Transport in Sand Piles, Interface Depinning, and Earthquake Models

Recent numerical results for a model describing dispersive transport in rice piles are explained by mapping the model to the depinning transition of an interface that is dragged at one end through a random medium. The average velocity of transport vanishes with system size $L$ as $<v> \sim L^{2-D}\sim L^{-0.23}$, and the avalanche size distribution exponent $\tau= 2 - 1/D \simeq 1.55$, where $D\simeq 2.23$ from interface depinning. We conjecture that the purely deterministic Burridge-Knopoff ``train'' model for earthquakes is in the same universality class.