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.

Motion of discrete interfaces on the triangular lattice

Scilla G
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/897716
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