Infinite pinning

TL;DR

This paper investigates the conditions under which an interface moving through a random medium with unbounded obstacles becomes infinitely pinned, providing a necessary criterion based on obstacle distribution.

Contribution

It introduces a model for interface pinning in a random medium with unbounded obstacle strengths and derives a necessary condition for infinite pinning to occur.

Findings

Derived a necessary condition on obstacle distribution for infinite pinning.

Model accounts for unbounded obstacle strengths.

Provides insights into interface behavior in disordered media.

Abstract

In this work, we address the occurrence of infinite pinning in a random medium. We suppose that an initially flat interface starts to move through the medium due to some constant driving force. The medium is assumed to contain random obstacles. We model their positions by a Poisson point process and their strengths are not bounded. We determine a necessary condition on its distribution so that regardless of the driving force the interface gets pinned.