Trying to sort particles by mass in a granular medium flowing around a wedge
Channel: Nils Berglund
Date: 22/09/2023

This simulation is similar to the recent simuation https://youtu.be/NGCkRNC-RKI?si=sNEJhfqdxE-Mz3Qo , featuring particles of two different sizes and masses. The larger particles are 1.4 times as large, and 20 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. 
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 slightly down, at a slope 1/5, and to a one-sided harmonic repulsion from the obstacle. The wedge-shaped obstacle has a tendency to concentrate the light particles behind it, acting somewhat like a mass spectrometer. The angle of gravity has been chosen such that the periodic boundary conditions don't bring the light particles back directly to the wedge, but rather some distance below. It may be that an improved version of this design would allow a more efficient separation of the two types of particles. 
This simulation has two parts, showing the evolution with two different color schemes:
Type of particle: 0:00
Initial position: 3:02
In the first part, the color of the particles depends on their type. In the second part, the particles' color depends on their initial x-coordinate. 
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: 37 minutes 49 seconds
This is much faster than the previous similar simulation, as I discovered an improvement in the way particles are drawn - in fact, many previous sims of LJ particles drew them as circles made of an unnecessarily large number of segments.

Color scheme: Part 1 - Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Part 2 - HSL/Jet

Music: "Asleep with the Sun" by the Unicorn Heads@UnicornHeads

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