Moss, George W.2014-03-142014-03-141999-07-27etd-081099-142433http://hdl.handle.net/10919/28607We 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.In Copyrightphase transitionquartzincommensuratebifurcationDissertationhttp://scholar.lib.vt.edu/theses/available/etd-081099-142433/