Winnowing 3: Throwing the particles from the ground @NilsBerglund

Nils Berglund | Winnowing 3: Throwing the particles from the ground @NilsBerglund | Uploaded October 2024 | Updated October 2024, 3 minutes ago.
This variant of the video youtu.be/jd5dmbsgqic shows again the process of sorting particles by size using wind, the difference being that here the particles are thrown from near the ground instead of being dropped from above. This is closer to the real process used for winnowing, or separating grain from chaff by throwing it into the air, after it has been threshed. There are a few more sorting errors than in the previous simulation, which seem to be due to collisions between particles.
In this simulation, the particles have different sizes, but the same mass. They are subjected to gravity, and to a horizontal force proportional to their radius, modeling the effect of wind. The wind stops a short distance above the bins at the bottom, to avoid that the particles bounce on the bins' walls.
The particles' color depends on their size.
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 en.wikipedia.org/wiki/Lennard-Jones_potential

Render time: 4 minutes 12 seconds
Compression: crf 23
Color scheme: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a

Music: "Two Sides" by SefChol@SefChol

Current version of the C code used to make these animations:
github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Some outreach articles on mathematics:
https://images.math.cnrs.fr/auteurs/nils-berglund/
(in French, some with a Spanish translation)

#molecular_dynamics #winnowing

Youngs double-slit experiment for a quantum particle, phase representation

Growing quasicrystals by dynamic aggregation of pentagons

Density and direction of speed of more stable vortices on a rotating sphere

Shallow water flowing over an immersed octahedron

Replicants are like any other machine: Trying to model DNA replication

Shallow water flowing over an immersed cube

$Waves escaping a ring of obstacles: Logarithmic spirals This is a simulation of waves originating from a point source crossing a set of circular obstacles placed on 60 logarithmic spirals, having 25 discs each. On each logarithmic spiral, the radial coordinate grows linearly, while the angular coordinate is an affine function of the logarithm of the radius. One particularity of this design is that the energy appears to leave the ring on straight lines that are not radial, but tangent to the spirals at their endpoints. This video has two parts, showing the same evolution with two different color gradients: Averaged wave energy: 0:00 Wave height: 1:14 In the first part, the color hue depends on the energy of the wave, averaged over a sliding time window. In the second part, it depends on the height of the wave. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction. The color in the central region has been brightened to white, because the waves tend to make large-amplitude oscillations there, which would not be very pleasant to watch. There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy). Render time: 26 minutes 6 seconds Compression: crf 23 Color scheme: Part 1 - Inferno by Nathaniel J. Smith and Stefan van der Walt Part 2 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firinghttps://github.com/BIDS/colormap Music: Plaidness by Francis Preve@francispreve See also https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations. The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf C code: https://github.com/nilsberglund-orleans/YouTube-simulations https://www.idpoisson.fr/berglund/software.html Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code! #wave #diffraction$ $Waves escaping a ring of obstacles: Poisson disc grid This is a simulation of waves originating from a point source crossing a set of circular obstacles placed randomly in an annular region. The centers of obstacles follow a so-called Poisson disc process, which is the most random distribution that keeps a minimal distance between the points. This video has two parts, showing the same evolution with two different color gradients: Averaged wave energy: 0:00 Wave height: 1:11 In the first part, the color hue depends on the energy of the wave, averaged over a sliding time window. In the second part, it depends on the height of the wave. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction. The color in the central region has been brightened to white, because the waves tend to make large-amplitude oscillations there, which would not be very pleasant to watch. There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy). Render time: 32 minutes 37 seconds Compression: crf 23 Color scheme: Part 1 - Magma by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Part 2 - Twilight by Bastian Bechtold https://github.com/bastibe/twilight Music: The Great Unknown by Audionautix is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/Artist: http://audionautix.com/ See also https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations. The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf C code: https://github.com/nilsberglund-orleans/YouTube-simulations https://www.idpoisson.fr/berglund/software.html Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code! #wave #diffraction$

Neutral soap and water with increasing force constant