A granular medium with two types of particles
Channel: Nils Berglund
Date: 15/09/2023

This simulation of a granular material was suggested in a comment to a previous video. It features particles of two different sizes and masses. The larger particles are 1.4 times as large, and 2.5 times as heavy as the smaller ones. Initially, particles are put on a regular lattice, and each particle is randomly assigned type 1 or 2, with probability 1/2 each. It appears that particles have a tendency to group in patches of the same type, as is the case in phase separation in alloys or mixtures of different fluids, though the effect is not very strong. It is possible that a larger mass ratio will increase the effect.
The particles in this simulation interact via a Lennard-Jones potential, and are subject to a viscous damping term, gravity directed to the right, and to a one-sided harmonic repulsion from the obstacle. There are periodic boundary conditions. 
This simulation has two parts, showing the evolution with two different color schemes:
Type of particle: 0:00
Initial x coordinate: 2:12
In the first part, the color of the particles depends on their type. In the second part, each particle is given a color at the beginning of the simulation, which is a function of its x-coordinate. The particle then keeps the same color throughout the simulation.
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 17 minutes
Color scheme: Part 1 - Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Part 2 - HSL/Jet

Music: George Street Shuffle by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1300035
Artist: http://incompetech.com/

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 #phonon