• Hayakawa Hisao
    Department of Physics, Tohoku University, Sendai 980–77, Japan
  • Nishimori Hiraku
    Department of Physics, Ibaraki University, Mito 310, Japan
  • Sasa Sin"ichi
    Department of Pure and Applied Science, University of Tokyo, Komaba, Meguro–ku, Tokyo 153, Japan
  • Taguchi Y–h.
    Department of Physics, Tokyo Institute of Technology, Oh–okayama, Meguro–ku, Tokyo 152, Japan

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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.

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