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