Motion of discrete interfaces in low-contrast periodic media

TL;DR

This paper investigates how discrete interfaces move in low-contrast periodic media, revealing that their effective motion depends on geometrical features beyond static descriptions and identifying thresholds affecting their dynamics.

Contribution

It introduces a coupled discrete-to-continuum analysis for interface motion in low-contrast media, showing dependence on geometric features and contrast thresholds, extending previous high-contrast results.

Findings

Effective motion depends on geometric features beyond Gamma-limit.

Existence of a critical contrast value $ ilde{ extdelta}$ influencing motion.

Identification of new pinning thresholds and velocity depending on $ extdelta$.

Abstract

We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional low-contrast periodic environment, by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuum analysis. As in a recent paper by Braides and Scilla dealing with high-contrast periodic media, we give an example showing that in general the effective motion does not depend only on the Gamma-limit, but also on geometrical features that are not detected in the static description. We show that there exists a critical value $\widetilde{\delta}$ of the contrast parameter $\delta$ above which the discrete motion is constrained and coincides with the high-contrast case. If $\delta<\widetilde{\delta}$ we have a new pinning threshold and a new effective velocity both depending on $\delta$. We also consider the case of non-uniform inclusions distributed into periodic uniform layers.