Inserted: 26 dec 2020
Last Updated: 6 aug 2021
Journal: J. Nonlinear Sci.
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