Nucleation and growth of lattice crystals

TL;DR

This paper introduces a variational lattice model for the nucleation and growth of lattice crystals, demonstrating convergence of the discrete scheme to expanding sets with constant velocity, influenced by the dissipation norm.

Contribution

It presents a novel variational lattice model for crystal nucleation and growth, with proven convergence to continuous expanding sets, highlighting the impact of dissipation norms.

Findings

Discrete evolution exhibits a checkerboard structure.

Convergence to expanding sets with constant velocity is established.

Shape evolution depends on the dissipation norm choice.

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.