Self-organized criticality in a rice-pile model

Abstract

We present a new model for relaxations in piles of granular material. The relaxations are determined by a stochastic rule which models the effect of friction between the grains. We find power-law distributions for avalanche sizes and lifetimes characterized by the exponents $τ= 1.53 \pm 0.05$ and $y = 1.84 \pm 0.05$, respectively. For the discharge events, we find a characteristic size that scales with the system size as $L^μ$, with $μ= 1.20 \pm 0.05$. We also find that the frequency of the discharge events decrease with the system size as $L^{-μ'}$ with $μ' = 1.20 \pm 0.05$.