A Continuum Description of Vibrated Sand
  The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is considered. We develop equations of motion for the local thickness and the horizontal velocity of the layer. The driving comes from the violent impact of the grains on the plate. A linear stability theory reveals that the waves are excited non-resonantly, in contrast to the usual Faraday waves in liquids. Together with the experimentally observed continuum scaling, the model suggests a close connection between the neutral curve and the dispersion relation of the waves, which agrees quite well with experiments. For strong hysteresis we find localized oscillon solutions. 
Jens Eggers (Universit\"at Gesamthochschule Essen, Germany) and   Hermann Riecke (Northwestern University, Evanston, USA)