Nils Berglund | Sorting magnetized bestagons by size @NilsBerglund | Uploaded September 2024 | Updated October 2024, 4 minutes ago.
This simulation uses the same sorting device as in the video youtu.be/EcCHSkKQ8ic , including sieves that "rattle" to avoid clogging, with hexagonal instead of square particles. The friction force is proportional to the radius of the hexagons, which helps stabillizing the larger hexagons in the rightmost bin. In addition, a torque between hexagons has been added, which tends to align their orientation.
The sorting set-up consists in three grids of obstacles with decreasing space between them, acting as particle sieves. The obstacles rotate and exert a tangential force on the particles, in order to decrease clogging of the sieves. The angular speed of the obstacles varies periodically in time, in order to reduce the chance of particles getting stuck. In addition, the obstacles have a circular motion of small amplitude, which reduces the chances of particles getting stuck even more.
The conveyor belt effect results from the segments forming the belt exerting a tangential force on the polygons, in addition to the normal force. The tangential force is proportional to the difference between the tangential speed of the polygon and the speed of the belt.
To compute the force and torque of polygon j on polygon i, the code computes the distance of each vertex of polygon j to the faces of polygon i. If this distance is smaller than a threshold, the force increases linearly with a large spring constant. In addition, radial forces between the vertices of the polygons have been added, whenever a vertex of polygon j is not on a perpendicular to a face of polygon i. This is important, because otherwise triangles can approach each other from the vertices, and when one vertex moves sideways, it is suddenly strongly accelerated, causing numerical instability. A weak Lennard-Jones interaction between polygons has been added, as it seems to increase numerical stability.
Unlike in some previous videos involving interacting polygons, there is no thermostat in this simulation. Instead, friction forces (both linear and angular) have been added for numerical stability. In addition, the particles are subject to a gravitational force directed downwards.
The color of the polygons 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: 25 minutes 45 seconds
Compression: crf 23
Color scheme: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Music: "Islabonita" by An Jone@SOYEMILIA
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 #polygons #conveyor
This simulation uses the same sorting device as in the video youtu.be/EcCHSkKQ8ic , including sieves that "rattle" to avoid clogging, with hexagonal instead of square particles. The friction force is proportional to the radius of the hexagons, which helps stabillizing the larger hexagons in the rightmost bin. In addition, a torque between hexagons has been added, which tends to align their orientation.
The sorting set-up consists in three grids of obstacles with decreasing space between them, acting as particle sieves. The obstacles rotate and exert a tangential force on the particles, in order to decrease clogging of the sieves. The angular speed of the obstacles varies periodically in time, in order to reduce the chance of particles getting stuck. In addition, the obstacles have a circular motion of small amplitude, which reduces the chances of particles getting stuck even more.
The conveyor belt effect results from the segments forming the belt exerting a tangential force on the polygons, in addition to the normal force. The tangential force is proportional to the difference between the tangential speed of the polygon and the speed of the belt.
To compute the force and torque of polygon j on polygon i, the code computes the distance of each vertex of polygon j to the faces of polygon i. If this distance is smaller than a threshold, the force increases linearly with a large spring constant. In addition, radial forces between the vertices of the polygons have been added, whenever a vertex of polygon j is not on a perpendicular to a face of polygon i. This is important, because otherwise triangles can approach each other from the vertices, and when one vertex moves sideways, it is suddenly strongly accelerated, causing numerical instability. A weak Lennard-Jones interaction between polygons has been added, as it seems to increase numerical stability.
Unlike in some previous videos involving interacting polygons, there is no thermostat in this simulation. Instead, friction forces (both linear and angular) have been added for numerical stability. In addition, the particles are subject to a gravitational force directed downwards.
The color of the polygons 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: 25 minutes 45 seconds
Compression: crf 23
Color scheme: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Music: "Islabonita" by An Jone@SOYEMILIA
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 #polygons #conveyor
