Two-Scale Models of Phase Transitions
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The model of phase transitions including nucleation and surface tension effects introduced in Chap. VIII is here amended. A mean field approach is introduced, via convolution with a Gaussian kernel to account for nonadiabatic nucleation at small undercooling. This can be interpreted as a transformation from mesoscopic to macroscopic length scale, and yields a two-scale Stefan problem.
A model of phase-field type including the perimeter functional is also briefly studied, as well as another model of mean field type.
A microscopic model of ferromagnetism due to Landau and Lifshitz is then outlined. These models of solid-liquid and ferromagnetic systems are briefly compared.
KeywordsMacroscopic Model Phase Field Model Surface Tension Effect Mesoscopic Model Ferromagnetic System
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