{"462371":{"#nid":"462371","#data":{"type":"event","title":"PhD Defense by Burak Budanur","body":[{"value":"\u003Cp\u003ETitle\u003Cstrong\u003E: Exact coherent structures in spatiotemporal chaos:\u0026nbsp;\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003E\u0026nbsp;From qualitative description to quantitative predictions\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EDate: Tuesday November 3, 2015\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003ETime: 3:00 PM\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003ERoom: N110, Howey Physics Building\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EThesis Advisor:\u003C\/strong\u003E Predrag Cvitanovic\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EAbstract:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EThe term spatiotemporal chaos refers to physical phenomena that exhibit irregular oscillations in both space and time. Examples of such phenomena range from cardiac dynamics to fluid turbulence, where the motion is described by nonlinear partial differential equations. It is well known from the studies of low dimensional chaotic systems that the state space, the space of solutions to the governing dynamical equations, is shaped by the invariant sets such as equilibria, periodic orbits, and invariant tori. State space of partial differential equations is infinite dimensional, nevertheless, recent computational advancements allow us to find their invariant solutions numerically. In this thesis, we try to elucidate the chaotic dynamics of nonlinear partial\u003C\/p\u003E\u003Cp\u003Edifferential equations by studying their exactly coherent solutions and invariant manifolds. Specifically, we investigate the Kuramoto-Sivashinsky equation, which describes the velocity of a flame front, and the Navier-Stokes equations for an incompressible fluid in a circular pipe. We argue with examples that this approach can lead to a theory of turbulence with predictive power.\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EThesis committee:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EPredrag Cvitanovic (Advisor, School of Physics)\u003C\/p\u003E\u003Cp\u003ERoman Grigoriev (School of Physics)\u003C\/p\u003E\u003Cp\u003EAhmet Turgay Uzer (School of Physics)\u003C\/p\u003E\u003Cp\u003EMichael Schatz (School of Physics)\u003C\/p\u003E\u003Cp\u003EWilfrid Gangbo (School of Mathematics)\u003C\/p\u003E\u003Cp\u003E \u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Exact coherent structures in spatiotemporal chaos: From qualitative description to quantitative predictions"}],"uid":"27707","created_gmt":"2015-10-26 10:38:30","changed_gmt":"2016-10-08 02:14:31","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2015-11-03T19:00:00-05:00","event_time_end":"2015-11-03T21:00:00-05:00","event_time_end_last":"2015-11-03T21:00:00-05:00","gmt_time_start":"2015-11-04 00:00:00","gmt_time_end":"2015-11-04 02:00:00","gmt_time_end_last":"2015-11-04 02:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78771","name":"Public"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}