Shaken, not stirred: why gravel packs better than bricks

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We explore the effect of shape -- jagged vs. regular -- in the jamming limit of very gently shaken packings. Our measure of shape 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) have ground states of perfect packing, which are irretrievably lost under zero-temperature shaking; the reverse is the case for jagged grains (irrational), 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.