Heavy particles solving a maze filled with lighter particles
Channel: Nils Berglund
Date: 2023-07-03

In this new maze-solving video, heavier particles, colored in dark blue, enter a maze filled by lighter particles, colored in cyan. All particles are subject to gravity and damping. The videos in this series are inspired by the video https://youtu.be/81ebWToAnvA by Steve Mould, where he shows that when pouring water in an airtight maze, the water follows the optimal path to the exit, because air trapped in the dead-ends, when compressed, prevents the water from entering. The cyan particles here are supposed to represent air molecules, and they indeed prevent, to some extent, the heavier particles from entering dead-ends. However, the simulation does not achieve to model surface tension, which is an important factor in real water-air interfaces. 
This simulation has two parts, showing the evolution at two different playback speeds:
Time lapse: 0:00
Slow motion: 1:00
In part 1, the playback speed has been multiplied by a factor 3. 
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 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: 2 hours 26 minutes
Color scheme: Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a

Music: "Mission Dub" by Track Tribe@TrackTribe

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)

#maze #Lennard-Jones