Renormalization methods and interface problems

摘要

The application of renormalization techniques to interface problems is considered after a brief review of the methodology. We study the standard sharp interface problem in the quasi-static limit (time derivative set to zero in the heat equation) for large time. The characteristic length, R(t), behaves as t~βwhere β has values in the continuous spectrum when the dynamical undercooling is nonzero, and β∈[1/3, ∞) when the undercooling is set at zero. The value of β = 1 obtained by Jasnow and Vinals is extracted from this spectrum as a consequence of boundary conditions that impose a plane wave. In almost all of these cases, the capillarity length is an irrelevant variable for large time, in sharp contrast to its role in linear stability for short time.