A two-species model of a two-dimensional sandpile surface: a case of asymptotic roughening

TL;DR

This paper introduces a coupled two-species model for a 2D sandpile surface, revealing a transition from initial smoothing to asymptotic roughening with novel scaling exponents.

Contribution

It presents a new coupled model of mobile and immobile grains in a sandpile, analyzing its asymptotic roughening behavior and identifying non-trivial scaling exponents.

Findings

Initial logarithmic smoothing at short scales

Transition to roughening in the asymptotic limit

Identification of novel scaling exponents

Abstract

We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is flat on average, so that there is no bias due to gravity. We find anomalous scaling: the expected logarithmic smoothing at short length and time scales gives way to roughening in the asymptotic limit, where novel and non-trivial exponents are found.