Shaken, not stirred: why gravel packs better than bricks

We explore the effect of shape -- jagged vs. regular -- in the jamming limit of very gently shaken packings. Our measure of shape $\eps$ is the void space occupied by a disordered grain; we show that depending on its number-theoretic nature, two generic behaviours are obtained. Thus, regularly shaped grains (rational $\eps$) have ground states of perfect packing, which are irretrievably lost under zero-temperature shaking; the reverse is the case for jagged grains (irrational $\eps$), where the ground state is only optimally packed, but entirely retrievable. At low temperatures, we find intermittency at the surface, which has recently been seen experimentally.