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Approximation Techniques for Incompressible Flows with Heterogeneous PropertiesSalgado Gonzalez, Abner Jonatan 2010 August 1900 (has links)
We study approximation techniques for incompressible
flows with heterogeneous
properties. Speci cally, we study two types of phenomena. The first is the flow of a
viscous incompressible fluid through a rigid porous medium, where the permeability
of the medium depends on the pressure. The second is the
ow of a viscous incompressible fluid with variable density. The heterogeneity is the permeability and the
density, respectively.
For the first problem, we propose a finite element discretization and, in the case
where the dependence on the pressure is bounded from above and below, we prove its
convergence to the solution and propose an algorithm to solve the discrete system. In
the case where the dependence is exponential, we propose a splitting scheme which
involves solving only two linear systems.
For the second problem, we introduce a fractional time-stepping scheme which,
as opposed to other existing techniques, requires only the solution of a Poisson equation
for the determination of the pressure. This simpli cation greatly reduces the
computational cost. We prove the stability of first and second order schemes, and
provide error estimates for first order schemes.
For all the introduced discretization schemes we present numerical experiments,
which illustrate their performance on model problems, as well as on realistic ones.
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Adaptive finite element methods for fluorescence enhanced optical tomographyJoshi, Amit 30 October 2006 (has links)
Fluorescence enhanced optical tomography is a promising molecular imaging
modality which employs a near infrared fluorescent molecule as an imaging agent
and time-dependent measurements of fluorescent light propagation and generation.
In this dissertation a novel fluorescence tomography algorithm is proposed to reconstruct
images of targets contrasted by fluorescence within the tissues from boundary
fluorescence emission measurements. An adaptive finite element based reconstruction
algorithm for high resolution, fluorescence tomography was developed and validated
with non-contact, planewave frequency-domain fluorescence measurements on
a tissue phantom. The image reconstruction problem was posed as an optimization
problem in which the fluorescence optical property map which minimized the
difference between the experimentally observed boundary fluorescence and that predicted
from the diffusion model was sought. A regularized Gauss-Newton algorithm
was derived and dual adaptive meshes were employed for solution of coupled photon
diffusion equations and for updating the fluorescence optical property map in
the tissue phantom. The algorithm was developed in a continuous function space
setting in a mesh independent manner. This allowed the meshes to adapt during
the tomography process to yield high resolution images of fluorescent targets and to accurately simulate the light propagation in tissue phantoms from area-illumination.
Frequency-domain fluorescence data collected at the illumination surface was used
for reconstructing the fluorescence yield distribution in a 512 cm3, tissue phantom
filled with 1% Liposyn solution. Fluorescent targets containing 1 micro-molar Indocyanine
Green solution in 1% Liposyn and were suspended at the depths of up to 2cm
from the illumination surface. Fluorescence measurements at the illumination surface
were acquired by a gain-modulated image intensified CCD camera system outfitted
with holographic band rejection and optical band pass filters. Excitation light at
the phantom surface source was quantified by utilizing cross polarizers. Rayleigh
resolution studies to determine the minimum detectable sepatation of two embedded
fluorescent targets was attempted and in the absence of measurement noise, resolution
down to the transport limit of 1mm was attained. The results of this work
demonstrate the feasibility of high-resolution, molecular tomography in clinic with
rapid non-contact area measurements.
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B-spline finite elements for plane elasticity problemsAggarwal, Bhavya 25 April 2007 (has links)
The finite element method since its development in the 1950âÂÂs has been used
extensively in solving complex problems involving partial differential equations. The
conventional finite element methods use piecewise Lagrange interpolation functions for
approximating displacements. The aim of this research is to explore finite element
analysis using B-spline interpolation. B-splines are piecewise defined polynomial curves
which provide higher continuity of derivatives than piecewise Lagrange interpolation
functions. This work focuses on the implementation and comparison of the B-spline
finite elements in contrast with the conventional finite elements. This thesis observes
that the use of B-spline interpolation functions can reduce the computational cost
significantly. It is an efficient technique and can be conveniently implemented into the
existing finite element programs.
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The genesis of natrocarbonatites : constraints from experimental petrology and trace element partitioning /Petibon, Caroline Marie, January 1999 (has links)
Thesis (Ph.D.), Memorial University of Newfoundland, 2000. / Bibliography: leaves R-1-R-17. Also available online.
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Assessment of trace element contamination in streambed sediment and spatial associations in Palolo Valley watershed, Honolulu, Oʻahu, HawaiʻiHotton, Veronica K. January 2005 (has links)
Thesis (M.A.)--University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 146-156).
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Assessment of trace element contamination in streambed sediment and spatial associations in Palolo Valley watershed, Honolulu, Oʻahu, Hawaiʻi /Hotton, Veronica K. January 2005 (has links)
Thesis (M.A.)--University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 146-156). Also available via World Wide Web.
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Efficacy of hair mineral analysis for assessing zinc statusHavey, Shawn Michael. January 2009 (has links)
Thesis (M.S.)--Rutgers University, 2009. / "Graduate Program in Chemistry." Includes bibliographical references (p.54-56).
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Trace element partitioning between coexisting metamorphic minerals and trace element zoning in metamorphic minerals from Gagnon Terrane, western Labrador /Yang, Panseok, January 2002 (has links)
Thesis (Ph.D.)--Memorial University of Newfoundland, 2002. / Bibliography: leaves R1-R38. Also available online.
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Trace analysis by direct potentiometry /Choi, Koon-kay, Louis. January 1980 (has links)
Thesis (M. Phil.)--University of Hong Kong, 1980.
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Trace analysis by crystal sorption detector and recovery of dental waste /Lee, Chau-wing. January 1981 (has links)
Thesis (M. Phil.)--University of Hong Kong, 1981.
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