Evolution equations in physical chemistry

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Title: Evolution equations in physical chemistry
Author: Michoski, Craig E.
Abstract: We 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 .
URI: http : / /hdl .handle .net /2152 /ETD -UT -2009 -05 -54
Date: 2010-08-05


Evolution equations in physical chemistry. Doctoral dissertation, The University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /ETD -UT -2009 -05 -54 .

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