Nucleation and growth of lattice crystals

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.

References in corpus (6)

• Checkerboards, stripes and corner energies in spin models with competing interactions
• Interfaces, modulated phases and textures in lattice systems
• Exact periodic stripes for a minimizers of a local/non-local interaction functional in general dimension
• Motion of discrete interfaces in periodic media
• Motion of discrete interfaces through mushy layers
• Motion of discrete interfaces in low-contrast periodic media