A granular material with pentagon-symmetric interaction flowing around a disc
Channel: Nils Berglund
Date: 13/07/2023

This is a variant of the simulation https://youtu.be/racNwiyr_0I of a granular material flowing around a disc. Unlike in the previous simulation, the interaction between particles is not purely radial, but has some dependence on the particles' orientation, having the symmetry of a regular pentagon. In addition, they interact with a magnetic-moment type torque that tends to align their orientation. We have seen in previous simulations on this channel that since pentagon cannot form a regular crystal, the interaction seems to make their motion more fluid. 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:
Number of neighbors: 0:00
Orientation: 1:21
In part 1, the color of the particles depends on the number of neighbors within a fixed distance, which allows to visualize defects in the crystalline arrangement. In part 2, they show the particles' orientation, that is, their angle modulo 72 degrees.
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: 1 hour 11 minutes
Color scheme: Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a

Music: "Palmtrees" by The Brothers Records@donguyRockwell

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