A conveyor belt with shovels

In this new variant of a conveyor belt simulation, I have added "shovels" to the belt (or whatever you call those things). The conveyor belt effect results from a combination of two factors: the shovels, and the fact that the segments forming the belt exert 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.
This simulation has two parts, showing the evolution with two different color gradients:
Initial x position: 0:00
Velocity: 3:04
In the first part, the particles' color depends on their initial x position. This allows to get a sense of how particles are mixed while falling through the funnel. In the second part, the due depends on the direction in which the particles are moving, while the luminosity depends on their speed. Both quantities are averaged over a time interval.
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: 26 minutes 7 seconds
Compression: crf 23
Color scheme: Part 1 - Turbo, by Anton Mikhailov
Part 2 - Twilight by Bastian Bechtold

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

#molecular_dynamics #polygons #sand

[jannikheidemann]

Precious freshly mined hexagons being belted into a nice pile.

[qujt]

"No human would stack hexagons like this."

[ewthmatth]

Finally he makes something I can almost understand

[NicosLeben]

Why are the dots not accelerating while falling? This looks odd.

[urosjarc]

I don't know why, but I found this simulation hilarious... 3:43 look how balls with every scoop jump like they are disturbed... Excuse me little hexagons, let me scoop you up... Little hexagons:

[Andrewzero]

I like how you can see the conveyor belt hitting the pile and the velocity visualization shows the wave propogating.

[grande]

was anyone else hoping for one of the hexagons to get past the scoops and under the conveyor belt?

[nkronert]

Excellent! Now do it with Tetris blocks 😉

[thatprogramer]

Very cool simulation! Thanks for sharing it!

[EdwardChan.]

This could be more efficient if the conveyor belt is lower than the floor on the left side...

[nathangonzales-hess]

Sorting algorithms are getting crazy these days.

[leyasep]

At the end, there is a weird "lifting" anomaly at the right side of the middle wall. Any hypothesis ? Is gravity and/or friction incorrectly tuned ?

[qujt]

You loved Pinball Construction Set as a kid didn't you Nils :)

[Rhino-Flea]

Is it truly ethical to develop this kind of technology for Hexacorp?

[atreidesson]

how is falling a 0 velocity while ascending even slower than falling is some value

[ukvaishnav]

Something seems wrong in falling particles. Why do the particle after hitting the conveyor belt not travel in straight-line and seem to keep constant distance from other falling particles.