Pinning and depinning: From periodic to chaotic and random media

N. Ankney, M. Avery, T. Khain, A. Scheel

Research output: Contribution to journalArticlepeer-review

Abstract

We study the 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.

Original languageEnglish (US)
Article number013127
JournalChaos
Volume29
Issue number1
DOIs
StatePublished - Jan 1 2019

Bibliographical note

Funding Information:
The authors gratefully acknowledge the support through the National Science Foundation (NSF) grant DMS-1612441.

PubMed: MeSH publication types

  • Journal Article

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