Abstract

Parametric waves arise spontaneously when a thin layer of granular material is oscillated vertically. A dynamical model of these waves accounting for the observed instability threshold and appearance of square patterns is presented. The proposed instability mechanism is due to two competing processes: a focusing effect that concentrates particles in space, and a diffusion effect that relaxes large thickness gradients in the layer. When the layer is in a liquid-type state, close to a solid-liquid transition, the model correctly predicts the presence of oscillons recently reported by P. Umbanhowar et al.