Self-organized criticality in a rice-pile model

TL;DR

This paper introduces a stochastic model for granular pile relaxations that exhibits self-organized criticality, characterized by power-law distributions of avalanches and size scaling with system size.

Contribution

The authors develop a new stochastic model incorporating friction effects, demonstrating self-organized criticality in granular pile relaxations with specific scaling laws.

Findings

Power-law distribution of avalanche sizes with exponent ~1.53

Avalanche lifetimes follow a power-law with exponent ~1.84

Discharge event sizes scale with system size as L^1.20

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