Скачать или смотреть A branched flow (super short version, energy flow direction)

Today, there will be two short simulations of a branched flow. For some reason I don't really understand, YT kept completely ruining the render of the video I uploaded after the first 15 seconds (it may have been an issue with resolution). I get the problem once in a while, but usually uploading the video again works, though this was not the case here. So I made two different short lasting about 15 seconds, with two different color gradients.
These simulations were suggested to me by Álvar Daza, one of the people running the web site https://www.blochbusters.com/ , which contains, among other things, simulations and background on branched flows.
A circular wave is emitted at the center of the displayed region. The wave speed depends on the position in the following way. It is given by a sum of Gaussians, which are centered at the vertices of a Poisson disc process. The amplitude of the Gaussians is also random. The wave speed is thus maximal near the points of the Poisson disc process, and drops nearly to zero in other regions. Due to the interaction with the random wave speed, the wave may be expected to branch when it encounters regions with low propagation speed, though the relation between branching and speed may be more complicated than that.
The color hue shows the direction of the energy flux, while the luminosity shows the intensity of the energy flux, slightly averaged over time. There are absorbing boundary conditions on the outer boundaries of the simulation.

Reference: Eric J. Heller, Ragnar Fleischmann, Tobias Kramer, Branched flow, Physics Today 74 (12), 44–51 (2021).
https://pubs.aip.org/physicstoday/art...
Poisson disc sampling: https://bl.ocks.org/mbostock/dbb02448...

Render time: 3 minutes 4 seconds
Color scheme: HSV/Jet

Music: News Theme 2 by Audionautix is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/...
Artist: http://audionautix.com/

See also https://images.math.cnrs.fr/Des-ondes... for more explanations (in French) on a few previous simulations of wave equations.

The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc...
C code: https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

#branched_flow #wave_equation #waves #refraction