2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97611We 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, $ε$, is a representation of granular shape. Rational and irrational values of $ε$ correspond to very different kinds of behavior, both in statics (structure of ground states) and in low-temperature dynamics (retrieval of ground states).17 pages. 8 figures. To appear in a special volume of Physica D (Serge Aubry 60th birthday symposium)Statistical Mechanicstext