MODEL FOR SUBHARMONIC WAVES IN GRANULAR-MATERIALS

Parametric waves arise spontaneously when a thin layer of granular mat erial is oscillated vertically. A dynamical model of these waves accou nting for the observed instability threshold and appearance of square patterns is presented. The proposed instability mechanism is due to tw o competing processes: a focusing effect that concentrates particles i n 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 so lid-liquid transition, the model correctly predicts the presence of os cillons recently reported by P. Umbanhowar et al.