Tracer Dispersion in a Self-Organized Critical System

TL;DR

This study investigates transport properties in a granular system exhibiting self-organized criticality, revealing how transit times, velocities, and active zone dynamics scale with system size through experiments and modeling.

Contribution

It provides experimental evidence and a cellular automaton model to understand transport and relaxation in self-organized critical granular systems.

Findings

Transit time distribution shows a constant followed by a power-law decay.

Average transport velocity decreases as system size increases.

Active zone depth grows with system size, influencing transport dynamics.

Abstract

We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette {\em et al., Nature} {\bf 379}, 49 (1996)]. Tracer particles were added to a pile and their transit times measured. The distribution of transit times is a constant with a crossover to a decaying power law. The average transport velocity decreases with system size. This is due to an increase in the active zone depth with system size. The relaxation processes generate coherently moving regions of grains mixed with convection. This picture is supported by considering transport in a $1D$ cellular automaton modeling the experiment.