Anisotropic Interface Depinning - Numerical Results

TL;DR

This paper numerically investigates an anisotropic interface depinning model, finding critical exponents consistent with the directed percolation depinning universality class, and reveals non-self-affine interface behavior near the transition.

Contribution

It introduces a numerical analysis of an anisotropic interface depinning model with a nonlinear term, linking its critical exponents to the DPD model and directed percolation.

Findings

Critical exponents match those of the DPD model.

Interface near depinning is not self-affine.

Results support the universality class of directed percolation.

Abstract

We study numerically a stochastic differential equation describing an interface driven along the hard direction of an anisotropic random medium. The interface is subject to a homogeneous driving force, random pinning forces and the surface tension. In addition, a nonlinear term due to the anisotropy of the medium is included. The critical exponents characterizing the depinning transition are determined numerically for a one-dimensional interface. The results are the same, within errors, as those of the ``Directed Percolation Depinning'' (DPD) model. We therefore expect that the critical exponents of the stochastic differential equation are exactly given by the exponents obtained by a mapping of the DPD model to directed percolation. We find that a moving interface near the depinning transition is not self-affine and shows a behavior similar to the DPD model.