A Langevin Approach to One-Dimensional Granular Media Fluidized by   Vibrations
  We present a Langevin approach to describe the steady-state dynamics of one-dimensional granular media fluidized by a vibrating bottom plate. We adopt a linear Langevin equation to describe the motion of the center of mass. Within this framework, we derive analytical expressions for several macroscopic quantities. We also predict the power spectrum for the height of the center of mass. We find good agreement between our theoretical predictions and extensive event-driven molecular dynamics simulations. 
Jun'ichi Wakou, Akinori Ochiai, Masaharu Isobe