Two-Scale Models of Phase Transitions

  • Augusto Visintin
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 28)


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.


Macroscopic Model Phase Field Model Surface Tension Effect Mesoscopic Model Ferromagnetic System 
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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Augusto Visintin
    • 1
  1. 1.Dipartimento di MatematicaUniversità Degli Studi di TrentoPovoItaly

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