From Individual to Collective Pinning: Effect of Long-range Elastic Interactions

TL;DR

This paper investigates how long-range elastic interactions influence the dynamics of an elastic chain in a quenched random environment, revealing three distinct regimes and the impact of driving mode on avalanche behavior.

Contribution

It introduces a comprehensive analysis of the effects of algebraic decay exponents on elastic interactions, identifying three regimes and their critical properties.

Findings

Identification of three regimes: MF, Laplacian, and intermediate.

Continuous interpolation of critical exponents between regimes.

Influence of driving mode on avalanche statistics.

Abstract

We study the effect of long-range elastic interactions in the dynamical behavior of an elastic chain driven quasi-statically in a quenched random pinning potential and in the strong pinning limit. This is a generic situation occuring in solid friction, crack propagation, wetting front motion, ... Tuning the exponent of the algebraic decay of the elastic interaction with the distance is shown to give rise to three regimes: a Mean-Field (MF) regime, a Laplacian (L) regime and an intermediate regime where the critical exponents interpolate continuously between the MF and L limit cases. The effect of the driving mode on the avalanche statistics is also analyzed.