Pinning and Depinning: from periodic to chaotic and random media

TL;DR

This paper investigates how dissipative structures propagate in complex inhomogeneous media, revealing universal laws for depinning transitions influenced by the medium's dynamical properties and identifying conditions where these laws break down.

Contribution

It introduces a modeling framework that captures transitions from periodic to chaotic media and uncovers universal depinning laws linked to extreme value statistics and ergodic measure dimensions.

Findings

Depinning bifurcations follow universal laws based on extreme value statistics.

Transitions from periodic to chaotic media are characterized and modeled.

Breakdown of universality occurs when medium fluctuations are on scales smaller than the interface width.

Abstract

We study propagation of dissipative structures in inhomogeneous media with a focus on pinning and depinning transitions. We model spatial complexity in the medium as generated by dynamical systems. We are thus able to capture transitions from periodic to quasiperiodic, to homoclinic and heteroclinic, and to chaotic media. Depinning bifurcations exhibit universal laws depending on extreme value statistics that are encoded in the dimension of ergodic measures, only. A key condition limiting this approach bounds spatial Lyapunov exponents in terms of interface localization and we explore the breakdown of smoothness and universality when this condition is violated and fluctuations in the medium occur on length scales shorter than a typical interface width.