Long-Tailed Trapping Times and Levy Flights in a Self-Organized Critical Granular System

TL;DR

This paper models scale-invariant grain transport in a self-organized critical rice pile using a continuous time random walk approach, revealing Levy flights and long-tailed trapping times, supported by analytical and cellular automaton results.

Contribution

It introduces a novel continuous time random walk model explaining grain dynamics with Levy flights and trapping times in a self-organized critical system.

Findings

Transport follows Levy flight statistics.

Trapping times have a long-tailed distribution.

Model predictions match cellular automaton simulations.

Abstract

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of L\'evy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.