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  • Power system reliability and power quality assessments with grid-connected wave energy converters

    Creator:
    Boller, Michael D.
    Abstract:
    Generating abundant, renewable energy from Earth’s oceans is an attractive option for meeting increasing energy demand. Marine renewable energy also comes with the variability of renewable sources, which impact the reliability and power quality of the electrical grid. On a transmission-level, this dissertation looks at ensuring reliability of the power...
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    committee, Dr. Bryony DuPont, Dr. Yue Cao and Dr. Nathan Gibson, thank you for providing me with advice on

  • Multiscale Methods and Energy Stable Discretizations for Maxwell’s Equations in Linearand Nonlinear Materials

    Creator:
    Sakkaplangkul, Puttha
    Abstract:
    In this dissertation, we introduce a family of fully discrete finite difference time-domain (FDTD) methods for Maxwell’s equations in linear and nonlinear materials. Onecategory of methods is constructed using multiscale techniques involving operator splittings. We present the sequential splitting scheme, the Strang Marchuk splitting scheme,the weighted sequential splitting scheme including...
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    , none of this would be possible. Many thanks to my committee members: to Dr. Nathan L. Gibson for

  • Stochastic analysis of flow and transport in porous media

    Creator:
    Vasylkivska, Veronika S.
    Abstract:
    Random fields are frequently used in computational simulations of real-life processes. In particular, in this work they are used in modeling of flow and transport in porous media. Porous media as they arise in geological formations are intrinsically deterministic but there is significant uncertainty involved in determination of their properties...
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    . Showalter, Dr. Nathan L. Gibson and Dr. Margaret L. Niess for agreeing to serve on my graduate committee

  • Coastal Soil and Structure Behavior during Earthquake-Tsunami Multi-Hazards

    Creator:
    Qiu, Yingqing
    Abstract:
    Coastal multi-hazards, i.e., earthquakes followed by tsunamis, induce severe damage to coastal infrastructure. The multi-hazards can cause soil liquefaction, which is one of the major concerns for evaluating sediments transport potential and structure failure mechanisms. The objectives for this work is threefold. First, to build and validate a soil numerical...
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    foundations of my PhD dissertation. Professor Nathan L. Gibson and Professor Vrushali A. Bokil, they opened

  • Risk and Uncertainty Quantification Methods in Electrical Power Systems

    Creator:
    Johnson, Brandon S.
    Abstract:
    Load flow studies are one of the most essential engineering applications for grid operators because they provide a clear picture of the operating conditions of the power system. Traditionally, the load flow problem is assumed to be deterministic; that is, the system variables contain no randomness. Unfortunately, this assumption is...
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    am today. Second, I’d like to thank my minor advisor, Dr. Nathan Gibson for the past year of work

  • 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...
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    offspring particle u during its lifetime is governed by the operator L given above, and is independent of

  • Model Adaptivity and Numerical Solutions Using Sensitivity Analysis

    Creator:
    Kennedy, Kenneth M.
    Abstract:
    In this work we consider the dependence of solutions to a partial differential equations system on its data. The problem of interest is a coupled model of nonlinear flow and transport in porous media, with applications, e.g. to environmental modeling. The model of flow we consider is known as the...
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    like to thank my committee members Dr. John Lee, Dr. Mina Ossiander, Dr. Nathan Gibson, and Dr. Lan

  • 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...
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    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...
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    ”, P.I.: Malgorzata Peszynska. I want to thank my collaborators Dr. Nathan Gib- son, Dr. Malgorzata

  • 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...
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    species. Consider the reaction-diffusion model ut = f(u) + ηuxx, x ∈ [0, L] (2.4.1) where η is the