Nonequilibrium Phase Transitions in a Driven Sandpile Model

TL;DR

This paper introduces a driven sandpile slope model studied via numerical simulations, revealing a complex nonequilibrium phase diagram with multiple phases distinguished by mean slopes and boundary types.

Contribution

It develops a new one-dimensional driven sandpile model with analytical and numerical analysis of its nonequilibrium phase transitions.

Findings

Multiple phases with different mean slopes identified

Phase boundaries include both continuous and first-order transitions

Analytical results obtained for some phase boundaries

Abstract

We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope $\sigma_c\/$, a parameter $\alpha\/$, governing the local current-slope relation (beyond threshold), and $j_{\rm in}$, the mean input current of sand. A nonequilibrium phase diagram is obtained in the $\alpha\, -\, j_{\rm in}\/$ plane. We find an infinity of phases, characterized by different mean slopes and separated by continuous or first-order boundaries, some of which we obtain analytically. Extensions to two dimensions are discussed.