Mathematical Models of the Alpha-Beta Phase Transition of Quartz
| dc.contributor.author | Moss, George W. | en |
| dc.contributor.committeechair | Rogers, Robert C. | en |
| dc.contributor.committeemember | Renardy, Michael J. | en |
| dc.contributor.committeemember | Boisen, Monte B. Jr. | en |
| dc.contributor.committeemember | Sun, Shu-Ming | en |
| dc.contributor.committeemember | Lin, Tao | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2014-03-14T20:15:02Z | en |
| dc.date.adate | 1999-08-25 | en |
| dc.date.available | 2014-03-14T20:15:02Z | en |
| dc.date.issued | 1999-07-27 | en |
| dc.date.rdate | 2000-08-25 | en |
| dc.date.sdate | 1999-08-10 | en |
| dc.description.abstract | 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. | en |
| dc.description.degree | Ph. D. | en |
| dc.identifier.other | etd-081099-142433 | en |
| dc.identifier.sourceurl | http://scholar.lib.vt.edu/theses/available/etd-081099-142433/ | en |
| dc.identifier.uri | http://hdl.handle.net/10919/28607 | en |
| dc.publisher | Virginia Tech | en |
| dc.relation.haspart | etd.pdf | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | phase transition | en |
| dc.subject | quartz | en |
| dc.subject | incommensurate | en |
| dc.subject | bifurcation | en |
| dc.title | Mathematical Models of the Alpha-Beta Phase Transition of Quartz | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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