Spherical pool with two pockets at the poles connected by one wall

This simulation was suggested in a comment. It is a variant of recent spherical pool simulations, but with two pockets located at the north and south pole of the sphere, and a reflecting well connecting the two pockets, running along a meridian.
The incoming particle is shot at a set of immobile particles, in a similar configuration to what one would do for pool billiard, but on a sphere. There is no friction acting on the particles, and also no thermostat. The motion of the particles is governed solely by a Lennard-Jones interaction between them.
The video has two parts, showing the same simulation with two different representations:
3D view: 0:00
2D view: 2:39
In both parts, the color of the particles depends on their kinetic energy. The 2D part shows an equirectangular projection, meaning that the x- and y-coordinates are proportional to the longitude and latitude of the particles. Particles move in apparently curved lines due to the projection - you see similar paths for spacecraft and satellites orbiting the Earth. Particles should actually have elongated elliptical shapes when approaching the poles, but we chose not to do this here. This is also why atoms of the same molecule can appear to be far from each other near the poles. In the 3D parts, the observer moves around the sphere in a plane containing the center of the sphere. The number of particles that have fallen into pockets over time is shown at the top right.
To save on computation time, particles are placed into a "hash grid", each cell of which contains between 3 and 10 particles. Then only the influence of other particles in the same or neighboring cells is taken into account for each particle.

Render time: 3D part: 29 minutes 3 seconds
2D part: 2 minute 16 seconds
Compression: crf 28
ffmpeg added noise option: -vf noise=alls=10:allf=t+u
Color scheme: Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-wor...

Music: "Leaky" by Max McFerren

Current version of the C code used to make these animations:
https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...
Some outreach articles on mathematics:
https://images.math.cnrs.fr/auteurs/n...
(in French, some with a Spanish translation)

#particles #sphere #LennardJones