Self-organized criticality in a rice-pile model

We present a 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 $\tau =1.53\mathrm{}\pm 0.05$ and $y=1.84\mathrm{}\pm 0.05$, respectively. For the discharge events, we find a characteristic size that scales with the system size as $L^{\mu }$, with $\mu =1.20\mathrm{}\pm 0.05$. We also find that the frequency of the discharge events decreases with the system size as $L^{-{\mu }^{\prime }}$ with ${\mu }^{\prime }=1.20\mathrm{}\pm 0.05$.