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 06 Apr 2016

[BibTeX]

Preprint

Inserted: 28 jul 2014
Last Updated: 6 apr 2016

Year: 2016

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 ``Wulff shape-like'' hexagons, i.e. hexagons with each side parallel to a side of the hexagonal Wulff shape related to the density of the anisotropic perimeter obtained by $\Gamma$-convergence from the ferromagnetic energies, which reflects the symmetries of the underlying lattice. We compare the resulting limit motion for the Wulff shape 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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