +**Program:** `cahnhilliard.c` + +**Initial condition in function `animation()`:** `init_random(0.0, 1.0, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* 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 JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 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 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 0.000002 +#define VISCOSITY 20.0 +#define GAMMA_INVERSE 1.0 + +#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 1.0 /* noise intensity */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2700 /* number of frames of movie */ +#define NVID 10 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 20.0 /* factor by which to increase NVID in course of simulation */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 25 /* initial still time */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* 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 */ + +/* Field representation */ + +#define FIELD_REP 0 + +#define F_INTENSITY 0 /* color represents intensity */ +#define F_GRADIENT 1 /* color represents norm of gradient */ + +#define PRINT_TIME 1 /* set to 1 to print running time */ + +#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 */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 2 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.99 /* 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 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 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 1 /* set to 1 to draw color scheme horizontally */ + +``` + +### 5 February 22 - An adiabatic piston ### + +**Program:** `lennardjones.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 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 -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.05 +#define INITYMAX 0.95 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#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 1.0 /* 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 5.0 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.015 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 3100 /* number of frames of movie */ +#define NVID 150 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#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 1 + +/* Plot type, see list in global_ljones.c */ + +#define PLOT 0 +#define PLOT_B 6 /* plot type for second movie */ + + +/* 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 PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 1.0e3 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 2.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.0 /* damping coefficient of particles */ +#define PARTICLE_MASS 1.0 /* mass of particle of radius MU */ +#define PARTICLE_MASS_B 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* moment of inertia of particle */ +#define PARTICLE_INERTIA_MOMENT_B 0.02 /* moment of inertia of second type of particle */ +#define V_INITIAL 0.5 /* initial velocity range */ +#define OMEGA_INITIAL 2.0 /* initial angular velocity range */ + +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.3 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e7 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 0.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 7.0 /* 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 5.0 /* 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 0.001 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 200 /* final phase in which temperature is constant */ + +#define DECREASE_CONTAINER_SIZE 1 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e10 /* maximal force */ + +#define HASHX 23 /* size of hashgrid in x direction */ +#define HASHY 14 /* 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 February 22 - Raindrops in a von Koch snowflake ### + +**Program:** `wave_billiard.c` + +**Initial condition in function `animation()`:** + +``` + init_circular_wave(0.6*cos((double)(period)*DPI/3.0), 0.6*sin((double)(period)*DPI/3.0), phi, psi, xy_in); + period++; + + if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == OSCILLATING_SOURCE_PERIOD - 1)) + { + add_circular_wave(-1.0, 0.6*cos((double)(period)*DPI/3.0), 0.6*sin((double)(period)*DPI/3.0), phi, psi, xy_in); + 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 JULIA_SCALE 1.0 /* 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 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 1.1 /* 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 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 0.002 /* frequency of periodic excitation */ +#define AMPLITUDE 1.0 /* amplitude of periodic excitation */ +#define COURANT 0.03 /* Courant number */ +#define COURANTB 0.01 /* Courant number in medium B */ +#define GAMMA 0.0 /* damping factor in wave equation */ +#define GAMMAB 5.0e-4 /* 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 100 /* 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 25 /* 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 50 /* number of still frames 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 5 /* plot type for second movie */ + +/* Color schemes */ + +#define COLOR_PALETTE 18 /* 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 0.2 /* sensitivity of color on wave amplitude */ +#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */ +#define E_SCALE 150.0 /* scaling factor for energy representation */ +#define LOG_SCALE 1.5 /* scaling factor for energy log representation */ +#define LOG_SHIFT 0.0 /* 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 6.0 /* 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 */ + +#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 */ + +``` + +### 3 February 22 - Deep impact: Throwing large discs into a Lennard-Jones crystal without a thermostat ### + +**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 */ + +/* 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 -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 0.0 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#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 1.0 /* 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 5.0 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.012 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2400 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#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 3 /* plot type for second movie */ + +/* 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 PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.5e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 4.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* 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 2.0 /* initial angular velocity range */ + +#define THERMOSTAT 0 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.3 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 1000.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 7.0 /* 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 5.0 /* 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 0.001 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 200 /* 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 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 1 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e10 /* maximal force */ + +#define HASHX 23 /* size of hashgrid in x direction */ +#define HASHY 14 /* 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 */ + +``` + +### 2 February 22 - Deep impact: Throwing large discs into a Lennard-Jones crystal ### + +**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 */ + +/* 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 -1.95 +#define INITXMAX 1.95 /* x interval for initial condition */ +#define INITYMIN -1.125 +#define INITYMAX 0.0 /* y interval for initial condition */ + +#define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_ljones.c */ + +#define TWO_TYPES 0 /* set to 1 to have two types of particles */ +#define TPYE_PROPORTION 0.8 /* proportion of particles of first type */ + +#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 1.0 /* 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 5.0 /* 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 2.0 /* parameter controlling the dimensions of domain */ +#define MU 0.012 /* parameter controlling radius of particles */ +#define MU_B 0.02427051 /* parameter controlling radius of particles of second type */ +#define NPOLY 3 /* number of sides of polygon */ +#define APOLY 0.5 /* 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 80 /* number of grid point for grid of disks */ +#define NGRIDY 25 /* 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 */ + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 2400 /* number of frames of movie */ +#define NVID 250 /* number of iterations between images displayed on screen */ +#define NSEG 150 /* number of segments of boundary */ +#define INITIAL_TIME 200 /* time after which to start saving frames */ +#define BOUNDARY_WIDTH 1 /* width of particle boundary */ +#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 3 /* plot type for second movie */ + + +/* 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 PARTICLE_HUE_MIN 330.0 /* color of original particle */ +#define PARTICLE_HUE_MAX 50.0 /* color of saturated particle */ +#define PARTICLE_EMAX 2.5e2 /* max energy for particle to survive */ + +#define RANDOM_RADIUS 0 /* set to 1 for random circle radius */ +#define DT_PARTICLE 4.0e-6 /* time step for particle displacement */ +#define KREPEL 10.0 /* constant in repelling force between particles */ +#define EQUILIBRIUM_DIST 4.0 /* Lennard-Jones equilibrium distance for second type of particle */ +#define EQUILIBRIUM_DIST_B 5.0 /* 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 0.1 /* mass of particle of radius MU */ +#define PARTICLE_INERTIA_MOMENT 0.05 /* 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 2.0 /* initial angular velocity range */ + +#define THERMOSTAT 1 /* set to 1 to switch on thermostat */ +#define SIGMA 5.0 /* noise intensity in thermostat */ +#define BETA 0.3 /* initial inverse temperature */ +#define MU_XI 0.05 /* friction constant in thermostat */ +#define KSPRING_BOUNDARY 2.0e6 /* confining harmonic potential outside simulation region */ +#define NBH_DIST_FACTOR 5.0 /* radius in which to count neighbours */ +#define GRAVITY 1000.0 /* gravity acting on all particles */ + +#define ROTATION 0 /* set to 1 to include rotation of particles */ +#define COUPLE_ANGLE_TO_THERMOSTAT 1 /* 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 7.0 /* 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 5.0 /* 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 0.001 /* factor by which to change BETA during simulation */ +#define N_TOSCILLATIONS 0.5 /* number of temperature oscillations in BETA schedule */ +#define NO_OSCILLATION 1 /* set to 1 to have exponential BETA change only */ +#define FINAL_CONSTANT_PHASE 200 /* 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 0.6 /* final size of container */ +#define RESTORE_CONTAINER_SIZE 0 /* set to 1 to restore container to initial size at end of simulation */ +#define RESTORE_TIME 400 /* 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 OBSTACLE_RADIUS 0.27 /* radius of obstacle for circle boundary conditions */ +#define OBSTACLE_XMIN 0.0 /* initial position of obstacle */ +#define OBSTACLE_XMAX 3.0 /* final position of obstacle */ + +#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 1 /* set to 1 to add particles */ +#define ADD_TIME 100 /* time at which to add first particle */ +#define ADD_PERIOD 500 /* time interval between adding further particles */ +#define SAFETY_FACTOR 3.0 /* no particles are added at distance less than MU*SAFETY_FACTOR of other particles */ + +#define FLOOR_FORCE 1 /* set to 1 to limit force on particle to FMAX */ +#define FMAX 1.0e10 /* maximal force */ + +#define HASHX 23 /* size of hashgrid in x direction */ +#define HASHY 14 /* 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 February 22 - Phase separation in the Allen-Cahn equation, with a start in slow motion ### + +**Program:** `allencahn.c` + +**Initial condition in function `animation()`:** `init_random(0.0, 1.0, phi, xy_in);` + +``` +#define MOVIE 1 /* set to 1 to generate movie */ + +/* 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 JULIA_SCALE 0.5 /* scaling for Julia sets */ + +/* Choice of the billiard table */ + +#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */ + +#define CIRCLE_PATTERN 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 1.5 /* parameter controlling the dimensions of domain */ +#define MU 0.8 /* parameter controlling the dimensions of domain */ +#define NPOLY 6 /* number of sides of polygon */ +#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */ +#define MDEPTH 5 /* 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 0.0000002 +#define VISCOSITY 20.0 +#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 1.0 /* noise intensity */ + +/* Boundary conditions, see list in global_pdes.c */ + +#define B_COND 1 + +/* Parameters for length and speed of simulation */ + +#define NSTEPS 4000 /* number of frames of movie */ +#define NVID 1 /* number of iterations between images displayed on screen */ +#define ACCELERATION_FACTOR 150.0 /* factor by which to increase NVID in course of simulation */ +#define NSEG 100 /* number of segments of boundary */ +#define BOUNDARY_WIDTH 2 /* width of billiard boundary */ + +#define PAUSE 100 /* number of frames after which to pause */ +#define PSLEEP 1 /* sleep time during pause */ +#define SLEEP1 2 /* initial sleeping time */ +#define SLEEP2 1 /* final sleeping time */ +#define INITIAL_TIME 25 /* initial still time */ +#define END_FRAMES 100 /* number of still frames at end of movie */ + +/* 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 */ + +/* Field representation */ + +#define FIELD_REP 0 + +#define F_INTENSITY 0 /* color represents intensity */ +#define F_GRADIENT 1 /* color represents norm of gradient */ + +#define PRINT_TIME 1 /* set to 1 to print running time */ + +#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 */ + +/* Color schemes, see list in global_pdes.c */ + +#define COLOR_PALETTE 2 /* Color palette, see list in global_pdes.c */ + +#define BLACK 1 /* black background */ + +#define COLOR_SCHEME 3 /* choice of color scheme */ + +#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */ +#define SLOPE 0.99 /* 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 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 12.0 /* scale of color scheme bar for 2nd part */ +#define ROTATE_COLOR_SCHEME 1 /* set to 1 to draw color scheme horizontally */ + +```