Скачать или смотреть Lennard-Jones particles in increasing gravity

Ever wondered what physics would look like in a spaceship that keeps accelerating to warp 27, or on the surface of a collapsing neutron star? This #short simulation shows 1152 particles interacting with a Lennard-Jones potential and confined to a box, subjected to a linearly increasing gravitational field. One can observe some nice avalanches triggering phonons as the particles try rearranging in more and more close-packed configurations. They are, however, hindered by the square boundary from forming a perfect triangular lattice, which is why some grain boundaries remain.
This simulation is inspired by the simulation    • Acceleration to over two million g's   by Hali Hammer @   / @halihammer  
Colors of particles indicate their kinetic energy: red particles move faster than blue ones. The motion can also be a fast oscillation with very small amplitude.
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. The temperature shown on the top right is in fact the temperature multiplied by Boltzmann's constant. 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...

For more molecular dynamics simulations, see the playlist    • Reaction-diffusion equations  

Render time: 15 minutes 30 seconds
Color scheme: Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-wor...

Music: Gold Rush by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/...
Source: http://incompetech.com/music/royalty-...
Artist: http://incompetech.com/

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/s10955-009-97...
http://www.maths.warwick.ac.uk/~theil...

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