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A comparison framework for interleaved persistence modules and applications of persistent homology to problems in fluid dynamics
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Levanger, Rachel. A comparison framework for interleaved persistence modules and applications of persistent homology to problems in fluid dynamics. Retrieved from https://doi.org/doi:10.7282/T3057JSD

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TitleA comparison framework for interleaved persistence modules and applications of persistent homology to problems in fluid dynamics
NameLevanger, Rachel (author); Mischaikow, Konstantin (chair); Weibel, Charles (internal member); Ferry, Stephen (internal member); Kondic, Lou (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2017
Other Date2017-05 (degree)
SubjectMathematics, Homology theory, Fluid dynamics, Rayleigh-Bénard convection
Extent1 online resource (vii, 179 p. : ill.)
DescriptionWe prove an algebraic stability theorem for interleaved persistence modules that is more general than any formulations currently in the literature. We show how this generalization leads to a framework that may be used to compare persistence modules locally, enabling the computation of non-uniform error bounds for persistence diagrams. We give several examples of how to use this comparison framework, and also address an open problem on non-uniform sublevel set filtrations. We also give two applications of persistent homology to problems in fluid dynamics. Our first application examines the structure of the dynamics of a time-evolving system on a two-dimensional domain, where we give examples for studying fixed points and periodic orbits. Our second application uses persistent homology in conjunction with techniques in computer vision to study pattern defects in the spiral defect chaos regime of Rayleigh-Bénard convection.
NotePh.D.
NoteIncludes bibliographical references
Noteby Rachel Levanger
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3057JSD
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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