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Mathematical Models of the Alpha-Beta Phase Transition of Quartz

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dc.contributor.authorMoss, George W.en
dc.contributor.committeechairRogers, Robert C.en
dc.contributor.committeememberRenardy, Michael J.en
dc.contributor.committeememberBoisen, Monte B. Jr.en
dc.contributor.committeememberSun, Shu-Mingen
dc.contributor.committeememberLin, Taoen
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:15:02Zen
dc.date.adate1999-08-25en
dc.date.available2014-03-14T20:15:02Zen
dc.date.issued1999-07-27en
dc.date.rdate2000-08-25en
dc.date.sdate1999-08-10en
dc.description.abstractWe 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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-081099-142433en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-081099-142433/en
dc.identifier.urihttp://hdl.handle.net/10919/28607en
dc.publisherVirginia Techen
dc.relation.haspartetd.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectphase transitionen
dc.subjectquartzen
dc.subjectincommensurateen
dc.subjectbifurcationen
dc.titleMathematical Models of the Alpha-Beta Phase Transition of Quartzen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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