Crystalline Evolutions in Chessboard-like Microstructures

TL;DR

This paper investigates how a periodic microstructure influences the evolution of crystalline shapes, revealing effects like pinning and confinement due to the medium's chessboard-like pattern.

Contribution

It introduces a model for crystalline curvature evolution in a periodic medium, highlighting microstructure-induced pinning and confinement effects.

Findings

Microstructure causes pinning of crystalline interfaces.

Periodic forcing leads to confinement effects.

Microstructure significantly alters geometric evolution.

Abstract

We describe the macroscopic behavior of evolutions by crystalline curvature of planar sets in a chessboard--like medium, modeled by a periodic forcing term. We show that the underlying microstructure may produce both pinning and confinement effects on the geometric motion.