Scholarly
    Communications Project


Document Type:Dissertation
Name:Gail S. Mackin
Email address:mackin@math.vt.edu
URN:1997/00103
Title:On an Order-Parameter Model of Solid-Solid Phase Transitions
Degree:Doctor of Philosophy
Department:Mathematics
Committee Chair: Robert C. Rogers
Chair's email:rogers@math.vt.edu
Committee\ Members:
Keywords:Parabolic PDEs, Phase Transition, Order Parameter, Existence
Date of defense:July 28, 1997
Availability:Release the entire work immediately worldwide.

Abstract:

We examine a model of solid-solid phase transitions that includes thermo-elastic effects and an order parameter. The model is derived as a special case of the Gurtin-Fried model posed in one space dimension with a symmetric triple-well free energy in which the relative heights of the wells vary with temperature. We examine the temperature independent case, showing existence of a unique classical solution of a regularized system of partial differential equations using semigroup theory. This is followed by numerical study of a finite element algorithm for the temperature independent model. Finally, we present computational material concerning the temperature dependent model.

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