Dynamics of Granular Matter

Abstract
Granular matter is a typical example of a new topic in statistical (phenomenology) mechanics. Reconsidering granular matter from the physical point of view, several new aspects have been clarified, although granular matter has been studied by engineers for a long (period of) time. This review examines three topics: (1) pattern dynamics of sand ripples and dunes, (2) mathematical structure of a fluidized bed, and (3) convection and turbulence in a vibrating bed. Investigating these topics, it is found that the dynamics of granular matter exhibits many typical nonlinear phenomena, for example, formations of pattern, localized states, and turbulence.