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The following situation interests me and I was wondering if there is software to model it?

A large set of n spheres of uniform density and discrete sizes, mass proportional to volume, are dropped together on a narrow inclined plane under low gravity (so they are free to bounce and sort themselves) . The spheres are assigned mutual repulsion and attraction functions according to size, such that balls of a certain size are at equilibrium a certain distance apart.

This doesn't reflect any physical phenomenon I am aware of, but it seems like the sort of thing a physicist might model. I have seen physical contraptions that drop balls into slots so they sort themselves into a more or less "normal" distribution, and this is not unlike what I have in mind. But the situation is a little more complicated and I don't really have any preconceived idea about the results.

It may be there is no simple program that does this sort of thing, and that too would be an answer.

Suggestions appreciated. Thanks.

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Since all the balls are accelerating together, this problem is equivalent, by the non-relativistic equivalence principle, to the problem of balls moving without gravity, or on a horizontal surface, which are free to sort themselves out according to the same force law. This reduced problem is interesting and widely studied. Depending on the force law, you can get either a 1-d integrable model, or a 1-d statistical equilibrium, and both have a massive literature.

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Your point about the reduced problem seems responsive and I will think about that, but the question is about software. Any suggestions? – daniel Sep 14 '12 at 4:03
@daniel: It's straightforward to write your own integrator, but you didn't specify the problem in great detail. Just have x,v for each particle, and update (t,x,v) at each time step to (t+\epsilon, x+\epsilon v, v+\epsilon F) for each particle, that's good enough for qualitative simulations. If you want better, use this for predicting the new positions, and then the average of the velocity and force at the new and old position to do the real update. These things are standard, and can be found in "Numerical Recipes in C". – Ron Maimon Sep 14 '12 at 5:11
As you note, I didn't specify in detail. The problem is a little stickier (the spheres aren't completely free to sort, for example). Yes I think I could do it myself but (even using recipes) it would take a long time. Well...perhaps that's the answer. Thanks. – daniel Sep 14 '12 at 11:33
@daniel: If you sit down and do it, you will find that it won't take a long time. The only thing that usually takes a long time is the graphics. – Ron Maimon Sep 14 '12 at 15:41

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