YouTube-simulations

Tool to create videos of particles or waves in different 2D domains.

Created by Nils Berglund and optimized by Marco Mancini

C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund

Parameter values used in specific simulations will be gradually added to file Parameters.md, Parameters_June21.md and so on.

There are four groups of 8 files, 19 files, 6 files and 4 files. In addition the following files handling color schemes have been included:

1. hsluv.cand hsluv.h from https://github.com/adammaj1/hsluv-color-gradient
2. turbo_colormap.c from https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
3. colormaps.c containing look-up tables from https://github.com/yuki-koyama/tinycolormap

The following file (beta version) provides support for creating mazes:

1. sub_maze.c

The files

1. *.ppm.gz

are required by wave_sphere.c and rde.c and should be unzipped before compiling.

Simulations of classical particles in billiards.

1. particle_billiard.c: simulation of a collection of non-interacting particles in a billiard
2. drop_billiard.c: simulation of an expanding front of particles
3. particle_pinball.c: variant of particle_billiard with some extra statistics plots
4. billiard_phasespace.c: variant of particle_billiard for phase portraits (only works for certain shapes)
5. global_particles.c: global variables and parameters
6. sub_part_billiard.c: drawing/computation routines common to particle_billiard and drop_billiard
7. sub_part_pinball.c: additional drawing/computation routines for particle_pinball
8. sub_billiard_phasespace.c: additional drawing/computation routines for billiard_phasespace

• Create subfolders tif_part, tif_drop
• Customize constants at beginning of .c file
• Compile with make particle_billiard, make_drop_billiard, etc, or

gcc -o particle_billiard particle_billiard.c-O3 -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lglut

gcc -o drop_billiard drop_billiard.c-O3 -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 lglut

• Many laptops claim to have 4 cores, but two of those are virtual. OMP acceleration may be more effective after executing

export OMP_NUM_THREADS=2

in the shell before running the program

• Generate movie with

ffmpeg -i part.%05d.tif -vcodec libx264 part.mp4

Simulations of wave equation and reaction-diffusion equations, including the Schrodinger equation.

1. wave_billiard.c: simulation of the (linear) wave equation
2. wave_3d.c: 3d rendering of wave equation
3. wave_sphere.c: wave equation on a sphere (3d and 2d render)
4. wave_comparison.c: comparison of the wave equation in two different domains
5. wave_energy.c: a version of wave_billiard plotting the energy profile of the wave
6. mangrove.c: a version of wave_billiard with additional features to animate mangroves
7. heat.c: simulation of the heat equation, with optional drawing of gradient field lines
8. rde.c: simulation of reaction-diffusion equations, plots in 2d and 3d (including Schrödinger equation, Euler equation, shallow water equation, Kuramoto and Keller-Segel models)
9. schrodinger.c: simulation of the Schrodinger equation in 2d (old version)
10. global_pdes.c: global variables and parameters
11. global_3d.c: additional global variables for 3d version
12. sub_wave.c: drawing/computation routines common to wave_billiard, heat and schrodinger
13. sub_wave_comp.c: some modified functions needed by wave_comparison
14. sub_wave_3d.c: additional functions for 3d version
15. wave_common.c: common functions of wave_billiard and wave_comparison
16. colors_waves.c: colormaps used by wave simulations
17. sub_rde.c: additional routines for rde.c
18. sub_wave_rde_3d.c: additional 3d drawing routines for rde.c
19. sub_sphere.c: additional routines for wave_sphere.c

• Create subfolders tif_wave, tif_heat, tif_bz, tif_schrod
• Customize constants at beginning of .c file
• Compile with make wave_billiard, etc, or

gcc -o wave_billiard wave_billiard.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lglut -O3 -fopenmp

gcc -o wave_comparison wave_comparison.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lglut -O3 -fopenmp

gcc -o heat heat.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp

gcc -o schrodinger schrodinger.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lglut -O3 -fopenmp

• Many laptops claim to have 4 cores, but two of those are virtual. OMP acceleration may be more effective after executing

export OMP_NUM_THREADS=2

in the shell before running the program

• Generate movie with

ffmpeg -i wave.%05d.tif -vcodec libx264 wave.mp4

Molecular dynamics simulations.

1. lennardjones.c: simulation of molecular dynamics
2. global_ljones.c: global variables and parameters
3. sub_lj.c: drawing and initialization routines
4. sub_hashgrid.c: hashgrid manipulation routines
5. sub_lj_sphere.c: additional routines for simulations on sphere (some functions from 'sub_lj.c' moved here)
6. lj_movie.c: render movie with precomputed particle positions (requires files lj_time_series.dat and lj_final_positions.dat generated by lennardjones)

• Create subfolder tif_ljones
• Customize constants at beginning of .c file
• Compile with make lennardjones or

gcc -o lennardjones lennardjones.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lglut -O3 -fopenmp

• Generate movie with

ffmpeg -i lennardjones.%05d.tif -vcodec libx264 lennardjones.mp4

Percolation simulations.

1. percolation.c: simulation of Bernoulli percolation
2. global_perc.c: global variables and parameters
3. sub_perco.c: drawing and cluster finding routines
4. sub_perco_3d.c: 3D drawing routines

• Create subfolder tif_perc
• Customize constants at beginning of .c file
• Compile with make percolation or

gcc -o percolation percolation.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lglut -O3 -fopenmp

• Generate movie with

ffmpeg -i percolation.%05d.tif -vcodec libx264 percolation.mp4

Some references

• Discretizing the wave equation: https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
• Absorbing boundary conditions: https://hal.archives-ouvertes.fr/hal-01374183
• Cloaking device: https://www.sciencedirect.com/science/article/pii/S0165212514001759
• Poisson disc sampling: https://bl.ocks.org/mbostock/dbb02448b0f93e4c82c3
• Thermostat algorithm: https://doi.org/10.1007/s10955-009-9734-0 or http://www.maths.warwick.ac.uk/~theil/HL12-3-2009.pdf