Velocity Fluctuations in a Homogeneous 2D Granular Gas in Steady State

Abstract

We have measured the spectrum of velocity fluctuations in a granular system confined to a vertical plane and driven into a homogeneous, steady state by strong vertical vibration. The distribution of horizontal velocities is not Maxwell-Boltzmann and is given by $P(v)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}C\mathrm{exp}[\ensuremath{-}\ensuremath{\beta}(|v|/\ensuremath{\sigma}{)}^{\ensuremath{\alpha}}]$ where $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.55\ifmmode\pm\else\textpm\fi{}0.1$ at all frequencies and amplitudes investigated, and also for varying boundary conditions. The deviation from Maxwell-Boltzmann statistics occurs in the absence of spatial clustering and does not result from an inhomogeneous average over regions of varying local density. Surprisingly, $P(v)$ has the same shape over a wide range of densities.