Late Stage Interface Dynamics and Renormalization Group Methods
by
Huseyin Merdan
University of Pittsburgh
Coauthors: G. Caginalp

This talk involves the application of renormalization group methods to interface problems. In this talk, we will study the standard sharp interface problem in the quasi-static limit (time derivative set to zero in the heat equation) for large time adaptating of methodology known in the physics literature as renormalization group and scaling theory.

We will consider a full two-phased model and implement a renormalization procedure in order to calculate the characteristic length, R(t), of a self-similar system that is the time dependent length scale characterizing the pattern growth. We will show that the characteristic length, R(t), behaves as t^\phi where \phi has values in the continuous spectrum (1/3, 1/2) when the dynamical undercooling (\alpha =/= 0) is non-zero, and \phi in (1/3, \infty) when the undercooling is set at zero, i.e. \alpha = 0. The single value of \phi obtained by Jasnow and Vinals is extracted from this spectrum as a consequence of boundary conditions that impose a plane wave. It will be also shown that in almost all of these cases, the capillarity length arising from surface tension is irrelevant for the large time behavior even though it has a crucial role at the early stage evolution of an interface.

Date received: October 20, 2003