Calculus of Variations and Geometric Measure Theory

A. Braides - G. Scilla - A. Tribuzio

Nucleation and growth of lattice crystals

created by braidesa on 26 Dec 2020
modified on 08 Oct 2021


Published Paper

Inserted: 26 dec 2020
Last Updated: 8 oct 2021

Journal: J. Nonlinear Sci.
Volume: 31
Number: 97
Year: 2021
Doi: 10.1007/s00332-021-09745-x

ArXiv: 2012.13772 PDF


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, MIcrostructure, Nucleation, geometric evolution