A denser granular material with square-symmetric interaction flowing around a disc
Channel: Nils Berglund
Date: 2023-07-20

This is a variant of the simulationhttps://youtu.be/AuEl-1csLL4 of a granular material flowing around a disc, in which the particles have a higher density. This creates some unexpected movements in the granular material: Instead of always flowing to the right, which is the direction of gravity, it sometimes changes direction. This might be an instance of the "flying ice cubes" phenomenon, in which energy is transferred from oscillatory modes to translational ones. 
The interaction between particles is not purely radial, but has some dependence on the particles' orientation, having the symmetry of a square. In addition, the particles interact with a magnetic-moment type torque that tends to align their orientation. The square-symmetric interaction tends to make the particles a bit more mobile, as they try to find arrangements that decrease the energy. Furthermore, the particles are subject to gravity and friction, and they interact with the walls via a one-sided stiff harmonic potential. 
This simulation has two parts, showing the evolution with two different color schemes:
Orientation: 0:00
Initial position: 1:53
In part 1, the color of the particles depends on their orientation, that is, their angle modulo 90 degrees. In part 2, it depends on their initial y-coordinate, so that one gets a sense of how particles are mixed. 
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: 50 minutes 25 seconds
Color scheme: Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a

Music: "Freeze Frame" by Stayloose@StayLoose

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)

#granular_material #lennardjones #LennardJones #molecular_dynamics