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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 φd, the roller always stops, for angles larger than φs, it spontaneously starts rolling down. But for angles between φd and φs, 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 φs corresponds to the angle for which the trap disappears; the dynamical angle φd 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.

@article{quartier_dynamics_2000, title = {Dynamics of a grain on a sandpile model}, volume = {62}, url = {http://link.aps.org/doi/10.1103/PhysRevE.62.8299}, doi = {10.1103/PhysRevE.62.8299}, abstract = {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 φd, the roller always stops, for angles larger than φs, it spontaneously starts rolling down. But for angles between φd and φs, 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 φs corresponds to the angle for which the trap disappears; the dynamical angle φd 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.}, number = {6}, urldate = {2014-09-25TZ}, journal = {Physical Review E}, author = {Quartier, L. and Andreotti, B. and Douady, S. and Daerr, A.}, month = dec, year = {2000}, pages = {8299--8307} }

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