Evolution equations in physical chemistry

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dc.contributor.advisorVasseur, Alexis F.en
dc.contributor.advisorStanton, John (John F.)en
dc.contributor.committeeMemberGamba, Irene M.en
dc.contributor.committeeMemberWyatt, Robert E.en
dc.contributor.committeeMemberSouganidis, Panagiotis E.en
dc.contributor.committeeMemberHenkelman, Graemeen
dc.creatorMichoski, Craig E.en
dc.date.accessioned2010-08-05T15:19:38Zen
dc.date.accessioned2010-08-05T15:20:07Zen
dc.date.accessioned2017-05-11T22:20:02Z
dc.date.available2010-08-05T15:19:38Zen
dc.date.available2010-08-05T15:20:07Zen
dc.date.available2017-05-11T22:20:02Z
dc.date.issued2009-05en
dc.date.submittedMay 2009en
dc.date.updated2010-08-05T15:20:07Zen
dc.descriptiontexten
dc.description.abstractWe analyze a number of systems of evolution equations that arise in the study of physical chemistry. First we discuss the well-posedness of a system of mixing compressible barotropic multicomponent flows. We discuss the regularity of these variational solutions, their existence and uniqueness, and we analyze the emergence of a novel type of entropy that is derived for the system of equations. Next we present a numerical scheme, in the form of a discontinuous Galerkin (DG) finite element method, to model this compressible barotropic multifluid. We find that the DG method provides stable and accurate solutions to our system, and that further, these solutions are energy consistent; which is to say that they satisfy the classical entropy of the system in addition to an additional integral inequality. We discuss the initial-boundary problem and the existence of weak entropy at the boundaries. Next we extend these results to include more complicated transport properties (i.e. mass diffusion), where exotic acoustic and chemical inlets are explicitly shown. We continue by developing a mixed method discontinuous Galerkin finite element method to model quantum hydrodynamic fluids, which emerge in the study of chemical and molecular dynamics. These solutions are solved in the conservation form, or Eulerian frame, and show a notable scale invariance which makes them particularly attractive for high dimensional calculations. Finally we implement a wide class of chemical reactors using an adapted discontinuous Galerkin finite element scheme, where reaction terms are analytically integrated locally in time. We show that these solutions, both in stationary and in flow reactors, show remarkable stability, accuracy and consistency.en
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2009-05-54en
dc.language.isoengen
dc.subjectEvolution Equationsen
dc.subjectPhysical Chemistryen
dc.subjectChemical Physicsen
dc.subjectThermodynamicsen
dc.subjectChemical Kineticsen
dc.subjectCompressible Flowen
dc.subjectQuantum Hydrodynamics (QHD)en
dc.subjectChemical Reactorsen
dc.subjectMulticomponent Flowsen
dc.subjectMultiphaseen
dc.subjectPartial Differential Equationen
dc.subjectMathematical Analysis, Finite Element Method (FEM)en
dc.subjectDiscontinuous Galerkin (DG)en
dc.subjectBoundary Conditions.en
dc.titleEvolution equations in physical chemistryen
dc.type.genrethesisen

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