Onset of avalanches in granular media

Marginal stability and avalanches at angles Θ≥${\mathrm{\Theta }}_{\mathit{a}\mathit{v}\mathit{a}\mathit{l}}$ 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 ‖v‖∝${\mathit{t}}^{\gamma }$, typically with 3.5≤γ, 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.