Active-Site Motion and Pattern Formation in Self-Organised Interface Depinning

TL;DR

This paper investigates the formation of patterns around the active growth site in a self-organised interface depinning model, revealing a power-law tail and size-dependent correlations driven by active site dynamics.

Contribution

It introduces an approximate integral equation linking interface profile and active site jumps, highlighting the generic nature of pattern formation in such systems.

Findings

Pattern exhibits a power-law tail in height gradients.

Two-point correlation function saturates to a size-dependent value.

Pattern formation is driven by correlated active site motion.

Abstract

We study a dynamically generated pattern in height gradients, centered around the active growth site, in the steady state of a self-organised interface depinning model. The pattern has a power-law tail and depends on interface slope. An approximate integral equation relates the profile to local interface readjustments and long-ranged jumps of the active site. The pattern results in a two-point correlation function saturating to a finite value which depends on system size. Pattern formation is generic to systems in which the dynamics leads to correlated motion of the active site.