Smaller interacting kites-and-darts-type molecules

This variant of the simulation • Looking for quasicryst... of interacting molecules shaped like kites and darts uses more than twice as many molecules (2025 instead of 900) of smaller size.
The kites are quadrilaterals with angles 144°, and three times 72°, while the darts have two angles of 36°, one angle of 72° and one angle of 216°. These are modeled by using four charges atoms on the vertices of the quadrilateral, and two additional neutral atoms on the symmetry axis for kites, and on the long sides for darts.
I'm not quite satisfied with this first try, because the single atoms still stand out too much. I may be able to improve things by modeling the molecules as collections of segments instead of point particles.
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.
The temperature is controlled by a thermostat with increasing temperature. There is a constant gravitational force directed downward.
This simulation has two parts, showing the evolution with two different color gradients:
Type: 0:00
Orientation: 1:08
In the first part, the particles' color depends on their type (kites or darts), 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.
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: 52 minutes 46 seconds
Compression: crf 23
Color scheme: Part 1 - Particles: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-wor...
Background: Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - HSL/Jet
Music: "Thug Dub" by Quincas Moreira‪@QuincasMoreira‬
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 #quasicrystal

[@emrahyalcin]

would be logical to keep the temperature stable at first to see the movement only under the gravitational effect, after a while until a constant phase, increase the temperature?

[@MDNQ-ud1ty]

The temperature is relatively stable. It starts about 1k and goes to 8k. Over the range of the temperature this is a small percentage. It likely would not produce a different effect.
E.g., one could also ask about starting off with a much higher temperature to see the effect. Both can be done and there will be differences but the basic difference will essentially be to change the average size of the "holes". Higher temp would produce smaller holes while lower temps would produces larger holes, on average. Likely some middle temp actually would have a maximum hole size.
E.g., maybe something better would be to calculate the average hole size(basically a density calculation) and plot that as the temperature changes. The temperature would have to get hot enough to break a lot of "bonds" to see a more gaseous phase. Plotting the density would show the effect of temperature on the substances. (with a very high temp one would get a lower density)

[@emrahyalcin]

@@MDNQ-ud1ty I see... about the "holes". wov, I would expect reverse, warmer, bigger. but I get the idea. warmer, means weaker bonds, hence, easier to break the structure arround big holes... Thank you for your comprehensive answer.

[@MDNQ-ud1ty]

@@emrahyalcin Well, if the temperature is high enough it might be bigger in some sense unless the volume is fixed.
Think of ice melting. It has holes in it when solid(air pockets) and when it melts all those pockets will be released.
As the atoms move around faster and faster they will have more of a chance to move into a free space(a hole) which would reduce the size(the size is technically hard or impossible to define). But think of all the atom all stacked up in a corner then there would be one large hole vs if they were uniformly spread out which there would be a slot of "small holes"(there would be no holes because the atoms wouldn't be connected but the sort of "average density" would be very different).

[@NilsBerglund]

Numerical algorithms such as temperature cycling and simulated annealing use this idea to try and find, at least approximately, the minimum of a complicated energy landscape. If you freeze a system too quickly (this is called quenching), it will typically end up in a state with a lot of holes. Move the temperature up and down with decreasing step size, and the system will be able to find a denser state. The idea apparently goes back to metallurgic processes centuries ago.

[@yuan-jiafan9998]

Why is gravity taken into account? Typically, gravity can be disregarded at the molecular level.

[@NilsBerglund]

Here I added gravity mainly to help the molecules coagulate. Think of a centrifuge, if you like.