Smarties on Mars: Particles on a rotating sphere with the topography of Mars

This is a variant of the video https://youtu.be/9z_7b1VKEzM using the topography of Mars, greatly exaggerated in the radial direction, instead of Earth. Mars is much lower in the upper part of its northern hemisphere, and features a high-altitude volcanic plateau, the Tharsis region, in its western hemisphere. These have a noticeable impact on the particles' motion.
The simulation shows particles on a rotating sphere, subjected to a force field derived from Mars's topography. More precisely, a digital elevation model (DEM) has been used as a potential, and particles are subject to a force given by the numerically estimated gradient of that potential, which goes from higher to lower altitudes. In this way, mountains act as barriers for the particles.
The rotation of the sphere manifests itself in two different inertial forces: a centrifugal force, and a Coriolis force. The centrifugal force pushes particles towards the equator, and is strongest at latitudes 45° and -45°. The Coriolis force is proportional to the particles' speed, and tends to make them turn in different ways in the two hemispheres.
This simulation has two parts, showing the same evolution with two different visualizations:
3D view: 0:00
2D view: 1:48
In the 3D part, the observer rotates around the sphere on an orbit in a plane containing the center of the sphere, at an angular speed slightly below the speed of the gravitational field. The 2D part shows an equirectangular projection (the x- and y-coordinates are proportional to longitude and latitude). The particles are represented by ellipses, instead of circles, to reflect the distortion of the projection near the poles. The particles' color depends on their kinetic energy. The shading of the sphere and the trajectory of the observer are with respect to the frame rotating with the sphere.
The temperature is controlled by a thermostat, implemented here with the "Nosé-Hoover-Langevin" algorithm introduced by Ben Leimkuhler, Emad Noorizadeh and Florian Theil, see reference below. The idea of the algorithm is to couple the momenta of the system to a single random process, which fluctuates around a temperature-dependent mean value. Lower temperatures lead to lower mean values. 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.
The Lennard-Jones potential is strongly repulsive at short distance, and mildly attracting at long distance. It is widely used as a simple yet realistic model for the motion of electrically neutral molecules. The force results from the repulsion between electrons due to Pauli's exclusion principle, while the attractive part is a more subtle effect appearing in a multipole expansion. For more details, see https://en.wikipedia.org/wiki/Lennard-Jones_potential

Render time: 3D part: 1 hour 42 minutes
2D part: 41 minutes 28 seconds
Color scheme: Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a

Music: "Cloud Wheels Castle Builder" by Puddle of Infinity

Reference: Leimkuhler, B., Noorizadeh, E. & Theil, F. A Gentle Stochastic Thermostat for Molecular Dynamics. J Stat Phys 135, 261–277 (2009). https://doi.org/10.1007/s10955-009-9734-0
http://www.maths.warwick.ac.uk/~theil/HL12-3-2009.pdf

Current version of the C code used to make these animations:
https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund-Nils-1343_.html
(in French, some with a Spanish translation)

Видео Smarties on Mars: Particles on a rotating sphere with the topography of Mars канала Nils Berglund