Renormalization Methods And Interface Problems
Author(s)
G. Caginalp & H. Merdan
Abstract
Renormalization methods and interface
problems
G. Caginalp & H. Merdan
Department of Mathematics, University of Pittsburgh
Pittsburgh, U. S.A
Abstract
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 tP where P has values
in the continuous spectrum [1/3,1/2] when the dynamical undercooling is nonzero,
and /I E [1/3, co) when the undercooling is set at zero. The value of p = 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.
1 Introduction
Renormalization group and scaling methods (RG) originated as part
Keywords
Related Book
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