Physical Sciences and Mathematics Commons^™

Non-Orientable Surfaces Bounded By Knots, Megan K. Fairchild

LSU Doctoral Dissertations

The non-orientable 4-genus of a knot $K$ in $S^{3}$ is defined to be the minimum first Betti number of a non-orientable surface $F$ in $B^{4}$ so that $K$ bounds $F$. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots, torus knots, and Whitehead doubles. We also will view obstructions to a knot bounding a M\"{o}bius band given by the double branched cover of $S^{3}$ branched over $K$. Additionally, we discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used …

Temporal Scales Of Sediment Accumulation, Mass Wasting, And Stratigraphy Across The Mississippi River Delta Front, Jeffrey E. Duxbury

LSU Doctoral Dissertations

The Mississippi River Delta Front (MRDF) is a subaqueous apron of rapidly deposited, weakly

consolidated sediment extending from the subaerial portions of the Mississippi River’s Birdsfoot Delta, historically known for sediment transport via mass wasting. To better understand the spatial and temporal dynamics of processes influencing the MRDF, 29 cores ranging from 5.8 to 8.71 meters in length were collected from the South Pass (SP) and Southwest Passes (SWP). These cores targeted specific depositional environments, including the undisturbed topset apron, medial mudflow gully, mudflow lobe, and prodelta. The cores were analyzed along their full lengths for gamma density, grain size, …

Thermal Noise Measurement Below The Standard Quantum Limit, Ronald Pagano

LSU Doctoral Dissertations

Quantum mechanics places sensitivity restrictions on physical measurements. These limitations manifest themselves in interferometric force and displacement measurements as uncertainty both in the photon number measured at a photodetector (shot noise), and in the quantum radiation pressure applied to the interferometer (quantum back action noise manifested as quantum radiation pressure noise). The balance between shot noise and quantum radiation pressure noise imposes the Standard Quantum Limit (SQL). A large body of work has been dedicated to measuring these quantum effects and mitigating them. Owing to the inherently small scale at which quantum effects are visible, classical effects must be subverted …

Studying The Low-Lying Structure Of 9b Via The 10b(3he,A)9b Reaction, Rachel M. Shaffer

LSU Doctoral Dissertations

The unstable nature of ⁹B makes it a challenging isotope to study. The first-excited state of ⁹B has been particularly difficult to characterize. Since the first experimental observation of this state in 1955, many experimental and theoretical nuclear structure studies have sought to classify it, but with large discrepancies in the energy and width values from these results, the properties of the state remain inconclusive.

An experiment using the ¹⁰B(³He,α)⁹B reaction was performed at the John D. Fox Superconducting Linear Accelerator Laboratory at Florida State University in an effort to populate and characterize …

Baryon Number Violation Search, Tyler D. Stokes

LSU Doctoral Dissertations

Understanding the fundamental forces and symmetries of nature has long been a central goal of particle physics. While the Standard Model (SM) provides a successful framework, it does not guarantee the conservation of baryon number B or lepton number L, thus motivating searches for their violation. Proton decay, a fundamental process violating B, has been at the forefront of experimental searches for decades.

The discovery of the weak neutral current in 1973 unified the electromagnetic and weak forces and inspired the creation of Grand Unified Theories (GUTs) that also unify the strong force. In 1974, the first-ever GUT, …

Synthesis And Characterization Of Bimetallic Plasmonic Nanoparticles Using Linear And Nonlinear Spectroscopy, Daniel Babayode

LSU Doctoral Dissertations

Recent exploration in the field of nanomaterials has led to the investigation of noble metal nanoparticles for various nanomedical applications. The spectroscopy of these nanoparticles is studied using both linear and nonlinear optical processes such as second harmonic generation (SHG), two-photon fluorescence (TPF), and extinction spectroscopy. Details pertaining to the growth dynamics of silver-gold core-shell (Ag@Au CS) nanoparticles (NPs) and gold-silver-gold core-shell-shell (Au@Ag@Au CSS) nanoparticles (NPs) are currently being investigated in order to obtain better control and optimization of the nanoparticle size and surface morphology. Transmission electron microscopy (TEM) images show that the nanoparticles have tunable core and shell sizes …

Nanofabrication Of Tetraphenyl Porphyrin Surface Assemblies Linked With Tin Tetrachloride: A Scanning Probe Microscopy Investigation, Quynh Do

LSU Doctoral Dissertations

Scanning probe microscopy (SPM) and colloidal lithography methods were used to study the covalent coupling of porphyrins to surfaces. In this dissertation, experimental methods for SPM operation, techniques, and applications are described. Measurement of tip-sample interactions between a sharp tip and surface is translated into digital image data maps with x-, y-, and z-data. Colloidal lithography can be used to fabricate test platforms for AFM studies. The periodicity and arrangement of the designed nanostructures is determined by the size of the colloidal particles used for surface masks. Data processing is required to obtain images and topography information from raw AFM …

Understanding Mechanisms For Coastal Marsh Sustainability In A Changing Climate, Ashley R. Booth

LSU Doctoral Dissertations

In the Chenier Plain of Louisiana and Texas, coastal marshes are subject to high rates of relative sea level rise (RSLR), restricted sedimentation, and declining elevation attributed to subsidence and decades of intensive management. These marshes were created via mineral sedimentation but now largely accrete via organic matter accumulation. This organic matter accumulation (OMA) – or the balance between plant productivity and decomposition – is essential for maintaining elevation and thus long-term sustainability. However, management for elevation is complicated by a poor understanding of how abiotic factors like flooding and salinity impact processes driving OMA and elevation. To better understand …

Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou

LSU Doctoral Dissertations

Stochastic differential equations (SDEs) are essential for modeling systems influenced by both deterministic dynamics and random fluctuations, with applications in a wide variety of disciplines. This thesis develops a Bayesian framework for nonparametric learning in SDEs, addressing key challenges in inference, particularly when dealing with complex systems and incomplete data. The thesis begins by establishing a theoretical foundation in optimization over Hilbert spaces, including a generalized representer theorem to address infinite-dimensional optimization problems encountered in nonparametric inference. Building on this, we introduce a Bayesian framework with shrinkage priors to learn drift functions from high-frequency data. Bayesian approach incorporates low-cost sparse …

Coloring Trivalent Graphs: A Defect Tft Approach, Amit Kumar

LSU Doctoral Dissertations

We show that the combinatorial matter of graph coloring is, in fact, quantum in the sense of satisfying the sum over all the possible intermediate state properties of a path integral. In our case, the topological field theory (TFT) with defects gives meaning to it. This TFT has the property that when evaluated on a planar trivalent graph, it provides the number of Tait-Coloring of it. Defects can be considered as a generalization of groups. With the Klein-four group as a 1-defect condition, we reinterpret graph coloring as sections of a certain bundle, distinguishing a coloring (global-sections) from a coloring …

Effects Of Longitudinal Training Walls On Two-Dimensional Flow Structure, Sediment Transport, And Bed Aggredation Using Numerical Methods And Sediment Core Analyses In Grand River, Michigan, Sumaiya Tul Siddique

LSU Doctoral Dissertations

Longitudinal training walls (LTWs) are structures oriented parallelly with the main flow and separate the channel into two sub-channels. One channel acts as the main navigational channel and the other is considered a secondary side channel. The long-term effects of the LTWs on morphodynamics and deposition remain poorly understood. This study investigated the long-term effects of the LTWs on flow, sediment transport and long-term deposition of the Grand River using numerical approaches and sediment core analysis. The effects of LTWs on 2D flow dynamics and sediment transport were investigated by using numerical approaches. The long-term deposition under the influence of …

Modern Lakeshore Processes And Historic Lake And Glacial Changes In Taylor Valley, Antarctica, Michael Stanley Stone

LSU Doctoral Dissertations

Taylor Valley, which opens to the Ross Sea, is one of several ice-free valleys comprising the McMurdo Dry Valleys, Antarctica. The valley is home to several close-basin, perennially ice-covered lakes, whose lake levels largely reflect a balance between meltwater inputs and lake ice ablation; both being driven by climate. A dynamic environment exists where the lake ice covers meet the lakeshore, with the ice grounding to the substrate throughout the cold and dark of winter, and melting to form a perimeter of thin-to-no ice around the lake during the summer. These marginal freeze-thaw regions are known as moats. Here, physical, …

Effect Of Electronegativity On Environmentally Persistent Free Radical (Epfr) Formation, Persistence, And Toxicity On Transition Metal Oxides, Syed Monjur Ahmed

LSU Doctoral Dissertations

Environmentally persistent free radicals (EPFRs) are a group of emerging environmental pollutants. Owing to their resonance structures, EPFRs have significantly higher lifetimes than typical free radicals, and can induce the formation of reactive oxygen species (ROS) known to cause pulmonary and cardiovascular dysfunction. EPFRs form by the adsorption of organic precursors on a transition metal oxide (TMO) surface and exhibit enough stability to cause negative health and environmental effects. While aromatic and substituted aromatic precursors form EPFRs on TMO surface at elevated temperatures and numerous substituted organics are ubiquitous in various industrial processes and household products, studies have largely overlooked …

Coastal Sedimentary Records Of Extreme Events And Human Activity: Examples From Hurricanes And Microplastics, Nicholas T. Culligan

LSU Doctoral Dissertations

Coastal regions are uniquely vulnerable to a myriad of natural and anthropogenically caused stresses such as hurricane strikes and chronic microplastic pollution. Both hurricanes and microplastics have major negative effects on global coastlines and are forecast to become more damaging in the future. However, current model trends are based on limited modern data and may not provide an accurate or comprehensive view of the future. Therefore, this dissertation investigates coastal stratigraphic records to determine long-term past trends of these presses and pulses so that researchers, stakeholders, and policy makers can use them to enact strategies to mitigate damages from worsening …

A Coarse-Grained Molecular Dynamics Study Of Gas Hydrate Formation And Dissociation, Meisam Adibifard

LSU Doctoral Dissertations

The study of gas hydrates has increased significantly over the last two decades because of their potential application in energy storage, production and transportation, water desalination, refrigeration, gas separation, etc. There is a significant interest in commercially developing natural gas hydrates because the energy content of methane hydrate reservoirs (MHRs) is at least twice that of all conventional fossil fuels combined. Additionally, due to the higher storage capacity of hydrates, it is proposed to sequester CO₂ in the form of CO₂ hydrate, thereby reducing the amount of greenhouse gases. Hence, hydrates offer a dual solution to two of …

Constraining Giant Planet Occurrence Rates With The Multi-Band Imaging Survey For High-Alpha Planets (Mishaps) Observations Of 47 Tucanae, Alison Crisp

LSU Doctoral Dissertations

Though the confirmed exoplanet population has now reached over 5,500 planets, we still have a plethora of unanswered questions, e.g., regarding their formation mechanisms, true demographics, occurrence rates, and habitability. One remaining question is whether hot Jupiters formed in situ or migrated to their current orbits, so close to their host stars that their periods are 10 days or less. This question can potentially be answered by probing the effects of elemental abundances on hot Jupiter occurrence rates. These rates have been found to correlate with metallicity, but the specific elements responsible for the correlation have largely been unresolved. The …

Synthesis Of Portions Of An Acinetobacter Baumannii Lipooligosaccharide (Los), Brandon Conrad

LSU Doctoral Dissertations

Glycoconjugate vaccines have become an effective strategy for protection against an array of globally persistent diseases resulting from pathogenic bacteria such as Haemophilus influenzae type b (Hib), Neisseria meningitidis, and Salmonella enterica serotype Typhi. Comprised of a carbohydrate (referred to as glycan) covalently inked to a carrier protein, these vaccines can initiate adaptive immunity by inducing B and T cell responses once in the lymphatic system. This is particularly relevant for infants two years of age and younger whose immune systems are not fully developed. A continuously emerging threat in clinical settings, Acinetobacter baumannii is a Gram-negative bacterium …

Quantum Classical Algorithm For Solving The Hubbard Model Via Dynamical Mean-Field Theory, Anshumitra Baul

LSU Doctoral Dissertations

Modeling many-body quantum systems is widely regarded as one of the most promising applications for near-term noisy quantum computers. However, in the near term, system size limitation will remain a severe barrier for applications in materials science or strongly correlated systems. A promising avenue of research is to combine many-body physics with machine learning for the classification of distinct phases. I present a workflow that synergizes quantum computing, many-body theory, and quantum machine learning (QML) for studying strongly correlated systems. In particular, it can capture a putative quantum phase transition of the stereotypical strongly correlated system, the Hubbard model. Following …

Novel Approaches To The Activation Of Chalcogenoglycosides For O-Glycosylation, Tiffany Duong

LSU Doctoral Dissertations

Carbohydrates are integral to various biological processes such as cell signaling, function and regulation. Carbohydrates also play critical roles in various disease and metastatic pathways. This has garnered considerable attention to the field of glycoscience, however, the study of carbohydrate-containing compounds remains a challenge due to the difficulty in obtaining pure samples from natural sources. As a result, the biological evaluation of carbohydrates relies on synthetic chemistry to produce pure compounds in significant quantities. However, the synthesis of carbohydrates present their own challenges owing to the complexity in controlling stereochemistry and regiochemistry. The most significant of these challenges is controlling …

Diving Deeper Into Supercuspidal Representations, Prerna Agarwal

LSU Doctoral Dissertations

In 2013, Reeder and Yu introduced certain low positive depth supercuspidal representations of $p$-adic groups called \textit{epipelagic} representations. These representations generalize the simple supercuspidal representations of Gross and Reeder, which have the lowest possible depth. Epipelagic representations also arise in recent work on the Langlands correspondence; for example, simple supercuspidals appear in the automorphic data corresponding to the Kloosterman $l$-adic sheaf. In this thesis, we take a first step towards the construction of ``\textit{mesopelagic} representation (of Iwahori type)'' which are the higher depth analogues of simple supercuspidal representations. We see that these constructions can be done in a similar way …

Investigation Of Solvation Structures And Dynamics Of Li-Ion Battery Electrolytes And Amides In Water: An Infrared Spectroscopy, Electrochemical And Computational Study, Ernest O. Nachaki

LSU Doctoral Dissertations

The investigation of solvation structures and dynamics in lithium-ion battery electrolytes and amides in water has significant implications for both fundamental science and practical applications. Understanding the solvation dynamics of lithium electrolytes can lead to the development of safer and more efficient LIBs. The study of hydrogen bond dynamics of N-alkyl substituted amides has important implications for the development of thermos-responsive polymers used in biomedical applications. By understanding how N-alkyl substitutions affect the hydration structure and dynamics of amides, this research can inform the design of polymers with tailored properties for drug delivery, tissue engineering, and other medical applications. This …

Topics In Photonic Quantum Technology: Polarization Entanglement Dynamics In Optical Fibers And Low-Light Imaging., Pratik J. Barge

LSU Doctoral Dissertations

Recent advances in quantum photonics promise transformative impacts on computing, communication, sensing, and imaging. This thesis explores two areas in photonic quantum technology: polarization entanglement dynamics in optical fibers and low-light imaging. Optical fibers are the most suitable medium for photonic qubits and long-distance entanglement distribution is a critical requirement to realize quantum technologies. We study the decay of polarization-entanglement of the Bell state photons propagating through imperfect optical fibers with spatially fluctuating refractive index. Furthermore, to extend the distribution distance, we propose the use of dynamical decoupling in the optical fiber using half waveplates and show that significant improvement …

Riesz Particle Markov Chain Monte Carlo Methods, Xiongming Dai

LSU Doctoral Dissertations

Markov chain Monte Carlo (MCMC) methods are simulations that explore complex statistical distributions, while bypassing the cumbersome requirement of a specific analytical expression for the target. This stochastic exploration of an uncertain parameter space comes at the expense of a large number of ``burn-in'' samples, and the computational complexity leads to the curse of dimensionality. Although at the exploration level, some methods have been proposed to accelerate the convergence of the algorithm, such as tempering, Hamiltonian Monte Carlo, Rao-redwellization, and scalable methods for better performance, they cannot avoid the stochastic nature of this exploration. We develop algorithms for the energy …

Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, Zachary Jermain

LSU Doctoral Dissertations

The goal of this work is to develop an asymptotic formula for the behavior of a scattered electromagnetic field in the presence of a thin metamaterial known as a metasurface. By using a carefully chosen Green’s function and the single and double layer potentials we analyze the perturbed scattering problem in the presence of the metamaterial and a background scattering problem. By using Lippman-Schwinger type representation formulas for the two fields we develop the asymptotic formula for the perturbed field. From here we prove the asymptotic formula holds up to a specific error term based on the size of the …

Advances In Stereoselective Glycosylation: Electron-Withdrawing Groups, Benzyne-Mediated Stereoinversion, And Visible-Light Photochemistry For 1,2-Cis O-Glycosylation, Erik Giovanni Alvarez Valenzuela

LSU Doctoral Dissertations

The symbiotic relationship between humans and their microbiota is essential for health, with imbalances in the complex microbiota ecosystem linked to a variety of disorders ranging from neurodegenerative to gastrointestinal diseases. Bacteria within the human microbiota, comprising over 1000 known species, are densely and diversely coated with oligosaccharides crucial for functions like cell recognition, communication, signaling, adhesion, proliferation, and pathogenic inhibition. However, studying the structure-activity relationships of these sugars which are also secreted by bacteria is challenging due to difficulties in obtaining homogenous samples from natural sources.

Chemical synthesis offers a solution by enabling the production of well-defined oligosaccharides in …

Investigations And Characterization Of Loud Transient Noise In Advanced Ligo Detectors, Shania Nichols

LSU Doctoral Dissertations

In the era of gravitational wave (GW) astronomy, the detection of cosmic events such as black hole and neutron star mergers has become routine due to the Advanced LIGO (aLIGO) detectors. However, the sensitivity of these detectors also makes them susceptible to loud transient noise, which can obscure GW signals. This thesis investigates loud transient noise with a Signal-to-Noise Ratio (SNR) greater than 100, focusing particularly on the most extreme transients with SNR exceeding 1000.

We begin by analyzing the impact of loud transient noise on the binary neutron star (BNS) range of aLIGO detectors across observation runs O2, O3, …

Higher Order Operator Splitting Schemes With Complex Coefficients And Applications, Arun Banjara

LSU Doctoral Dissertations

The goal of this dissertation is to apply the concept of Lie generators for linear semigroups induced by nonlinear flows, originally developed by J. R. Dorroh and J. W. Neuberger in the 1990’s [15], to approximate solutions of initial value problems like

x′(t) = F(x(t)), x(0) = x₀, (1)

where F = (F₁,··· ,F_N), and F_i : R^N ⊃ Ω -> R^N. The method, sometimes referred to as ``Bernard Koopman’s Global Linearization Method,” traces its origins back to the works of Sophus Lie in the 1890’s [30], Gerhard Kowalewski in …

Design Of Long-Distance Entanglement Distribution Protocols For Quantum Networks, Stav Haldar

LSU Doctoral Dissertations

Future quantum technologies such as quantum communication, quantum sensing, and distributed quantum computation, will rely on networks of shared entanglement between spatially separated nodes. Distributing entanglement between these nodes, especially over long distances, currently remains a challenge, due to limitations resulting from the fragility of quantum systems, such as photon losses, non-ideal measurements, and quantum memories with short coherence times. In the absence of full-scale fault-tolerant quantum error correction, which can in principle overcome these limitations, we should understand the extent to which we can circumvent these limitations. In this work, we provide improved protocols and policies for entanglement distribution …

Evaluating Past Progress And Assessing Prediction Breeding Strategies For Sustained Genetic Gains In The Louisiana Sugarcane Variety Development Program, Brayden A. Blanchard

LSU Doctoral Dissertations

The aim of this dissertation is to outline important considerations for the Louisiana Sugarcane Variety Development Program (LSVDP) as it pertains to historical progress, impact, goal setting, and new strategies for continued genetic gains. Industry progress was evaluated with robust regression models to quantify rates of productivity gains. Over the last 50 years, statistically significant productivity gains were identified in sucrose content (45%), cane yield (32.2%), and sugar yield (93%) while pairwise comparisons of decades showed that progress was incremental rather than rapid and sustained once achieved. The decade from 1990-1999 was identified as the only decade with a significant …

Molecular-Level Studies Of Nanopatterned Biomolecules With Atomic Force Microscopy, Ashley R. Walker

LSU Doctoral Dissertations

Atomic force microscopy (AFM) is an analytical technique in which a tipped probe is gently scanned across the surface in a raster pattern to generate digital images of a sample at the nanoscale. The AFM instrument has three general operational modes, which are contact, non-contact and tapping-mode, that can be used to examine materials at the atomic level. Single-molecular details of biological molecules and other soft organic materials can be captured with minimal denaturation in either ambient or liquid environments when using tapping-mode AFM. In tapping-mode, the probe is driven to oscillate vertically while the tip is scanned across the …