Calculus of Variations and Geometric Measure Theory
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A. Braides - G. Scilla - A. Tribuzio

Nucleation and growth of lattice crystals

created by braidesa on 26 Dec 2020
modified by scilla on 29 Dec 2020

[BibTeX]

Preprint

Inserted: 26 dec 2020
Last Updated: 29 dec 2020

Year: 2020

ArXiv: 2012.13772 PDF

Abstract:

A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of “maximization” of the perimeter. At a discrete level, the evolution has a “checkerboard” structure and its shape is affected by the choice of the norm defining the dissipation term. For every choice of the scales, the convergence of the discrete scheme to a family of expanding sets with constant velocity is proved.

Keywords: discrete systems, minimizing movements, Nucleation, geometric evolution, mocrostructure


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