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.
Braides, A., Scilla, G., Tribuzio, A. (2021). Nucleation and growth of lattice crystals. JOURNAL OF NONLINEAR SCIENCE, 31(6) [10.1007/s00332-021-09745-x].
Nucleation and growth of lattice crystals
Andrea Braides
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2021-01-01
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.File in questo prodotto:
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