Onset of avalanches in granular media.

Abstract

Marginal stability and avalanches at angles \ensuremath{\Theta}\ensuremath{\ge}${\mathrm{\ensuremath{\Theta}}}_{\mathit{a}\mathit{v}\mathit{a}\mathit{l}}$ are associated with granular media (GM) subject to special conditions. We study the Newtonian dynamics of random size-mismatched hard-core-like disks in a two-dimensional box which confirm claims that avalanches in GM are restricted to a few topmost boundary layers. We find that the velocity profile of the top layer grains, which obey \ensuremath{\Vert}v\ensuremath{\Vert}\ensuremath{\propto}${\mathit{t}}^{\ensuremath{\gamma}}$, typically with 3.5\ensuremath{\le}\ensuremath{\gamma}, signal the onset of an avalanche in GM. Our studies suggest that the dynamics of a single particle in a cosine potential in the presence of a linear field well describes the onset of motion of a top layer grain.