Random-Manifold to Random-Periodic Depinning of an Elastic Interface

TL;DR

This paper investigates the depinning transition of elastic interfaces in a random-periodic medium, revealing multiple characteristic length scales and their scaling behaviors, which unify the understanding of different depinning regimes.

Contribution

It introduces a comprehensive dynamical roughness diagram for elastic interfaces in random-periodic media, extending depinning analysis to include creep regimes and boundary condition effects.

Findings

Identified multiple length scales separating different roughness regimes.

Derived scaling laws for these lengths as functions of physical parameters.

Extended the depinning roughness diagram to include creep regimes.

Abstract

We study numerically the depinning transition of driven elastic interfaces in a random-periodic medium with localized periodic-correlation peaks in the direction of motion. The analysis of the moving interface geometry reveals the existence of several characteristic lengths separating different length-scale regimes of roughness. We determine the scaling behavior of these lengths as a function of the velocity, temperature, driving force, and transverse periodicity. A dynamical roughness diagram is thus obtained which contains, at small length scales, the critical and fast-flow regimes typical of the random-manifold (or domain wall) depinning, and at large length-scales, the critical and fast-flow regimes typical of the random-periodic (or charge-density wave) depinning. From the study of the equilibrium geometry we are also able to infer the roughness diagram in the creep regime, extending the depinning roughness diagram below threshold. Our results are relevant for understanding the geometry at depinning of arrays of elastically coupled thin manifolds in a disordered medium such as driven particle chains or vortex-line planar arrays. They also allow to properly control the effect of transverse periodic boundary conditions in large-scale simulations of driven disordered interfaces.