We don't have a good way of describing quantitatively what happens when you shake a bunch of sand, or other granular media. This has been a problem for a long time, but faster, more powerful computers that can do realistic computer simulations and gather huge amounts of data from experiments have opened up the possibility of making some real progress on this. Also, it looks really neat. You can view some images and some movies of shaking granular matter (actually a bunch of ball bearings on a plate) at the Granular Dynamics Home Page.

Crystallization in a computer simulation of vibrated inelastic spheres.