Transport in Sand Piles, Interface Depinning, and Earthquake Models

TL;DR

This paper links dispersive transport in rice piles and earthquake models to interface depinning transitions, revealing universal scaling behaviors and suggesting a common universality class.

Contribution

It maps a rice pile transport model to interface depinning, providing new insights into scaling laws and universality in complex systems.

Findings

Transport velocity scales with system size as L^{-0.23}

Avalanche size distribution exponent is approximately 1.55

Proposes earthquake models share the same universality class

Abstract

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.