Rigid interacting tripod molecules
Channel: Nils Berglund
Date: 01/03/2024

This simulation uses "multi-armed" molecules as in the video https://youtu.be/rMsMF9S6byA , but here the molecules have been made more rigid, by adding forces between the central and external atoms of each molecule, that tend to keep their distance constant. I was hoping to get a kind of foamy structure self-assembling from the molecules. While this is not quite successful here, forthcoming simulations in this series will show improvements.
Each molecule in this simulation is made of a central atom, to which three "arms" are attached. The last atom in each arm is electrically charged. The charge is the same in each molecule, but its sign can be different for different molecules. Atoms in different molecules interact via a Coulomb potential, which is complemented by a Lennard-Jones interaction between atoms of different charge, in order to prevent their collapse on a single point. Atoms within one molecule interact with stiff harmonic potentials, that tend to keep certain distances constant. A thermostat keeps the system at a constant temperature, and there are periodic boundary conditions. 
The video has two parts, showing the same simulation with two different color schemes:
Charge: 0:00
Kinetic energy: 1:37
In the first part, the particles' color hue depends on their charge. In the second part, it depends on their kinetic energy.
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 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 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: 12 minutes 46 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
https://github.com/bastibe/twilight
Part 2 - Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a

Music: "Stand" by Anno Domini Beats@AnnoDominiBeats

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/s10955-009-9734-0
http://www.maths.warwick.ac.uk/~theil/HL12-3-2009.pdf

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)

#molecular_dynamics #water_molecules #ice