Motion of discrete interfaces on the triangular lattice

created by scilla on 28 Jul 2014
modified on 30 Jun 2018

[BibTeX]

Submitted Paper

Inserted: 28 jul 2014
Last Updated: 30 jun 2018

Year: 2018

Abstract:

We study the motion of discrete interfaces driven by ferromagnetic interactions on the two-dimensional triangular lattice by coupling the Almgren, Taylor and Wang minimizing movements approach and a discrete-to-continuum analysis, as introduced by Braides, Gelli and Novaga in the pioneering case of the square lattice. We examine the motion of convex Wulff-like'' hexagons, i.e. convex hexagons with sides having the same orientations as those of the hexagonal Wulff shape related to the density of the anisotropic perimeter $\Gamma$-limit of the ferromagnetic energies as the lattice spacing vanishes. We compare the resulting limit motion with the corresponding evolution by crystalline curvature with natural mobility.