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dc.contributor.authorGameiro, Marcio Fuzetoen_US
dc.date.accessioned2005-09-16T15:11:34Z
dc.date.available2005-09-16T15:11:34Z
dc.date.issued2005-07-19en_US
dc.identifier.urihttp://hdl.handle.net/1853/7207
dc.description.abstractWe use computational homology to characterize the geometry of complicated time-dependent patterns. Homology provides very basic topological (geometrical) information about the patterns, such as the number of components (pieces) and the number of holes. For 3-dimensional patterns it also provides the number of voids. We apply these techniques to patterns generated by experiments on spiral defect chaos, as well as to numerically simulated patterns in the Cahn-Hilliard theory of phase separation and on spiral wave patterns in excitable media. These techniques allow us to distinguish patterns at different parameter values, to detect complicated dynamics through the computation of positive Lyapunov exponents and entropies, to compare experimental data with numerical simulations, to quantify boundary effects on finite size domains, among other things.en_US
dc.format.extent6424682 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectPatternsen_US
dc.subjectTopology
dc.subjectHomology
dc.titleTopological Analysis of Patternsen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Konstantin Mischaikow; Committee Member: Andrzej Szymczak; Committee Member: Guillermo Goldsztein; Committee Member: Luca Dieci; Committee Member: Michael Schatzen_US


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