Dynamics of a grain on a sandpile model

The dynamics of a macroscopic grain rolling on an inclined plane composed of fixed identical grains is investigated both experimentally and theoretically. As real sand, the system exhibits an hysteretic transition between static and dynamical states: for angles smaller than ${\phi }_d,$ the roller always stops, for angles larger than ${\phi }_s,$ it spontaneously starts rolling down. But for angles between ${\phi }_d$ and ${\phi }_s,$ it can be either at rest or in motion with a constant velocity. It is shown that the limit velocity is given by the equilibrium between gravity driving and dissipation by the shocks. Moreover, the rough plane acts as a periodic potential trap whose width and depth decrease when the angle is increased: the static angle ${\phi }_s$ corresponds to the angle for which the trap disappears; the dynamical angle ${\phi }_d$ to that for which the limit velocity is sufficient to escape from the trap. Finally, a continuous description of the force globally acting on the grain is proposed, which preserves this hysteretic behavior.