Bistability and hysteresis in tilted sandpiles

Abstract

We show that tilting a model sandpile that has dynamic disorder leads to bistability and hysteresis at the angle of repose. Also the distribution of {\it local slopes} shows an interesting dependence on the amount of tilt - weakly tilted sandpiles retain the quasi-continuous distributions of the steady state, while large tilt makes the distribution more discrete, with local slopes clustered round particular values. These observations are used to explain recent experimental results on avalanche shapes; we give a theoretical framework in terms of directed percolation.