The Pinning Paths of an Elastic Interface

TL;DR

This paper introduces a new model for elastic interface pinning paths in disordered media, revealing distinct scaling properties and characterizing their roughness and cluster statistics.

Contribution

The study presents a novel model for elastic pinning paths with unique scaling behavior, differing from known directed percolation paths, and provides numerical analysis of cluster properties.

Findings

Elastic pinning paths have a roughness exponent of 1.25.

The roughness exponent is intermediate between known processes.

Numerical results include mean cluster size and distribution.

Abstract

We introduce a model describing the paths that pin an elastic interface moving in a disordered medium. We find that the scaling properties of these ``elastic pinning paths'' (EPP) are different from paths embedded on a directed percolation cluster, which are known to pin the interface of the ``directed percolation depinning'' class of surface growth models. The EPP are characterized by a roughness exponent $\alpha=1.25$, intermediate between that of the free inertial process ($\alpha=3/2$) and the diode-resistor problem on a Cayley tree ($\alpha=1$). We also calculate numerically the mean cluster size and the cluster size distribution for the EPP.