Pentagonal foam with gravity

This video shows a simulation similar to the one in the video • A pentagonal foam bath... , but gravity has been added in order to favor coagulation. The initial configuration is twice as high as what is visible in on screen. The number of particles is thus larger than in the previous simulation, requiring a longer computation time.
The molecules in the simulation have a pentagonal symmetry, except that the symmetry is broken by the charge they are carrying. Some molecules have 3 positively and 2 negatively charged atoms, while for other molecules, the charge distribution is the other way round. When molecules come close enough, they can merge, gradually forming larger clusters.
I once again had in mind the formation of some kind of quasicrystal, but the molecules appear not to be rigid enough for that. The resulting effect looks more like a foam bath.
The particles in this simulation interact via a Coulomb potential when they belong to different molecules, and a harmonic potential within the same molecule. The Coulomb potential is complemented by a Lennard-Jones interaction between particles of opposite charge, to avoid their collapse on a single point.
There are periodic boundary conditions, and the temperature is controlled by a thermostat with increasing temperature.
This simulation has two parts, showing the evolution with two different color gradients:
Charge: 0:00
Orientation: 1:39
In the first part, the particles' color depends on their kinetic charge, while the background indicates the local charge density, slightly averaged over space and time. In the second part, the molecules' color depends on the orientation modulo 72 degrees, because of the five-fold symmetry.
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 en.wikipedia.org/wiki/Lennard...
Render time: 1 hour 48 minutes
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - Turbo, by Anton Mikhailov
gist.github.com/mikhailov-wor...
Music: Dance Monster - Electronic Medium by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. creativecommons.org/licenses/...
Source: incompetech.com/music/royalty-...
Artist: incompetech.com/
Reference: Leimkuhler, B., Noorizadeh, E. & Theil, F. A Gentle Stochastic Thermostat for Molecular Dynamics. J Stat Phys 135, 261-277 (2009). doi.org/10.1007/s10955-009-97...
www.maths.warwick.ac.uk/~theil...
Current version of the C code used to make these animations:
github.com/nilsberglund-orlea...
www.idpoisson.fr/berglund/sof...
Some outreach articles on mathematics:
images.math.cnrs.fr/_Berglund...
(in French, some with a Spanish translation)
#molecular_dynamics #ions #foam

[@blas5i]

with no background knowledge. Just love this channel

[@TymexComputing]

IF there exists gravity then how is the vector field applied , is there also some viscose medium present? I cant see the particles gaining momentum as if they were free falling 😕
"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" - can we call the attractive part simply van der Waals type of attraction - thats made of the ^6 and ^12 multipole terms.

[@NilsBerglund]

There is also a thermostat acting on the system, which has an effect somewhat similar to damping. It is in fact damping at high speeds, and adding energy at low speeds.

[@r.e.m.s]

Do you see a pentagonal structure at large scale, on a Fourier transformation ?

[@NilsBerglund]

I haven't tried taking a Fourier transform so far, but it seems like a good idea to try.