Physical Sciences and Mathematics Commons^™

Geometry Of Scales, Kyle Stephen Austin

Doctoral Dissertations

The geometry of coverings has widely been used throughout mathematics and it has recently been a promising tool for resolving longstanding problems in topological rigidity such as the Novikov conjecture and Gromov's positive scalar curvature conjecture. We discuss rigidity conjectures and how large scale geometry is being applied in order to resolve them for important cases.

Not only is small scale and large scale geometry very applicable to understanding global geometry of objects, but it is an interesting topic in its own right. The first chapter of this paper is devoted to building a framework for small scale geometry alongside …

Population Modeling For Resource Allocation And Antimicrobial Stewardship, Jason Bintz

Doctoral Dissertations

This dissertation contains two types of population models with applications in conservation biology and epidemiology. In particular, it considers models for resource allocation and antimicrobial stewardship.

In a population model with a parabolic differential equation and density dependent growth, we study the problem of allocating resources to maximize the net benefit in the conservation of a single species while the cost of the resource allocation is minimized. The net benefit is measured in terms of maximizing population abundance and the goal of maximizing abundance is divided between the goal of maximizing the overall abundance across space and time and the …

Domain Decomposition Methods For Discontinuous Galerkin Approximations Of Elliptic Problems, Craig Dwain Collins

Doctoral Dissertations

The application of the techniques of domain decomposition to construct effective preconditioners for systems generated by standard methods such as finite difference or finite element methods has been well-researched in the past few decades. However, results concerning the application of these techniques to systems created by the discontinuous Galerkin method (DG) are much more rare.

This dissertation represents the effort to extend the study of two-level nonoverlapping and overlapping additive Schwarz methods for DG discretizations of second- and fourth-order elliptic partial differential equations. In particular, the general Schwarz framework is used to find theoretical bounds for the condition numbers of …

Numerical Approximation Of Stochastic Differential Equations Driven By Levy Motion With Infinitely Many Jumps, Ernest Jum

Doctoral Dissertations

In this dissertation, we consider the problem of simulation of stochastic differential equations driven by pure jump Levy processes with infinite jump activity. Examples include, the class of stochastic differential equations driven by stable and tempered stable Levy processes, which are suited for modeling of a wide range of heavy tail phenomena. We replace the small jump part of the driving Levy process by a suitable Brownian motion, as proposed by Asmussen and Rosinski, which results in a jump-diffusion equation. We obtain L^p [the space of measurable functions with a finite p-norm], for p greater than or equal to …

The Congruence-Based Zero-Divisor Graph, Elizabeth Fowler Lewis

Doctoral Dissertations

Let R be a commutative ring with nonzero identity and ~ a multiplicative congruence relation on R. Then, R/~ is a semigroup with multiplication [x][y] = [xy], where [x] is the congruence class of an element x of R. We define the congruence-based zero-divisor graph of R ito be the simple graph with vertices the nonzero zero-divisors of R/~ and with an edge between distinct vertices [x] and [y] if and only if [x][y] = [0]. Examples include the usual …

Numerical Methods For Deterministic And Stochastic Phase Field Models Of Phase Transition And Related Geometric Flows, Yukun Li

Doctoral Dissertations

This dissertation consists of three integral parts with each part focusing on numerical approximations of several partial differential equations (PDEs). The goals of each part are to design, to analyze and to implement continuous or discontinuous Galerkin finite element methods for the underlying PDE problem.

Part One studies discontinuous Galerkin (DG) approximations of two phase field models, namely, the Allen-Cahn and Cahn-Hilliard equations, and their related curvature-driven geometric problems, namely, the mean curvature flow and the Hele-Shaw flow. We derive two discrete spectrum estimates, which play an important role in proving the sharper error estimates which only depend on a …

Intrusion Detection System Of Industrial Control Networks Using Network Telemetry, Stanislav Ponomarev

Doctoral Dissertations

Industrial Control Systems (ICSs) are designed, implemented, and deployed in most major spheres of production, business, and entertainment. ICSs are commonly split into two subsystems - Programmable Logic Controllers (PLCs) and Supervisory Control And Data Acquisition (SCADA) systems - to achieve high safety, allow engineers to observe states of an ICS, and perform various configuration updates. Before wide adoption of the Internet, ICSs used "air-gap" security measures, where the ICS network was isolated from other networks, including the Internet, by a physical disconnect [1]. This level of security allowed ICS protocol designers to concentrate on the availability and safety of …

Microfluidic Syntheses Of Pet Radiotracers Via Fluorodenitration, Thomas Madison Moore

Doctoral Dissertations

This research study is focused on the syntheses of radiotracers for use in positron emission tomography [PET] via fluorodenitration and fluorodehalogenation under microfluidic conditions. Methodology has been developed for radiolabeling via fluorodenitration under microfluidic conditions and comparisons made to dehalogenation reactions. Developmental work was carried out on commercially available compounds containing a variety of functional groups. Subsequent production of radiotracers has been performed with precursors provided by collaborators as well as those synthesized in our laboratory.

Synthesis And Characterization Of Support-Modified Nanoparticle-Based Catalysts And Mixed Oxide Catalysts For Low Temperature Co Oxidation, Andrew Justin Binder

Doctoral Dissertations

Heterogeneous catalysts are responsible for billions of dollars of industrial output and have a profound, if often understated, effect on our everyday lives. New catalyst technologies and methods to enhance existing catalysts are essential to meeting consumer demands and overcoming environmental concerns. This dissertation focuses on the development of catalysts for low temperature carbon monoxide oxidation. CO [carbon monoxide] oxidation is often used as a probe reaction to test overall oxidation activity of a given catalyst and is an important reaction in the elimination of toxic pollutants from automotive exhaust streams. The work included here presents three new heterogeneous catalysts …

Studies Of Metalloporphyrins And Tantalum Amide Imide Compounds, Seth Carlton Hunter

Doctoral Dissertations

The focus of this dissertation is on two different subjects. The first examines the magnetic and structural properties of metalloporphyrins. In these studies, neutrons were used to probe the magnetic properties of metalloporphyrins. Insight on the structural properties of metalloporphyrins was also gained by examining the intermolecular interactions in the solid state. The second subject is the synthesis and characterization of new tantalum complexes and studies of their reactions with O₂ [dioxygen]. These complexes are potential precursors to make metal oxide and metal nitride thin films.

In the first part of this dissertation, the zero-field parameters D have been …

An Investigation Of Inorganic Compound Scattering., Karl Jay Bernstein

Doctoral Dissertations

Raman and its associated forms of spectroscopy are powerful tools that have been under-utilized. Presented within are three inorganic compounds studied with some form of Raman spectroscopy: normal Raman, hyper-Raman (HR), surface-enhanced Raman spectroscopy (SERS), surface-enhanced hyper-Raman spectroscopy (SEHRS), or resonance Raman spectroscopy (RR).

The first study involves the investigation of phosphine binding with silver metal. Phosphines find wide use in synthetic circles yet have had little study into their method of binding, unlike similar compounds comprised of sulfur. In order to understand the binding of phosphines, several tertiary phosphines, secondary phosphines and secondary phosphine oxides are examined with SERS. …

Oxygen Reduction Reaction By Copper Complex Based Electrocatalysts, Congling Zhang

Doctoral Dissertations

My research focuses on catalysis of oxygen reduction reaction (ORR) by a series of Cu(II) [copper with positive two valence] -1,2,4-triazole complex-based electrocatalysts at the cathode of PEMFC (polymer electrolyte membrane fuel cell), an efficient and environmental friendly energy conversion system compared to internal combustion engines in use today. The sluggish kinetics of ORR considerably limited the performance of PEMFCs. Understanding of ORR mechanism is important for developing affordable, active and durable ORR catalysts for such devices.

The first part of my work focused on improving the ORR performance of Cu(II)-1,2,4-triazole complex-based catalysts in an acidic environment by exploring synthesis …

Event Localization In Bulk Scintillator Crystals Using Optical Coded Apertures, Joshua Brian Braverman

Doctoral Dissertations

Scintillation-based radiation detectors provide an effective method to detect radioactive materials. In medical physics, astrophysics, and national security technology oftentimes it is optimal to have the ability to localize a radioactive interaction in a scintillator to as small a region as possible within the crystal. Current methods rely on the ability to centroid a light spot as read onto a phototransducer (commonly a photomultiplier tube), and due to the typical width of the light spot when it reaches the phototransducer, the resolution is generally limited to several millimeters. One method to achieve a finer resolution is to use a segmented …

Elucidating The Impact Of Roseophage On Roseobacter Metabolism And Marine Nutrient Cycles, Nana Yaw Darko Ankrah

Doctoral Dissertations

As the most abundant biological entities in marine environments, viruses are an important component of marine food webs. The activity of viruses contributes significantly to the mortality of marine microorganisms, ultimately influencing biological function and chemical composition of aquatic systems by impacting species composition and flow of carbon, nitrogen and other nutrients. Despite the growing recognition that viral activity contributes to marine biogeochemical cycles, the extent to which virus infection reshapes host metabolism and the effect of this alteration on the composition of host lysate remains poorly understood. Additionally, the degree to which natural bacterioplankton communities metabolise the released lysate …

Neuroscience-Inspired Dynamic Architectures, Catherine Dorothy Schuman

Doctoral Dissertations

Biological brains are some of the most powerful computational devices on Earth. Computer scientists have long drawn inspiration from neuroscience to produce computational tools. This work introduces neuroscience-inspired dynamic architectures (NIDA), spiking neural networks embedded in a geometric space that exhibit dynamic behavior. A neuromorphic hardware implementation based on NIDA networks, Dynamic Adaptive Neural Network Array (DANNA), is discussed. Neuromorphic implementations are one alternative/complement to traditional von Neumann computation. A method for designing/training NIDA networks, based on evolutionary optimization, is introduced. We demonstrate the utility of NIDA networks on classification tasks, a control task, and an anomaly detection task. There …

Novel Physical Properties Of Non-Trivial Magnetic Materials: Cr1/3nbs2, Mnsi And Fe3gete2, Jieyu Yi

Doctoral Dissertations

Helimagnets and quasi-two-dimensional layered materials have attracted much recent interest due to their rich physical properties and potential for spintronics applications. In this dissertation, the helimagnets Cr_1/3NbS₂ [chromium one-third niobium disulfide] and thin-film MnSi [manganese silicide] as well as the layered magnetic material Fe₃GeTe₂ [iron three germanium ditelluride] were extensively and carefully studied. Cr_1/3NbS₂ was previously reported to be helimagnet with a transition temperature of approximately 120 K. Cr_1/3NbS₂ has a layered structure with Cr³⁺ ions intercalating between NbS­₂ sheets, and is easily cleaved. Using in-situ …

Distinguishing Primary Versus Secondary Geochemical And Silicon Isotope Characteristics Of Precambrian Chert And Iron Formation, Latisha Ashley Brengman

Doctoral Dissertations

Precambrian chert and banded iron formation (BIF) are defined as chemical sediments precipitated directly from seawater. As such, their geochemistry, including trace elements, rare earth elements (REE), and isotopes (O, Si) may preserve Precambrian seawater conditions. However, the chemical signature of these rocks may not simply reflect seawater, because hydrothermal interactions and metasomatism may produce rocks that petrographically and chemically resemble chert and BIF, including seawater-like compositional characteristics acquired during mineral replacement. Interpreting the major-, trace-, and rare-earth element signatures of these rocks requires the identification of geochemical and isotopic fingerprints that differentiate rocks formed from chemical sedimentation from rocks …

The Fabrication Of Micro- And Nano- Scale Deterministic And Stochastic Pillar Arrays For Planar Separations, Teresa Byers Kirchner

Doctoral Dissertations

Planar chromatography, unlike high performance liquid chromatography (HPLC), has not experienced a significant evolution in stationary phase media since the development of the technique. This has lead HPLC to become a much more popular and robust analytical method. Main factors that contribute to improved performance of chromatographic systems include a reduction in particle size, homogeneity of the stationary phase, and an increase in velocity of the mobile phase. In general, a reduction in particle size should lead to an improvement in the performance of all chromatography systems. However, the main obstacle of improving the performance of planar chromatography systems is …

Computational Framework For Small Animal Spect Imaging: Simulation And Reconstruction, Sang Hyeb Lee

Doctoral Dissertations

Small animal Single Photon Emission Computed Tomography (SPECT) has been an invaluable asset in biomedical science since this non-invasive imaging technique allows the longitudinal studies of animal models of human diseases. However, the image degradation caused by non-stationary collimator-detector response and single photon emitting nature of SPECT makes it difficult to provide a quantitative measure of 3D radio-pharmaceutical distribution inside the patient. Moreover, this problem exacerbates when an intra-peritoneal X-ray contrast agent is injected into a mouse for low-energy radiotracers.

In this dissertation, we design and develop a complete computational framework for the entire SPECT scan procedure from the radio-pharmaceutical …

Studies Of Strongly Correlated Electron Systems Using Neutron Scattering, Yuen Yiu

Doctoral Dissertations

The world presents many natural and man-made crises and challenges that require scientific solutions. Condensed matter physics is one of the most influential and solution oriented disciplines in science. The field saw a significant rise in popularity especially during the past century as mankind enters the Information Age, when energy and computing related technologies become ubiquitous. This technological progress has been driven by efforts from scientists and engineers, through the synthesis, understanding, and implementation of new materials. Condensed matter physicists strive to solve puzzles at the frontier of material research. In the 21st century we have many advance tools at …

Computational Electrodynamics And Second Hyper-Raman Scattering, Philip Dwaine Simmons Jr.

Doctoral Dissertations

Surface-enhanced second hyper-Raman spectroscopy is a type of nonlinear light scattering in which three photons are simultaneously annihilated to produce one photon whose color is slightly shifted from its third harmonic. This process, while incredibly weak, can be magnified by many orders of magnitude with the aid of plasmonic substrates. In this dissertation, three different studies are presented probing both the nature of plasmonics and nonlinear Raman scattering. In the first, nanoparticle aggregates were dosed with two isotopologues of Rhodamine 6G to determine single-molecule activity. Plasmon maps of the aggregates were then generated from electron energy-loss spectroscopy (EELS) and 3D …

Monte Carlo Methods In Finance, Je Guk Kim

Doctoral Dissertations

Monte Carlo method has received significant consideration from the context of quantitative finance mainly due to its ease of implementation for complex problems in the field. Among topics of its application to finance, we address two topics: (1) optimal importance sampling for the Laplace transform of exponential Brownian functionals and (2) analysis on the convergence of quasi-regression method for pricing American option. In the first part of this dissertation, we present an asymptotically optimal importance sampling method for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals via Large deviations principle and calculus of variations the closed form …

Beta Decay Of Neutron-Rich Isotopes Of Zinc And Gallium, Mohammad Faleh M. Al-Shudifat

Doctoral Dissertations

Beta-decays of neutron-rich nuclei near the doubly magic ⁷⁸Ni [78Ni] were studied at the Holifield Radioactive Ion Beam Facility. The half-life and the gamma-gamma coincidence spectra were used to study the nuclear structure. A new ^82,83Zn [82Zn, 83Zn] decay-scheme was built, where a 71±7% beta-delayed neutron branching ratio was assigned in ⁸²Zn [82Zn] decay. New gamma-ray lines and energy levels observed in ^82,83Ga [82Ga, 83Ga] beta-decay were used to update previously reported decay-schemes. The experimental results were compared to shell model calculations, which postulate the existence of Gamow-Teller transitions in these decays. The half-lives of 155±17 …

Energy Selective Neutron Imaging For The Characterization Of Polycrystalline Materials, Robin Woracek

Doctoral Dissertations

This multipart dissertation focuses on the development and evaluation of advanced methods for material testing and characterization using neutron diffraction and imaging techniques. A major focus is on exploiting diffraction contrast in energy selective neutron imaging (often referred to as Bragg edge imaging) for strain and phase mapping of crystalline materials. The dissertation also evaluates the use of neutron diffraction to study the effect of multi-axial loading, in particular the role of applying directly shear strains from the application of torsion. A portable tension-torsion-tomography loading system has been developed for in-situ measurements and integrated at major user facilities around the …

Development And Demonstration Of Critical Components Of Aluminum Based Energy Storage Devices Using The Chloroaluminate Ionic Liquids, Mengqi Zhang

Doctoral Dissertations

This dissertation considers the development of porous carbon materials as the substrates for Al deposition/dissolution in an Al based ionic liquid flow battery (ILFB) and demonstration of an Al based hybrid supercapacitor. The Aluminum chloride/ 1-ethyl-3-methylimidazolium chloride chloroaluminate ionic liquid is utilized as the electrolyte for these Al based energy storage devices. The ILFB has less capital cost than the all-vanadium redox flow battery because of the inexpensive AlCl₃. The feasibility to equip a tank of solid aluminum chloride in an ILFB system aiming to improve energy density is investigated. A critical range of temperature data (50-130 celsius …

Numerical Analysis Of Convex Splitting Schemes For Cahn-Hilliard And Coupled Cahn-Hilliard-Fluid-Flow Equations, Amanda Emily Diegel

Doctoral Dissertations

This dissertation investigates numerical schemes for the Cahn-Hilliard equation and the Cahn-Hilliard equation coupled with a Darcy-Stokes flow. Considered independently, the Cahn-Hilliard equation is a model for spinodal decomposition and domain coarsening. When coupled with a Darcy-Stokes flow, the resulting system describes the flow of a very viscous block copolymer fluid. Challenges in creating numerical schemes for these equations arise due to the nonlinear nature and high derivative order of the Cahn-Hilliard equation. Further challenges arise during the coupling process as the coupling terms tend to be nonlinear as well. The numerical schemes presented herein preserve the energy dissipative structure …

Sensitivity Of Mixed Models To Computational Algorithms Of Time Series Data, Gunaime Nevine

Doctoral Dissertations

Statistical analysis is influenced by implementation of the algorithms used to execute the computations associated with various statistical techniques. Over many years; very important criteria for model comparison has been studied and examined, and two algorithms on a single dataset have been performed numerous times. The goal of this research is not comparing two or more models on one dataset, but comparing models with numerical algorithms that have been used to solve them on the same dataset.

In this research, different models have been broadly applied in modeling and their contrasting which are affected by the numerical algorithms in different …

Discrete Analogues Of Some Classical Special Functions, Thomas Joseph Cuchta

Doctoral Dissertations

"Analogues of special functions on time scales are studied with special focus on the time scale 𝕋 = hℤ. Functions investigated in particular include complex monomials, new trigonometric functions, Gaussian bell, Hermite and Laguerre polynomials, Bessel functions, and hypergeometric series"--Abstract, page iii.

Quantum Inspired Algorithms For Learning And Control Of Stochastic Systems, Karthikeyan Rajagopal

Doctoral Dissertations

"Motivated by the limitations of the current reinforcement learning and optimal control techniques, this dissertation proposes quantum theory inspired algorithms for learning and control of both single-agent and multi-agent stochastic systems.

A common problem encountered in traditional reinforcement learning techniques is the exploration-exploitation trade-off. To address the above issue an action selection procedure inspired by a quantum search algorithm called Grover's iteration is developed. This procedure does not require an explicit design parameter to specify the relative frequency of explorative/exploitative actions.

The second part of this dissertation extends the powerful adaptive critic design methodology to solve finite horizon stochastic optimal …

Information Fusion Architectures For Security And Resource Management In Cyber Physical Systems, Brijesh Kashyap Chejerla

Doctoral Dissertations

"Data acquisition through sensors is very crucial in determining the operability of the observed physical entity. Cyber Physical Systems (CPSs) are an example of distributed systems where sensors embedded into the physical system are used in sensing and data acquisition. CPSs are a collaboration between the physical and the computational cyber components. The control decisions sent back to the actuators on the physical components from the computational cyber components closes the feedback loop of the CPS. Since, this feedback is solely based on the data collected through the embedded sensors, information acquisition from the data plays an extremely vital role …