Crossover to Self-Organized Criticality in an Inertial Sandpile Model

TL;DR

This paper introduces a one-dimensional inertial sandpile model that demonstrates a transition from self-organized criticality to non-critical behavior as particle inertia increases, supported by numerical and mean-field analyses.

Contribution

It presents a novel inertial sandpile model and analyzes the criticality transition using both numerical simulations and mean-field theories.

Findings

System transitions from critical to non-critical as inertia increases

Mean-field theories confirm numerical results

Potential applications discussed in physical contexts

Abstract

We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the system no longer evolves to a self-organized critical state. A range of mean-field theories based on a kinetic equation approach is presented which confirm the numerical findings. We conclude by considering the physical applications of this model, particularly with reference to recent experimental results.