2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/21394We investigate a stochastic model describing a column of grains in the jamming limit, in the presence of a low vibrational intensity. The key control parameter of the model, $ε$, is a representation of granular shape, related to the reduced void space. Regularity and irregularity in grain shapes, respectively corresponding to rational and irrational values of $ε$, are shown to be centrally important in determining the statics and dynamics of the compaction process.29 pages, 14 figures, 1 table. Various minor changes and updates. To appear in EPJ BStatistical Mechanicstext