Path-integral variational methods for flow through porous media.
Item
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Title
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Path-integral variational methods for flow through porous media.
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Identifier
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AAI9530921
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identifier
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9530921
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Creator
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Tanksley, Michael Allan.
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Contributor
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Adviser: Joel Koplik
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Date
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1995
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics, Fluid and Plasma
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Abstract
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We characterise a porous medium as a statistically homogeneous continuum with local fluctuations in physical parameters. We consider the steady-state flow of a single incompressible fluid through an infinite medium, the dissipation of a passive tracer in such a flow, and the first passage problem for tracer transport in a stratified medium. For each problem we average a path-integral expression for the Green function over parameter fluctuations, and obtain large-distance, long-time effective parameters via Feynman's variational method. For the permeability problem, and the tracer problem at small Peclet number P, the variational results are consistent with results obtained by first-order perturbation theory. For the tracer problem at large P, the variational method predicts the expected linear dependence of the effective dispersion tensor on P, which perturbation theory does not. This indicates that, for these problems and others like them, a first-order perturbation expansion can be of limited utility. For the first passage problem, we assume that the medium is infinite in the direction normal to the layering but finite (of length 2L) in the direction parallel to the layering. We calculate the exit time distribution and the mean first passage time. The latter is proportional to {dollar}L\sp{lcub}4/3{rcub},{dollar} consistent with previous work.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
