Linear vs Hertz (clockwise)

As there is no energy input in the simulation, for the Hertz law, set the restitution coefficient to something close to one, like .99 - we need to dissipate a little bit to avoid numerical explosion (it should not happen, but, oh well - I will check what the energy evolution is, the stuff should be normally conservative); the default value 0.7 probably dissipates too much and the simulation slows down (http://woodem.eu/doc/theory/contact/hertzian.html#coefficient-of-restitution).

I am a bit suspicious about alignment and going in circles, there is inherent axial symmetry and the simulation should not prefer one direction; it might be chaos-like thing where a random perturbation eventually propagates to the global state, but even like that it should be statistically the same probability whether it turns left or right.

Contact models are documented in http://woodem.eu/doc/theory/contact/index.html in detail if you need that.

Cheers, v.

Yes, mentioning ‘Clockwise’ is rather incidental, it was just to point out that they go round like a clock, CW or CCW is of no importance. I’ve just uploaded a short simulation of this type of action where they go CCW (Counter Clock Wise):

http://youtu.be/t1AHWO4FgMk

And indeed boosting the ‘Restitution coefficient’ up to .99 makes them move more dynamic for a longer time, but by doing so the subtle interaction is gone and they become again chaotic, acting similar to the ‘Linear’ method ... and that *special* circular motion is gone : /

In the text you linked to it says:

“Observable collisions of particles usually result in some energy dissipation of which measure is coefficient of restitution which can be expressed as the ratio of relative velocity before and after collision, ϵ=v0/v1 where v0, v1 are relative velocities before and after collision respectively.” (http://woodem.eu/doc/theory/contact/hertzian.html#coefficient-of-restitution)

… now wouldn’t it be a possible to short-cut the dissipation and put in some sort of recharge-action after each collision where V1 is reset to V0 (V1 => V0). Don’t know if such an intervention is even technically possible?

Incase it would be doable to integrate such a tweak, than the Ellipsoids could keep on moving round like those circular flocking fish at a constant velocity … if this is real or not isn’t so important, cause this method is already ‘unphysical’ as mentioned in the quote in my initial question:

“Strictly speaking, the simplified contact force-displacement law is thermodynamically inconsistent (i.e., unphysical), since it permits energy generation at no cost.”

I’m just think out loud here … and probably seeing things too simplistic : )

best,

m.

Hi, what you suggest for the short-cut collision computation, that is not possible with this method (there is a method capable of doing that - called smooth particle dynamics - but it has its own limitations and is not efficient for something denser than very loose media such as gas (as far as I know)). Instead, the integration must e adjusted such that after a number of timesteps, the resulting velocity has the magnitude it should have - that's what the article http://woodem.eu/doc/references.html#antypov2011 deals with. So even when the restitution coefficient is not directly applied, the simulation should have it as result (plus minus numerical noise), so when yo uset it to 1, there should be no energy lost ( there is energy plot in the preprocessor starting from rev 3423).

For the Hertz-Mindlin text you cite (which is a nice reference BTW): the model is thermodynamically inconsistent when there is shear force (IIRC that is the "Mindlin" part), for purely normal deformation (Hertz), it should be energy-conserving (nonlinearly elastic).

ok, I was wrong in presuming that the material method 'Hertz' you have in your program was the same as 'Hertz-Mindlin' ... it's a variation.

None the less there's an interesting illustration in that paper, where it shows how to spheres are squashed against each other, and there's dissipation. The outcome of this 'squashing' is (almost) identical as the rotation deflection that I'm looking for; during the squashing there is an Internal Action going on, similar to the Internal Action that would happen when the Ellipsoid rotates during a sliding collision, here's a sketch to explain this thought:

http://bit.do/Rotate_Compress

On the left there's a fully elastic particle rotating, on the right there's one that's being compressed.

--

Now the problem with dissipation (COR) set to 1, is that when the particles make contact that there is no Inter-action or Internal-action happening, so they quickly bounce away again in a sharp angle.

Look at the left collision drawing; when the ellipsoid makes contact at point A the oval would immediately move away from that point in a sharp angle, so no sliding and turning nor making longer contact with the floor; or in the case of the drawing on the right, the Squashed contact area probably becomes a single point, and the contact action isn't splashed out. The problem with this seems to be that there is no longer any alignment going on, which is what I'm after.

One extra point regarding conservation of energy or dissipation of it, is that when 2 particles collide, they give each other a push or as on the clear-top-illustration, the squash each other, so what they give the get equally back and there is no loss of energy, unless you start saying that there is some 'heat' production, but this shouldn't be the case for the elastic turning particles.

Anyway, what I don't get is that you can start a simulation in your program with a random tessellated setting and a given velocity for all the particles (V0=1) just out of the blue; so from my layman point of view, I would think that its possible to stop your program, or the individual collisions, and after each fished collision resume with the existing setting, but with the difference that V0 is reset to 1 and perhaps also with Angular velocity set back to 0. So the tessellation is replaced by a newly generated tessellation.

cheers,

m.

Thanks Václav Šmilauer, that solved my question.