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Filtering by: Committee Member Scharen, A. L. Remove constraint Committee Member: Scharen, A. L. Academic Affiliation Mathematics Remove constraint Academic Affiliation: Mathematics

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  • Operator splitting methods for Maxwell's equations in dispersive media

    Creator:
    Keefer, Olivia A.
    Abstract:
    Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive...
    Resource Type:
    Masters Thesis
    Full Text:
    AN ABSTRACT OF THE THESIS OF Olivia A. Keefer for the degree

  • On the Dynamic Likelihood Approach to Data Assimilation for Stochastic Hyperbolic Geophysical Processes

    Creator:
    Foster, Dallas A.
    Abstract:
    Many geophysical phenomena exhibit complicated dynamics that, due to a variety of factors, diverge quickly from physical models. The arrival of new observations allows researchers to combine the model estimate with measurements in a statistical process called data assimilation to produce a revised estimate of the phenomenon. This assimilation of...
    Resource Type:
    Dissertation
    Full Text:
    . Robert L. Higdon, Dr. Enrique A. Thomann, my graduate committee representative Katherine McLaughlin, and

  • Branching Brownian Motion with One Absorbing and One Reflecting Boundary

    Creator:
    Felder, William F.
    Abstract:
    In this work we will analyze branching Brownian motion on a finite interval with oneabsorbing and one reflecting boundary, having constant drift rate toward the absorbingboundary. Similar processes have been considered by Kesten ([12]), and more recently byHarris, Hesse, and Kyprianou ([11]). The current offering is motivated largely by the...
    Resource Type:
    Dissertation
    Full Text:
    work we will analyze branching Brownian motion on a finite interval with one absorbing and one

  • The Variable Speed Wave Equation and Perfectly Matched Layers

    Creator:
    Kim, Dojin
    Abstract:
    A perfectly matched layer (PML) is widely used to model many different types of wave propagation in different media. It has been found that a PML is often very effective and also easy to set, but still many questions remain. We introduce a new formulation from regularizing the classical Un-Split...
    Resource Type:
    Dissertation
    Full Text:
    equation with a PML, L(x, ∂t, ∂x)U := ∂tU + d∑ l=1 Al∂lU + B(x)U = 0, (1.5) with the principal part of L

  • Mathematical treatment and simulation of methane hydrates and adsorption models

    Creator:
    Medina, Francis Patricia
    Abstract:
    In this dissertation we develop mathematical treatment for two important applications: (i) evolution of methane in coalbeds with the associated phenomena of adsorption, and (ii) formation of methane hydrates in seabed. We use simplified models for (i) and (ii) since we are more interested in qualitative properties of the solutions...
    Resource Type:
    Dissertation
    Full Text:
    solutions rather than direct applications to engineering. For methane hydrates we focus on a scalar

  • A heterogeneous flow numerical model based on domain decomposition methods

    Creator:
    Zhang, Yi
    Abstract:
    In this study, a heterogeneous flow model is proposed based on a non-overlapping domain decomposition method. The model combines potential flow and incompressible viscous flow. Both flow domains contain a free surface boundary. The heterogeneous domain decomposition method is formulated following the Dirichlet-Neumann method. Both an implicit scheme and an...
    Resource Type:
    Masters Thesis
    Full Text:
    ), (v, q)) = (f ,v) , ∀(v, q) ∈ W0. We also define the linear map L : W → W such that L(w) , (−µ∆u+ a

  • Non-spatial and spatial models for multi-host pathogen spread in competing species : applications to barley yellow dwarf virus and rinderpest

    Creator:
    Manore, Carrie Anna
    Abstract:
    Modeling and analyzing the combined effects of disease and population dynamics is important in understanding the effects of mechanisms such as pathogen transmission and direct competition between host species on the distribution and abundance of different species in an ecological community. Mathematical analysis of such models in a spatially explicit...
    Resource Type:
    Dissertation
    Full Text:
    : Vrushali A. Bokil Modeling and analyzing the combined effects of disease and population dynamics is

  • Trace forms and self-dual normal bases in Galois field extensions

    Creator:
    Kang, Dong Seung
    Abstract:
    Let G be a finite group, G₂ be a Sylow 2-subgroup of G, and L/K be a G-Galois extension. We study the trace form qL/K of L/K and the question of existence of a self-dual normal basis. Our main results are as follows: (1) If G₂ is not abelian and...
    Resource Type:
    Dissertation