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Trajectories in a Galton board
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=3CQ5iLYoE24
This simulation was suggested in a comment. It shows a Galton board, like the simulation • A molecular Galton board , but with particles of different size. In addition, trajectories are shown over a time interval. • The particles interact with each other via a Lennard-Jones potential. They are subjected to gravity, viscous friction, and harmonic repulsion forces from the obstacles and walls. In a Galton board, particles are assumed to have probability 1/2 to move left or right upon encountering an obstacle. As a result, the distribution of particles in the bins at the bottom should follow a binomial distribution. Here the friction is quite low, which allows the particles to bounce further away, sometimes flying over several obstacles. However, the resulting distribution still seems close enough to a binomial. • The simulation has two parts, showing the same evolution with two different color schemes: • Particle size: 0:00 • Kinetic energy: 2:36 • In the first part, the particles' color depends on their size. In the second part, it depends on their kinetic energy. The particles' trajectories are shown in the same color, and slowly fade over time. • 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... • Render time: 7 minutes 52 seconds • Compression: crf 23 • Color scheme: Turbo, by Anton Mikhailov • https://gist.github.com/mikhailov-wor... • Music: Dub Star by Topher Mohr and Alex Elena • Current version of the C code used to make these animations: • https://github.com/nilsberglund-orlea... • https://www.idpoisson.fr/berglund/sof... • Some outreach articles on mathematics: • https://images.math.cnrs.fr/auteurs/n... • (in French, some with a Spanish translation) • #molecular_dynamics #winnowing
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