Analysis of Kolmogorov flow and Rayleigh-Benard convection using persistent homology

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dc.contributor.authorKramar, Miroslaven
dc.contributor.authorLevanger, Rachelen
dc.contributor.authorTithof, Jeffreyen
dc.contributor.authorSuri, Balachandraen
dc.contributor.authorXu, Muen
dc.contributor.authorPaul, Mark R.en
dc.contributor.authorSchatz, Michael F.en
dc.contributor.authorMischaikow, Konstantinen
dc.date.accessioned2024-10-07T18:37:49Zen
dc.date.available2024-10-07T18:37:49Zen
dc.date.issued2016-11-01en
dc.description.abstractWe use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium. In particular, we analyze image time series of flow field patterns from numerical simulations of two important problems in fluid dynamics: Kolmogorov flow and Rayleigh–Bénard convection. For each image we compute a persistence diagram to yield a reduced description of the flow field; by applying different metrics to the space of persistence diagrams, we relate characteristic features in persistence diagrams to the geometry of the corresponding flow patterns. We also examine the dynamics of the flow patterns by a second application of persistent homology to the time series of persistence diagrams. We demonstrate that persistent homology provides an effective method both for quotienting out symmetries in families of solutions and for identifying multiscale recurrent dynamics. Our approach is quite general and it is anticipated to be applicable to a broad range of open problems exhibiting complex spatio-temporal behavior.en
dc.description.versionPublished versionen
dc.format.extentPages 82-98en
dc.format.extent17 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1016/j.physd.2016.02.003en
dc.identifier.eissn1872-8022en
dc.identifier.issn0167-2789en
dc.identifier.orcidPaul, Mark [0000-0002-0701-1955]en
dc.identifier.urihttps://hdl.handle.net/10919/121286en
dc.identifier.volume334en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000384791000007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.relation.urihttp://dx.doi.org/10.1016/j.physd.2016.02.003en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleAnalysis of Kolmogorov flow and Rayleigh-Benard convection using persistent homologyen
dc.title.serialPhysica D-Nonlinear Phenomenaen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-groupVirginia Techen
pubs.organisational-groupVirginia Tech/Engineeringen
pubs.organisational-groupVirginia Tech/Engineering/Mechanical Engineeringen
pubs.organisational-groupVirginia Tech/All T&R Facultyen
pubs.organisational-groupVirginia Tech/Engineering/COE T&R Facultyen

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