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.
Nucleation and Growth of Lattice Crystals / Braides, Andrea; Scilla, Giovanni; Tribuzio, Antonio. - In: JOURNAL OF NONLINEAR SCIENCE. - ISSN 0938-8974. - 31:6(2021). [10.1007/s00332-021-09745-x]
Nucleation and Growth of Lattice Crystals
Braides, Andrea;Scilla, Giovanni;
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 | Dimensione | Formato | |
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