Title page for ETD etd-081099-142433

Type of Document Dissertation
Author Moss, George W.
Author's Email Address mossgeo@math.vt.edu
URN etd-081099-142433
Title Mathematical Models of the Alpha-Beta Phase Transition of Quartz
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Rogers, Robert C. Committee Chair
Boisen, Monte B. Jr. Committee Member
Lin, Tao Committee Member
Renardy, Michael J. Committee Member
Sun, Shu-Ming Committee Member
  • phase transition
  • quartz
  • incommensurate
  • bifurcation
Date of Defense 1999-07-27
Availability unrestricted
We examine discrete models with hexagonal symmetry

to compare the sequence of transitions with the

alpha-inc-beta phase transition of quartz. We

examine a model by Parlinski which employs

interactions of nearest and next-nearest neighbor

atoms. We numerically determine the configurations

which lead to minimum energy for a range of

parameters. We then use Golubitsky's results on

systems with hexagonal symmetry to derive the

bifurcation diagram for Parlinski's model. Finally,

we study a large class of modifications to

Parlinski's model and show that all such

modifications have the same bifurcation picture

as the original model.

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