On an Order-Parameter Model of Solid-Solid Phase Transitions

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1997

Author dc:creator

• Mackin, Gail S.

Chair dc:contributor.committeechair

• Rogers, Robert C.

Committee members dc:contributor.committeemember

• Yan, Yin
• Sun, Shu-Ming
• Rossi, John F.
• Lin, Tao

• Parabolic PDEs
• Phase Transition
• Order Parameter
• Existence

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-72097-132414

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/30676