  We report on a toy model for the glassy compaction dynamics of granular
systems, introduced and investigated in collaboration with Anita Mehta and
Peter Stadler. A stochastic dynamics is defined on a column of grains. Grains
are anisotropic and possess a discrete orientational degree of freedom. Gravity
induces long-range directional interactions down the column. The key control
parameter of the model, $\epsilon$, is a representation of granular shape.
Rational and irrational values of $\epsilon$ correspond to very different kinds
of behavior, both in statics (structure of ground states) and in
low-temperature dynamics (retrieval of ground states).
