Rapid Growth and Critical Behavior 
          in Phase Field Models of Solidification              

                                   by

                               Karl Glasner

               INSCC 110, 3:30pm  Monday, December 7, 1998


                                Abstract

 

Phase field models have become a popular way of describing the
evolution of solid-liquid interfaces.  At large undercoolings these models
may exhibit very rapid growth which is related to traveling wave solutions of
the one dimensional equations.  The solution set for this problem is
complicated and shows that existence of solutions is critically
dependent on the physical parameters of the problem.  An asymptotic study
of various limits allows a complete qualitative picture to be
constructed. A situation where intermediate states may appear can also be
analyzed in a similar manner.

                            

Request for preprints and reprints to the speaker at glasner@math.utah.edu
This information can be found at http://www.math.utah.edu/research/