The aim of this dissertation is to construct a virtual element method (VEM) for models in magneto-hydrodynamics (MHD), an area that studies the behavior and properties of electrically conducting fluids such as a plasma. MHD models are a coupling of the Maxwell’s equations for electromagnetics and models for fluid flow....
In this report we consider the Debye model along with Maxwell's equations (Maxwell-Debye) to model electromagnetic wave propagation in dispersive media that exhibit orientational polarization. We construct and analyze a sequential operator splitting method for the discretization of the Maxwell-Debye system. Energy analysis indicates that the operator splitting scheme is...
In 1877 John Kerr described an experiment that demonstrated a quadratic change in refractive index in a plate glass placed in a strong external electric field. This results in a nonlinear relationship between the average electric polarization within the materials and the intensity of the applied electric field. This opened...
In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to
21st century problems. We also discuss the previous work on the numerical simulations of
Maxwell's equations. Introductions to Maxwell's equations and the Yee finite difference...
In this thesis we analyze a model for Kerr optical materials consisting of Maxwell's equations along with the dispersive Duffing model. We consider Duffing models with cubic and quintic polynomial nonlinearities. We assume a traveling wave solution to this nonlinear electromagnetic system and analyze it using the theory of dynamical...
We construct an implicit derivative matching (IDM) technique for restoring the accuracy of the Yee scheme for Maxwell's equations in dispersive media with material interfaces in one dimension. We consider media exhibiting orientational polarization, which are represented using a Debye dispersive model, examples of which are water and living tissue....
Barley and cereal yellow dwarf viruses (B/CYDV) are a suite of aphid-vectored pathogens that affect diverse host communities, including economically important crops. Coinfection of a single host by multiple strains of B/CYDV can result in elevated virulence, incidence, and transmission rates. We develop a model for a single host, two...
In this thesis, we consider Maxwell's Equations and their numerical discretization using finite difference and finite element methods. We first describe Maxwell's equations in linear dielectrics and then present finite difference and finite element methods for this case. We then describe Maxwell's equations in linear metamaterials using the Lorentz and...
Temperature data from above and below the Cougar Dam collected by the U.S. Geological Survey prior to the construction of the temperature control structure was analyzed to determine how the di®ering temperature regimes a®ect the growth and survival of threatened spring- run Chinook salmon. An ARIMA time-series model was used...
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...
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...
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...
We consider an SI model of three competing species that are all affected by a single pathogen which is transmitted directly via mass action. The total population sizes of the three species satisfy a three-dimensional Lotka-Volterra competition model. We address the interaction between competition and disease dynamics, and show that...
We study the stability properties of, and the phase error present in, several higher order (in space) staggered finite difference schemes for Maxwell's equations coupled with a Debye or Lorentz polarization model. We present a novel expansion of the symbol of finite difference approximations, of arbitrary (even) order, of the...
In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of...
At the macroscopic scale, we have pumps that use the classical laws of physics to move liquids at a well defined rate. In the microscopic world, physicists are exploring pumps that make use of quantum mechanical behavior to build analogous pumps for quantum particles. The importance of such “quantum pumps”...
The main goal of this project is to implement an algorithmic music composition procedure and present all procedures and results in a reproducible fashion by creating a web application produced by R. To approach the implementation of the algorithmic composition of music, we start by exploring various models, but ultimately...
We consider numerical methods for finding approximate solutions to Ordinary Differential Equations (ODEs) with parameters distributed with some probability by the Generalized Polynomial Chaos (GPC) approach. In particular, we consider those with forcing functions that have a random parameter in both the scalar and vector case. We then consider linear...
Gender has been the subject of study in engineering education and science social research for decades. However, little attention has been given to transgender and gender nonconforming (TGNC) experiences or perspectives. The role of cisgender or gender conforming status has not been investigated nor considered in prevailing frameworks of gender...
Results are provided that highlight the effect of interfacial discontinuities in the
diffusion coefficient on the behavior of certain basic functionals of the diffusion, such
as local times and occupation times, extending previous results in [2, 3] on the behavior
of first passage times. The main goal is to obtain...
The fate of biologically available nitrogen (N) and carbon (C) in stream ecosystems is controlled by the coupling of physical transport and biogeochemical reaction kinetics. However, determining the relative role of physical and biogeochemical controls at different temporal and spatial scales is difficult. The hyporheic zone (HZ), where groundwater–stream water...
Understanding the dynamics of seasonal epizootics of vector-borne pathogens infecting multiple host species presents several challenges. The transmission potential of competent hosts depends on factors influencing the contact rate between hosts and vectors. Feeding preferences of vectors can determine which host species drive the prevalence of infection throughout the overall...
The introduction of an Magnetohydrodynamic (MHD) generator in coal or natural gas energy plants could significantly increase the efficiency by converting kinetic and thermal energy of the combustion exhaust to electrical energy by the generation of a Faraday and Hall current. The traditional MHD system was transformed into a simplified...
This work presents improvements to a multi-core performance/power simulator. The improvements which include updated power models, voltage scaling aware models, and an application specific benchmark, are done to increase the accuracy of power models under voltage and frequency scaling. Improvements to the simulator enable more accurate design space exploration for...
Malaria is a vector-borne disease that has affected humans and other animals for a long time and which has shown high prevalence among different populations. During the beginning of the 20th century, Sir Ronald Ross and George Macdonald developed a model that represents the spread of malaria through the interaction...
Microplastics (<5mm diameter) are present in a considerable number of marine and aquatic species. Understanding which species, the global spatial distribution, and what quantities of microplastics are present is extremely important for understanding the potential impacts they could have on recreationally important organisms and for the assessment of risk. We...
This thesis consists of three subsequent parts addressing the applications of stochastic
processes to the analysis and solutions of parabolic equations with discontinuous coefficients
that are of mathematical interest.
The first two parts consist of three manuscripts, in which we analyze solutions
of Fickian convection dispersion equations with discontinuous coefficients...
Biological invasions provide a unique opportunity to study the mechanisms that regulate community composition and ecosystem function. Invasive species that are also ecosystem engineers can substantially alter physical features in an environment, and this can lead to cascading effects on the biological community. Aquatic-terrestrial interface ecosystems are excellent systems to...
The feedbacks between hydrology and biogeochemical cycling of nitrogen (N) are of critical importance to global bioavailable N budgets. Human activities are dramatically increasing the amount of bioavailable N in the biosphere, which is causing increasingly frequent and severe impacts on ecosystems and human welfare. Streams are important features in...
The goal of this research was to explore if an inkjet 3D printing technology, known as Multi Jet Fusion (MJF), could be used to fabricate magnetic polymer nanocomposites with systematically varied volume fractions of magnetic nanoparticles. Soft magnetic nanoparticles were chosen because of their applications in communications technologies and other...
Apart from the traditional role of preventing progression from HIV to AIDS, antiretroviral drug therapy (ART) has an additional benefit of substantially reducing infectiousness, making them potentially an important strategy in the fight against HIV. Recent advances in drug therapy have also seen the use of antiretroviral drugs as a...
A central challenge for ecology is to understand the dynamic nature of species interactions. A classic approach to community ecology assumes that individuals within a species are functionally identical and that consumer-resource dynamics can be predicted solely by using species abundances. However, one species can consist of multiple functional groups,...
In this work we consider a mathematical and computational model for biofilm growth and nutrient utilization. In particular, we are interested in a model appropriate at a scale of interface. The model is a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs). One of these PDEs is subject...
Two-phase flows in microtechnology based devices are purposefully present in multiphase reactors, phase separators, analytical devices and others. Two-phase flows can also be an undesirable side effect occurring during operation due to phase transitions or, more commonly, introduction of surrounding air through equipment gaps and with process feed. In both...
Engineers have long been inspired by nature's flyers. Such animals navigate complex environments gracefully and efficiently by using a variety of evolutionary adaptations for high-performance flight. Biologists have discovered a variety of sensory adaptations that provide flow state feedback and allow flying animals to feel their way through flight. A...
Within this dissertation, we develop tools and techniques to demonstrate the feasibility of real-time optimization of a magnetohydrodynamics generator. To ease computational complexity, we work on the kinematic magnetohydrodynamic system, prescribing the fluid-flow and model the material response of the system through an updated Generalized Ohm’s law. We focus on...
Given an initial opinion matrix in which every member of a population gives an opinion score of all the members in a population, natural questions to ask could be regarding what happens to those opinions over time, both in forward time and in backward time. While what happens over time...
Modern scientific and engineering problems often require simulations with a level of resolution difficult to achieve in reasonable amounts of time—even in effectively parallelized programs. Therefore, applications that exploit high performance computing (HPC) systems have become invaluable in academia and industry over the past two decades. Addressing the questions that...
Emerging infectious diseases impact both human and wildlife populations. Infectious agents, in particular the aquatic fungus Batrachochytrium dendrobatidis (chytrid), have an influential role in driving global amphibian population declines. The emergence of the chytrid fungus has aspects of both geographic spread as well as climate shifts altering environmental conditions and...
This dissertation examines properties and representations of several isotropic Gaussian random fields in the unit ball in d-dimensional Euclidean space. First we consider Lévy's Brownian motion. We use an integral representation for the covariance function to find a new expansion for Lévy's Brownian motion as an infinite linear combination of...
We develop several a-priori and a-posteriori error estimates for two-grid finite element discretization of coupled elliptic and parabolic systems with a set of parameters P. We present numerical results that verify the convergence order of the numerical schemes predicted by the a-priori estimates. We present numerical results that verify the...
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...
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...
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...
This thesis studies connections between disorder type in tree polymers and the branching random walk and presents an application to swarm site-selection. Chapter two extends results on tree polymers in the infinite volume limit to critical strong disorder. Almost sure (a.s.) convergence in the infinite volume limit is obtained for...
Advective skew dispersion is a natural Markov process defined ned
by a di ffusion with drift across an interface of jump discontinuity in
a piecewise constant diff usion coeffcient. In the absence of drift this
process may be represented as a function of -skew Brownian motion
for a uniquely determined...
In this dissertation, we use Fourier-analytic and spectral theory methods to analyze the behavior of solutions of the incompressible Navier-Stokes equations in 2D and 3D (with an eye towards better understanding turbulence). In particular, we investigate the possible existence of so-called ghost solutions to the Navier-Stokes Equations. Such solutions, if...
To investigate the dynamic response of the outer accretionary wedge updip from the patch of greatest slip during the Mw8.8 2010 Maule earthquake, 10 Ocean Bottom Seismometers (OBS) were deployed from May 2012 to March 2013 in a small array with an inter-instrument spacing of ~10 km. Nine instruments were...
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...
Each chapter in this expository paper considers a mathematical model of an aspect of animal behavior, and how it affects the patterns of movement across and within a landscape. These models are all directly or indirectly related to questions in either Behavioral Ecology or Landscape Ecology, or both. I first...
The modeling and analysis of laboratory-generated nonlinear intermediate- to deep-water wave fields, using existing wavemaker theories and analysis tools, is one of the most challenging tasks in ocean science and engineering. On one hand, harmonics function (sine and cosine) -based wavemaker theories result in an inherent (linear) instability of the...
This dissertation concerns several problems in the fields of light interaction with nanostructured media, metamaterials, and plasmonics. We present a technique capable of extending operational bandwidth of hyperbolic metamaterials based on interleaved highly-doped InGaAs and undoped AlInAs multilayer stacks. The experimental results confirm theoretical predictions, exhibiting broadband negative refraction response...
For cell-like upper semicontinuous(usc) decompositions G of finite dimensional manifolds M, the decomposition space M/G turns out to be an ANR provided M/G is finite dimensional ([Dav07], page 129 ). Furthermore, if M/G is finite dimensional and has the
Disjoint Disks Property (DDP), then M/G is homeomorphic to M ([Dav07],...
Animals aggregate and interact in nonuniform and nonrandom patterns, which lead to group level characteristics that have important evolutionary and ecological consequences. Network analysis provides a useful conceptual framework for linking animal interactions at all scales from dyads to communities, to populations and ecosystems. Despite exciting theoretical and applied advances...
This thesis consists of extensions of results on a perpetual American swaption problem. Companies routinely plan to swap uncertain benefits with uncertain costs in the future for their own benefits. Our work explores the choice of timing policies associated with the swap in the form of an optimal stopping problem....