Falling sticks

This is a preparatory simulation, for a new way to simulate interacting polygonal shapes. The particles in this simulation are very thin rectangles. They interact via a harmonic potential as soon as they come close to each other, and their dynamics is determined from the total force and torque. A weak Lennard-Jones interaction has been added for stability, but it may not be necessary.
If the motion of the sticks does not seem very realistic, this can probably be improved by tweaking the parameters (force constants of the harmonic interaction, moment of inertia, friction for the rotational dynamics). The temperature is controlled by a thermostat with constant temperature. There is a constant gravitational force directed downward.
This simulation has two parts, showing the evolution with two different color gradients:
Orientation: 0:00
Kinetic energy: 1:08
In the first part, the particles' color depends on their orientation. In the second part, it depends on their kinetic energy, averaged over a sliding time window.
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 - HSL/Jet
Part 2 - Turbo, by Anton Mikhailov
gist.github.com/mikhailov-wor...
Music: "Come and Get It!" by Dan Lebowitz‪@lebo_tone‬
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/auteurs/n...
(in French, some with a Spanish translation)
#molecular_dynamics #ions #quasicrystal

[@SillySussySally]

is it me or do the sticks not have rotational inertia.

[@mistycremo9301]

You make a very good point

[@NilsBerglund]

I used a high rotational friction, which essentially kills inertia. This is the "tweaking parameters" I allude to in the description: one could use a lower friction by increasing the moment of inertia of the sticks.
Forthcoming simulations will involve polygons with 3 sides or more, for which the parameter choices have been improved.

[@JosuaKrause]

also it seems the sticks can overlap on occasion

[@NilsBerglund]

@JosuaKrause: Indeed. This is because the spring constant in the harmonic interaction is large but finite. I managed to improve that for polygons with three or more sides, as a forthcoming video will show.

[@jannikheidemann3805]

Fitting that the music on this video is made with sticks.

[@Schoohness]

Sprimkle

[@seb612schuth]

Ok this is hilarious 😂 Sticks be fallin' 🍡

[@nzuckman]

OH GOD MY BONES AAAAAAAAHHHHH

[@ilyadorokhov7827]

There is no rotation?

[@NilsBerglund]

The sticks do rotate. But I put a high friction on rotation, so there is almost no inertia. The next simulation in this series will improve on that.