Physical Sciences and Mathematics Commons^™

An Exploration Of Absolute Minimal Degree Lifts Of Hyperelliptic Curves, Justin A. Groves

Doctoral Dissertations

For any ordinary elliptic curve E over a field with non-zero characteristic p, there exists an elliptic curve E over the ring of Witt vectors W(E) for which we can lift the Frobenius morphism, called the canonical lift. Voloch and Walker used this theory of canonical liftings of elliptic curves over Witt vectors of length 2 to construct non-linear error-correcting codes for characteristic two. Finotti later proved that for longer lengths of Witt vectors there are better lifts than the canonical. He then proved that, more generally, for hyperelliptic curves one can construct a lifting over …

Sub-Chandrasekhar Type Ia Supernovae Scenarios With Increased Pathways For Neutronization, Fernando Hernan Rivas

Doctoral Dissertations

Type Ia supernovae are thermonuclear explosions of white dwarfs (WD), electron-degenerate cores of old intermediate mass stars(under 8$M_{\odot}$). Reaching energies of $10^{51}$\si{\erg}, they outshine whole galaxies as they synthesize and distribute most of the iron group elements (IGE; V, Cr, Mn, Fe, Co, Ni) into the interstellar medium, thus being one of the main agents in cosmic chemical evolution. Also, given their notably homogeneous lightcurves, they form the last step in the cosmic distance ladder outdistancing Cepheid variables by orders of magnitude. Though calibration of said lightcurves is dependent on a high number of confirmed events, the limits of statistical …

Synthesizing, Purifying, And Characterizing Molten Chloride Salts, Phillip W. Halstenberg

Doctoral Dissertations

Molten chloride salts have vast potential as heat transfer fluids with both nuclear and concentrated solar power applications. For application in energy systems, the characteristics that govern these systems must be well understood. This work focuses on inorganic molten chloride salts with a special emphasis on the experimental aspect of chemical research. Chapter 2 covers the synthetic approaches for the formation of molten chloride mixtures. Many salts can be purchased from industrial suppliers, but most must be purified therefore, Chapter 3 evaluates various methodology developed for removal of impurities in salt mixtures. Once the salt of proper content and purity …

Mechanochemical Synthesis Of Task-Specific Conjugated Porous Networks Towards Enhanced Energy Storage, Juntian Fan

Doctoral Dissertations

Conjugated scaffolds with high electronic conductivity, high surface area, etc. are promising materials for diverse technological applications, especially in the electrochemical field. However, the current synthesis methods are still limited to the traditional solution-based method or the ionothermal method, which always require an inert atmosphere shield, large amounts of organic solvents, noble catalysts, long reaction time up to days, and high temperatures, etc. Therefore, there is a common goal of developing conjugated scaffolds through facile, green, straightforward pathways. Mechanochemistry, which is an efficient, sustainable, solvent-free methodology, could provide a unique reaction environment to synthesize this kind of functionalized materials, resulting …

Space-Angle Discontinuous Galerkin Finite Element Method For Radiative Transfer Equation, Hang Wang

Doctoral Dissertations

Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and others. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables, which are 3 dimensions in space and 2 dimensions in the angular direction. This high dimensionality and the presence of the integral term present serious challenges when solving the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation (RTE) have been introduced. These include, but are certainly not limited to, Monte Carlo …

Utilizing Ultra-Performance Chromatography High-Resolution Mass Spectrometry To Investigate Fatty Acid Mediated Antibiotic Tolerance, Brittni Woodall

Doctoral Dissertations

The lipid membrane is the first component necessary to sustain life. To maintain homeostasis, segregate cellular machinery, provide protection from the environment, and reproduce, an organism must establish a boundary in which the processes can occur. Throughout the last two decades, research has propelled our knowledge of lipid membranes much beyond original hypotheses. Once thought of to be static and uniform, the understanding of the lipid membrane has evolved to encompass a structure that is responsive, unique, and intricately constructed by the organism itself. By chance or by choice, organisms adapt the lipid membrane according to the environment for which …

Fabrication, Measurements, And Modeling Of Semiconductor Radiation Detectors For Imaging And Detector Response Functions, Corey David Ahl

Doctoral Dissertations

In the first part of this dissertation, we cover the development of a diamond semiconductor alpha-tagging sensor for associated particle imaging to solve challenges with currently employed scintillators. The alpha-tagging sensor is a double-sided strip detector made from polycrystalline CVD diamond. The performance goals of the alpha-tagging sensor are 700-picosecond timing resolution and 0.5 mm spatial resolution. A literature review summarizes the methodology, goals, and challenges in associated particle imaging. The history and current state of alpha-tagging sensors, followed by the properties of diamond semiconductors are discussed to close the literature review. The materials and methods used to calibrate the …

Pointing Control And Stabilization Of The High-Energy Uv Laser For Laser-Assisted Charge Exchange, Martin Joseph Kay

Doctoral Dissertations

Laser-Assisted Charge Exchange (LACE) is an experimental method of charge exchange injection into a proton accumulator ring that is being developed at the Spallation Neutron Source (SNS) in Oak Ridge National Laboratory (ORNL) as an alternative to hazardous injection foils. The current scheme of LACE requires a high-energy, low-repetition-rate UV (355 nm) laser beam (140 mJ pulses at 10 Hz) to be transported over 65 meters to the laser-particle interaction point (IP) in a high-radiation area of the accelerator. Thermal effects and other disturbances along the free-space laser transport line cause the beam to slowly drift away from the IP …

Total Absorption Spectroscopy Of Mo-106 And Tc-106, Michael Cooper

Doctoral Dissertations

Total absorption spectroscopy is a method of gamma-ray spectroscopy that has gained prominence in the past several decades, as nuclear data revisions are performed on older nuclear data, which is often incomplete. A strong understanding of underlying nuclear data, particularly fission and beta decay data, is essential for nuclear reactors and nuclear fuel decay heat. This PhD work involves the analysis of fission fragments 106Mo [Mo-106] and 106Tc [Tc-106]. These neutron rich isotopes contribute upwards of 6% of the cumulative fission yield of 241Pu [Pu-241] fission, and 4% of 239Pu [Pu-239] fission. Prior data for these two fission fragments only …

Large-Scale Volcanism On The Terrestrial Planets, Keenan Ben Golder

Doctoral Dissertations

Evidence for mafic volcanism has been found on each planet in the inner Solar System. Lava flows on these planets range in size from 10s to 1000s of kilometers in extent. I investigated large-scale lava flows on Mercury, Earth, and Mars throughout the chapters in this dissertation. Each of these lava flows provides an avenue to study the emplacement and evolution of lava on various planets and under differing conditions, the factors that affect their overall extent, and potential source areas.

Chapter One investigates large-scale lava flows in the Cerberus region on Mars, specifically to understand their emplacement history, material …

The Novel Chlorination Of Zirconium Metal And Its Application To A Recycling Protocol For Zircaloy Cladding From Spent Nuclear Fuel Rods, Breanna K. Vestal

Doctoral Dissertations

A novel protocol has been developed for the chemical removal of zirconium alloy (Zircaloy) cladding from spent nuclear fuel rods and subsequent isolation and purification of nuclear-grade zirconium chloride derived therefrom. This protocol is based on the chemistry developed from two new scientific findings.

First, two new oxidative chlorination reactions have been discovered for zirconium metal. In both solvents, zirconium can be quantitatively chlorinated at temperatures less than 150°C, with the operative equations seen below. In sulfur monochloride, the reaction is completed in 2 – 4 hours via surface etching, exhibiting 0^th order kinetic behavior. The elemental sulfur byproduct …

Climatological Analysis Of Tropical Cyclone Occurrence Dates And Landfall Characteristics In The North Atlantic And Eastern North Pacific, Nicholas Sava Grondin

Doctoral Dissertations

Tropical cyclones (TCs) are significant hazards to coastal and inland regions across the globe, especially in North America. North America is affected by TCs from two basins, the North Atlantic (NATL) and eastern North Pacific (ENP), with the former being the predominate focus of past research. In this dissertation, I present three studies that directly compare TCs in the NATL and ENP by using the same methods for each basin in studying occurrence dates and intraseasonal variability, effects of environmental parameters on occurrence dates and seasonal forecasting, and the behavior of TCs during the final 36 hours before landfall in …

Neutrino Physics At A Research Reactor: Backgrounds And Analysis, Blaine Alexander Heffron

Doctoral Dissertations

The field of neutrino physics has a rich history and is currently the subject of much active research. The discovery of neutrino oscillations led to the conclusion that neutrinos have mass which was in contradiction to the Standard Model. Now researchers are investigating a number of open questions regarding neutrino properties such as their mass values or the existence of CP violation in the weak interaction. In order to answer these questions experimental and analytical techniques of neutrino detection are becoming more advanced, entering into an era of precision neutrino detection.

Nuclear reactors as a source of antineutrinos have played …

Understanding And Simulating Wildfire Changes Using Advanced Statical And Process-Oriented Models, Rongyun Tang

Doctoral Dissertations

This study aims to investigate the spatiotemporal dynamic of global wildfires, their underlying climate-driving mechanisms, and their predictability by utilizing multiple data sources (both process-based model simulations and satellite-based observations) and multiple analytical methods including machine learning techniques (MLTs).

We first explored the global wildfire interannual variability (IAV) and its climate sensitivity across nine biomes from 1997 to 2018, leveraging the state-of-art U.S. Department of Energy’s Energy Exascale Earth System Model (E3SM) land component (ELM-v1) simulations with six sets of climate forcings. Results indicate that 1) ELM simulations could reproduce the IAV of wildfire in terms of magnitudes, distribution, bio-regional …

Probing Gas Transport Structure-Property Relationships In Vinyl-Addition Polynorbornenes, Trevor Jonas Wilson

Doctoral Dissertations

Polynorbornenes are ideal materials for systematic structure-property investigations designed to correlate gas-transport properties to polymer structure. The modular nature of norbornene-derived systems provides a facile route towards the synthesis of diverse polymeric materials, whose structure may be systematically altered through targeted design of monomers, alterations in polymerization mechanism, or some combination of these two strategies. Though many valuable correlations between gas-permeability and polynorbornene structure have been summarized in prior literature, many of these efforts have focused on homopolymer materials with structural changes imposed — almost exclusively — through modifications in substituent chemistry, or through targeted modulation of molar ratios in …

Unlocking The Potential Of Machine Learning In The Derivation Of Low-Energy Models For Metallic Magnets, Vikram Sharma

Doctoral Dissertations

Condensed matter physics often grapples with complex many-particle problems lacking definitive closed-form solutions, necessitating approximation strategies to investigate low-energy sectors of the Hilbert space. Perturbation theory, though widely used for this purpose, is limited when expansion terms diverge. This work introduces a machine learning (ML) assisted protocol to extract effective low-energy models for lattice models of fermions interacting with classical fields, specifically focusing on the Kondo Lattice Model (KLM).

Skyrmions, featuring whirling spin texture and topological protection, are promising candidates for future spintronic devices. Materials featuring conduction electrons coupled to localized $f$-electrons' net moment are ideal for realizing skyrmions and …

Development Of Artificial Lipids For Metal Ion-Responsive Liposomes And Related Medicinal Applications, Ruhani Sagar

Doctoral Dissertations

Liposomes are synthetic vesicles made of phospholipids that are effective for wide-ranging applications in drug delivery and studying biological membranes. Understanding and controlling membrane properties such as fluidity and permeability is crucial for designing liposomes for specific biomedical applications. Pathological changes in these properties can also help us gain insights into disease mechanisms and develop effective treatments. In this dissertation, we describe the design, synthesis, and study of several lipid analogs for a range of applications including liposome triggered cargo release and therapeutic treatment related to lipids.

In Chapters 2-3, we developed smart liposome platforms that can respond to changes …

Explicit Constructions Of Canonical And Absolute Minimal Degree Lifts Of Twisted Edwards Curves, William Coleman Bitting Iv

Doctoral Dissertations

Twisted Edwards Curves are a representation of Elliptic Curves given by the solutions of bx^2 + y^2 = 1 + ax^2y^2. Due to their simple and unified formulas for adding distinct points and doubling, Twisted Edwards Curves have found extensive applications in fields such as cryptography. In this thesis, we study the Canonical Liftings of Twisted Edwards Curves and the associated lift of points Elliptic Teichmu ̈ller Lift. The coordinate functions of the latter are proved to be polynomials, and their degrees and derivatives are computed. Moreover, an algorithm is described for explicit computations, and some properties of the general …

Computational Aspects Of Mixed Characteristic Witt Vectors And Denominators In Canonical Liftings Of Elliptic Curves, Jacob Dennerlein

Doctoral Dissertations

Given an ordinary elliptic curve E over a field 𝕜 of characteristic p, there is an elliptic curve E over the Witt vectors W(𝕜) for which we can lift the Frobenius morphism, called the canonical lifting of E. The Weierstrass coefficients and the elliptic Teichmüller lift of E are given by rational functions over 𝔽_p that depend only on the coefficients and points of E. Finotti studied the properties of these rational functions over fields of characteristic p ≥ 5. We investigate the same properties for fields of characteristic 2 and 3, make progress on …

Path Integral Monte Carlo For Entanglement In Bosonic Lattices At T = 0, Emanuel Casiano-Diaz

Doctoral Dissertations

Path-Integral Monte Carlo Worm Algorithm is one of many Quantum Monte Carlo (QMC) methods that serve as powerful tools for the simulation of quantum many-body systems. Developed in the late 90’s, this algorithm has been used with great success to study a wide array of physical models where exact calculation of observables is not possible due to the exponential size of the Hilbert space. One type of systems that have eluded PIMC-WA implementation are lattice models at zero temperature, which are of relevance in experimental settings, such as in optical lattices of ultra-cold atoms. In this thesis, we develop a …

Multidimensional Investigation Of Tennessee’S Urban Forest, Jillian L. Gorrell

Doctoral Dissertations

Preserving existing trees in urban areas and properly cultivating urban forest conservation and management opportunities is valuable to the ever-growing urban environment and necessary for creating optimal experiences and educational tools to meet the needs of increasing urban populations. This dissertation contains studies investigating several facets of the urban forest, including environmental effects of deforestation and urbanization, tree equity, and urban forest facility management and accessibility. Community education and outreach at arboreta about the importance of the tree canopy can help promote environmental stewardship. A digital questionnaire was electronically distributed to representatives of arboreta certified through the Tennessee Division of …

The Development Of Tailored Amphiphilic Copolymers For Detergent-Free Integral Membrane Protein Extraction, Cameron Edward Workman

Doctoral Dissertations

Integral membrane proteins are prolific targets for the design, development, and delivery of pharmaceuticals. In fact, over 60% of all currently available drugs target these proteins to accomplish their therapeutic effect. However, integral membrane proteins remain the least characterized class of all proteins, accounting for only ~2% of all solved protein structures. One of the primary reasons for this low number of solved protein structures is that many membrane proteins lose their native conformation when extracted using conventional methods (e.g. detergents), convoluting accurate structure determination. In contrast, amphiphilic styrene-maleic acid copolymers (SMAs) were recently discovered to readily isolate membrane proteins …

Development Of Surface-Modified Liposomes For Drug Delivery Applications, Megan Louise Qualls

Doctoral Dissertations

Liposomes are spherical vesicles composed of a lipid bilayer membrane that assembles around an internal aqueous core. This duality gives liposomes the ability to encapsulate both hydrophobic cargo within the lipid bilayer and hydrophilic cargo in the aqueous core, making them versatile molecular carriers for drug delivery. Liposome platforms have many advantages and are promising drug delivery carriers, and research is ongoing to improve their designs for continued clinical applications. Many liposome types have been developed, but further work is needed to improve surface modification, site-specific targeting, and triggered cargo release in order to further the therapeutic applications of these …

Large Deviations For Self Intersection Local Times Of Ornstein-Uhlenbeck Processes, Apostolos Gournaris

Doctoral Dissertations

In the area of large deviations, people concern about the asymptotic computation of small probabilities on an exponential scale. The general form of large deviations can be roughly described as: P{Yn ∈ A} ≈ exp{−bnI(A)} (n → ∞), for a random sequence {Yn}, a positive sequence bn with bn → ∞, and a coefficient I(A) ≥ 0. In applications, we often concern about the probability that the random variables take large values, that is we concern about the P{Yn ≥ λ}, where λ > 0. Here, we consider the Ornstein-Uhlenbeck process, study the properties of the local times and self intersection …

Adaptive And Topological Deep Learning With Applications To Neuroscience, Edward Mitchell

Doctoral Dissertations

Deep Learning and neuroscience have developed a two way relationship with each informing the other. Neural networks, the main tools at the heart of Deep Learning, were originally inspired by connectivity in the brain and have now proven to be critical to state-of-the-art computational neuroscience methods. This dissertation explores this relationship, first, by developing an adaptive sampling method for a neural network-based partial different equation solver and then by developing a topological deep learning framework for neural spike decoding. We demonstrate that our adaptive scheme is convergent and more accurate than DGM -- as long as the residual mirrors the …

Coefficients Of Modular Forms And Applications To Partition Theory, Michael Anthony Hanson

Doctoral Dissertations

We begin with an overview of the theory of modular forms as well as some relevant sub-topics in order to discuss three results: the first result concerns positivity of self-conjugate t-core partitions under the assumption of the Generalized Riemann Hypothesis; the second result bounds certain types of congruences called "Ramanujan congruences" for an infinite class of eta-quotients - this has an immediate application to a certain restricted partition function whose congruences have been studied in the past; the third result strengthens a previous result that relates weakly holomorphic modular forms to newforms via p-adic limits.

Electrodeposition Of Epitaxial Wide Bandgap P-Type Semiconductors And Copper Metal For Energy Conversion And Flexible Electronics, Bin Luo

Doctoral Dissertations

"Epitaxial electrodeposition is a simple, low-cost technology to produce highly ordered materials on single-crystal surfaces. This research focuses on the epitaxial electrodeposition of wide bandgap p-type semiconductors and epitaxial Cu thin films via a self-assembled monolayer for energy conversion and flexible electronics. Paper I introduces the epitaxial electrodeposition of hole conducting CuSCN nanorods onto Au (111) surface, and lift-off to produce flexible and transparent foils. Highly ordered CuSCN could serve as an inorganic transport layer in various opto-electronic devices such as perovskite solar cells, LEDs, and transistors. An ordered and transparent CuSCN foil was also produced by epitaxial lift-off following …

Near-Ir Spectroscopic Analysis Of The Primary Volatile Composition Of Long And Short-Period Comets, Younas Khan

Doctoral Dissertations

"Comets are among the most well-preserved objects that formed in the protosolar nebula ∼4.5 Gyr ago. Hence, they are important for understanding various aspects of the formation, evolution, and habitability of the solar system. Multiple primary volatiles (molecules directly sublimating into the coma from the nucleus) emit via rovibrational transitions in the near-IR, providing opportunities to calculate their abundances. To date, only ∼50 comets have been characterized for their primary volatiles, with the short-period Jupiter-family comets (JFCs) being significantly underrepresented. In contrast, hundreds of comets have been sampled at optical/UV wavelengths, primarily for the composition of daughter species, leading to …

Fluorination Of Rubisco-Mimetic Co2 Capture Systems. Theoretical And Experimental Studies Of Ammonium Ion Acidity Depression And Carbamylation, Brian Michael Jameson

Doctoral Dissertations

"RuBisCO-inspired CO₂ capture and release (CCR) systems featuring amines have been developed for the purpose of reversable CO₂ capture from air. The enzyme active site consists of the tetrapeptide sequence Lys-Asp-Asp-Glu. The Lys sidechain amine undergoes carbamylation and an Mg²⁺ cation stabilizes the resulting carbamate. The N^a-acyl-lysinyl-aspratyl-aspartyl-glutamide (Lys-Asp-Asp-Glu, KDDE) peptide featured maximum capture at pH ≈ 10; a pH region too high for Mg²⁺ ions to remain in solution. This work aims to achieve pKa depression by introducing fluorine in the proximity of the lysine’s sidechain amine. A comparative analysis was made of butylamine, …

Applied Geochemistry, Geochronology And Biostratigraphy: Case Studies From The 38th Parallel Structures In Missouri And Orange Basin, Offshore Western South Africa, Marissa Kay Spencer

Doctoral Dissertations

"The unique alignment of the Decaturville, Crooked Creek, and Weaubleau geological structures in central Missouri, three of nine known such structures along the 38th parallel in Illinois, Missouri, and Kansas, has puzzled geoscientists for decades. Research using palynology (palynomorphs and particulate organic matter) and radiometric dating of impact spherules were used to constrain age and a relationship between these enigmatic structures and infer their paleoenvironmental conditions. Novel melting damages, unique to impact, were documented in the palynomorphs in all the three structures. Early Ordovician acritarchs with melted processes correlate with ⁴⁰Ar-³⁹Ar stepwise heating age of impact spherules …