Dissipative properties and scaling law for a layer of granular material on a vibrating plate

The dissipative properties and scaling law for a layer of vertically vibrated granular materials were investigated by means of a dynamical model of a single sphere colliding completely inelastically with a massive, oscillating plate. A relationship is presented of how the temperature of the layer scales with the acceleration of the plate and the restitution coefficient of the grains. The numerical calculation shows the existence of an "energy well" and a "temperature well," which could be used to explain the existence of a f/2 flat (where f is the external driving frequency) state in an experiment on vibrated granular material.