Calculus of Variations and Geometric Measure Theory
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G. Scilla

Motion of discrete interfaces on the triangular lattice

created by scilla on 28 Jul 2014
modified on 20 May 2020

[BibTeX]

Accepted Paper

Inserted: 28 jul 2014
Last Updated: 20 may 2020

Journal: Milan J. Math.
Year: 2020

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 origin-symmetric convex ``Wulff-like'' hexagons, i.e. origin-symmetric 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.

Keywords: discrete systems, minimizing movements, wulff shape, motion by curvature, crystalline curvature, triangular lattice, natural mobility


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