Liquid crystals

The interaction potential is given in polar coordinates by
V(r,phi) = (req/r)^12 - A(phi- theta)*(req/r)^6,
where req is 2.5 times the size of the particles, theta is their orientation, and
A(phi) = a - b*cos(2*phi)
with a = 11.6 and b = 6.78 (these values have been chosen such that there are four stable equilibrium positions approximately compatible with a tiling by lozenges with angles 36° and 144°).
The angular coupling between particles with orientations theta1 and theta2 is proportional to -sin(2(theta2-theta1)), and decays like the inverse of the square of the distance between particles.
The temperature is controlled by a thermostat, which is here 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. 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.

Render time: 3 minutes
Color gradients: Jet

Current version of the C code used to make these animations:
Some outreach articles on mathematics:
(in French, some with a Spanish translation)

[cheydinal]

The music makes me say "Wait, yeah, it does kind of look like a Bond film title scene animation!"

[ventishiddencentralmilker]

Wow. One of the most interesting simulations yet. I remember studying LCDs at college this would have been great.

[mishael]

It's finally here! Great stuff. Now to conquer the quasicrystal :p

[Andrewzero]

Ahhh, now he’s trying to simulate an lcd display :P

[eelcohoogendoorn]

Thats really cool, never seen liquid crystal dynamics animated like this before. There is a lot going on here; there is a funny sort of recycling dynamic going on in the thin filament; and eventually it thins out and breaks off completely, rather than behaving in some kind surface energy minimizing fashion, as youd normally expect. I suppose this can be understood as arising from the bulk orientation of the filament; if its at an angle to the bigger body, the whole filament would need to rotate to get into an attractive state, but that wont happen so easily; so itd rather break off. Very interest emergent behavior, wonder if this can be related to real world known physical effects.

[punkerts]

Love your music choice. Always a different tune 👍🎶

[deandrereichelle]

Weirdly, reminds me of a slide I saw of the San Andreas fault slippage

[coppertones]

do you run the simulation then pick the music? because this is perfect music for rhombuses sneakily sliding over each other.

[David_Rg]

the music reminds me of minute physics... kinda?

[adrien]

That's neat! And once again a great music choice.

[a.i.chemist]

Reminds me of the DNA production electronic microscope videos.
We are crystals.

[toastybowl]

This is godly. Can I view a code sample anywhere ? ?
E: oh I see it. * It's long-press -> description -> very bottom section

[fukuokainternationaldemocr]

Wow. Things I didn't know that I wanted to watch.

[GiacomoFranzil]

What is the name of the soundtrack? XD

[YSPACElabs]

Are these the same liquid crystals that are used in lcd screens? I would like to see a simulation where n electric field is applied to liquid crstsls.

[ARBB]

I've never seen these in motion. Try applying a electric field to see the twisting!