Digital Commons Network^™

Decadal To Millennial-Scale Morphodynamic Evolution Of Microtidal Marshes, Samuel Mason Zapp

LSU Doctoral Dissertations

Tidal marshes are susceptible to rapidly converting to open water due to their low elevations within the tidal frame. A continuous supply of externally supplied mineral sediment and in situ organic material production is necessary to offset elevation losses from relative sea level rise and erosion. Complex feedbacks between hydrodynamics, the erosion, transport, and deposition of sediment, and physical modification of the landscape by the establishment of intertidal vegetation govern the spatial and temporal patterns of elevation response. This dissertation focuses on modeling how these dynamics drive marsh landscape evolution in the past, present, and into the future under changing …

Disentanglement In Representation Learning: Interpretability In Dimension Reduction With Vae, Minh Hong Vu

LSU Doctoral Dissertations

This research explores both theoretical and practical aspects of disentangled representation learning by extending the VAE framework. We address the core challenge of extracting independent generative factors from observed data while preserving high reconstruction fidelity. To this end, we propose two novel VAE variants: (i) the $\lambda\beta$-VAE, which incorporates an additional $\ell^2$-norm reconstruction loss to improve accuracy, and (ii) the $\gamma\beta$-VAE, which introduces a mutual information regularization term to encourage independence across latent dimensions.

Our theoretical analysis is conducted in a linear Gaussian setting, where we derive optimal solutions for these VAE-based models. We further examine how varying levels of …

Modeling And Simulation Of Methane And Co2 Hydrates In Porous Media, Chico Sambo

LSU Doctoral Dissertations

This dissertation presents a comprehensive study on modeling and simulation for
methane hydrate production and CO2 sequestration. The research focuses on pore-
scale and reservoir-scale modeling techniques to understand the dynamics of gas
hydrate dissociation, the associated risks of subsidence, and the potential for CO2
storage in deep-sea environments.
This dissertation begins with an investigation into pore-scale modeling. Specif-
ically, a detailed pore network model was developed to simulate the processes of
methane hydrate dissociation and formation. However, the numerical simulations
revealed that assuming an isothermal process for hydrate formation and dissociation
is not physically realistic. Consequently, the results obtained …

“When Black Women Whisper”: An Exploration Of Why Black Women Stay In K-12 Education, Chelsea Lynne Murry

LSU Doctoral Dissertations

Abstract

From low retention rates to race and gender biases to being overworked and undervalued in the classroom, Black women leave education at higher rates than any other demographic. This study highlighted the experiences of Black women in K-12 education settings, the role of support systems in their retention and advancement, and why they stay in K-12 education. The study used Counter-storytelling in Critical Race Theory, Black Feminist Thought, and Womanism to examine the race and gender inequities that Black women face and to highlight their lived experiences. Through the use of Sista Circles/focus groups and one-on-one interviews, the research …

Unfitted Finite Element Methods For Shape Optimization And Liquid Crystals, Jeremy T. Shahan

LSU Doctoral Dissertations

We present an approach to shape optimization problems that uses an unfitted finite element method (FEM). The domain geometry is represented, and optimized, using a (dis- crete) level set function and we consider objective functionals that are defined over bulk domains. For a discrete objective functional, defined in the unfitted FEM framework, we show that the exact discrete shape derivative essentially matches the shape derivative at the continuous level. In other words, our approach has the benefits of both optimize-then- discretize and discretize-then-optimize approaches.

Specifically, we establish the shape Fréchet differentiability of discrete (unfitted) bulk shape functionals using both the …

Innovative Design Methodology For Durable Open-Graded Friction Course Asphalt Mixtures, Anas Abualia

LSU Doctoral Dissertations

Open-graded friction course (OGFC) is a thin asphalt mixture surface layer with a high percentage of coarse aggregates and high interconnected air voids, which provides improved skid resistance, visibility, and decreased pavement-tire noise. However, construction personnel at DOTD reported that conventional OGFC mixtures have short service life (raveling distress). Further, their structural contribution to the pavement structure is commonly neglected and designed only for functionality purposes.

The objective of this study was to develop a rational mix design methodology to improve the durability of OGFC asphalt mixtures. Specific objectives are to: (1) conduct a rheological and chemical characterization of polymer-, …

Chain Theorems For Different Classes Of 3-Connected Graphs, Avin Sunuwar

LSU Doctoral Dissertations

This dissertation explores the structural properties of graphs by extending the classical result of Tutte's Wheel Theorem. In particular, we develop an improved version of Tutte's Wheel Theorem along with new chain theorems for subclasses of 3-connected graphs. These chain theorems provide a systematic approach to characterizing graphs that exclude certain minors, leading to significantly shorter proofs of established results.

In Chapter 5, we present a generalization of the block-tree theorem for connected graphs, which removes the restriction on cut vertices and allows greater flexibility in separator sizes. By integrating the results from Chapters 3, 4, and 5, we …

Optimizing Fisher Information In Quantum Technology, Bran Purvis

LSU Doctoral Dissertations

Fisher information is a statistical metric whose inverse represents a lower bound on the variance of an unbiased estimator. Naturally, in order to make the best estimates of a given unknown parameter, one would desire to find ways to minimize the value of this lower bound. Thus, the Fisher information can also be used to compare the quality of different estimators for a given parameter: whichever estimator has a lower value for its Fisher information must also provide better estimates. The same holds true in the framework of quantum information theory, where an analog to the Fisher information, dubbed quantum …

19ne Excited States In Explosive Nucleosynthesis, Khang Pham

LSU Doctoral Dissertations

Classical novae and Type I X-ray bursts are stellar explosions that occur in binary systems, where nuclear reactions involving ¹⁹Ne play a crucial role in nucleosynthesis. In novae, the destruction of ¹⁸F via the ¹⁸F(p,alpha)¹⁵O reaction significantly affects the amount of ¹⁸F remaining in the ejecta, directly influencing the detectability of predicted 511-keV gamma rays. However, discrepancies between observed and predicted ¹⁸F abundances highlight uncertainties in the reaction rates, primarily due to unknown properties of resonances in the compound nucleus ¹⁹Ne. In Type I X-ray bursts, the ¹⁵O(alpha,gamma)¹⁹Ne reaction …

How Financial Aid Affects The Odds Of Study Abroad Participation For Students Of Color, Patrick Newcomb

LSU Doctoral Dissertations

Prior research has shown that studying abroad provides students with enriching, diverse educational experiences with positive personal, academic, and professional outcomes. Despite the benefits, only a small portion of American higher education students participate in study abroad programs. Students of color disproportionately study abroad at lower rates than White students. Since cost is often cited as the primary barrier preventing education abroad, this study examined the types of financial aid associated with study abroad access and participation.

This study used data from the National Postsecondary Student Aid Study, which is a nationwide dataset designed to represent the makeup of institutions …

Approximations Of Koopman Operator Semigroups, Ibrahem Al Jabea

LSU Doctoral Dissertations

The main purpose of this dissertation is to study approximation methods for nonlinear systems using Bernhard Koopman's Global Linearization Method or Sophus Lie's method of continuous transformation groups. This approach enables the application of linear semigroup methods to a nonlinear system by focusing on the dynamics of the observables of the states, rather than directly studying the dynamics of the states. In this dissertation, we studied the pointwise semigroup and introduce the modified space $C_m(\Omega)$ and the modified Koopman-Lie semigroups. We use a splitting operator and outline a systematic approach for approximating the pointwise Koopman-Lie semigroup flows \begin{equation*} t\to T(t)g(x) …

Unavoidable Immersions And Topological Minors Of K-Edge-Connected Graphs, Brittian Qualls

LSU Doctoral Dissertations

In this work, we present results concerning the unavoidable structures in large and infinite k-edge-connected graphs. These results are inspired by the classical result of Ramsey, who proved that for every positive integer r, every sufficiently large graph contains as an induced subgraph either K_r or $\overline{K_r}$. We consider different graph containment relations, focusing primarily on the immersion relation. In the case of finite graphs, we provide the unavoidable immersions of 4-edge-connected graphs and prove that linear edge-connectivity suffices to immerse the graph C_t,r.

This dissertation also considers infinite graphs. We present the …

Optical Spring Tracking For Enhancing Quantum-Limited Interferometers, Scott M. Aronson

LSU Doctoral Dissertations

Gravitational waves were first predicted by Albert Einstein in 1916. Calculations in the 1970s by Rainer Weiss showed an interferometer of sufficient size could realistically detect gravitational waves, which led to a grant by the National Science Foundation (NSF). With steady progress and over decades of funding by the NSF, the construction of two full scale 4km interferometers was approved and began construction in 1994. This project, coined LIGO the Laser Interferometer Gravitational-wave Observatory, came to be a worldwide collaboration of scientists dedicated to the discovery and study of gravitational waves. In 2015, both LIGO detectors detected a coincident inspiral …

Understanding The Experiences Of Biology Teachers During The Covid-19 Pandemic, Amber R. Collins

LSU Doctoral Dissertations

ABSTRACT

The 2020 COVID-19 Pandemic has caused the world to focus on the transition of learning environments that are more digital and virtual than any other time in educational history. Schools all over the world were required to adjust not only the mode of instruction, such as in virtual, hybrid, or in-person, but also create guidelines and procedures that reduce the amount of interaction between the teacher and the student (Garbe, Ogurlu, Uzeyir, & Cook, 2020). The research questions that guided this study were: 1) What are the experiences of five Biology teachers during the COVID-19 pandemic in transitioning to …

Assessing Groundwater Availability And Land Subsidence Risk Associated With Anthropogenic Activities In A Complex Aquifer System, Aya Bakr Attya Mohamed

LSU Doctoral Dissertations

The Southern Hills aquifer system (SHAS) is the primary source of water in the Capital area of Louisiana. However, the overexploitation of freshwater-bearing aquifers and the presence of two active faults, the BR fault and the DSS fault, have resulted in groundwater depletion, saltwater intrusion, and increased the risk of land surface subsidence. Such critical issues pose substantial threats to groundwater availability and exert detrimental effects on the environment and urban infrastructures. This dissertation presents a comprehensive investigation of the SHAS for recognizing the consequences of groundwater depletion and its potential long-term impacts on groundwater availability and land stability. A …

On Unavoidable Infinite Hypergraphs, Samuel Weiner

LSU Doctoral Dissertations

Ramsey's Theorem states that every infinite graph contains either K_∞ or $\overline{K_∞}$ as an induced subgraph. For this reason, K_∞ and $\overline{K_∞}$ are often referred to as the unavoidable infinite graphs. Many similar results have characterized the unavoidable members for various classes of infinite graphs; perhaps the most notable of these is König's Infinity Lemma, which states that every infinite, connected, locally finite graph contains a ray as an induced subgraph. From these findings, one can easily deduce that every infinite, connected graph contains an infinite clique, star, or ray as an induced subgraph; …

Quaternary Subsurface Characterization Of The Mississippi River Valley Alluvial Aquifer: Insights From Interval Kriging And Airborne Em-Borehole Data Integration, Yuqi Song

LSU Doctoral Dissertations

The Pleistocene period significantly contributed to the formation of alluvial aquifer worldwide. These productive aquifers are crucial for domestic, industrial, and agricultural water supplies. The Mississippi River Valley alluvial aquifer (MRVA), a principal aquifer in the U.S., is crucial for national food security and global agricultural supply. This study aims to characterize the subsurface architecture of the MRVA, thereby enhancing fundamental understanding of sedimentological processes involved in the genesis of glacio-fluvial aquifers worldwide. The research objectives are threefold: (1) to provide a detailed characterization of the MRVA; (2) to develop 3D geostatistical methods for geological modeling; and (3) to develop …

On Regularity And Convergence Of Solutions To The Boltzmann-Enskog Equations, Christian Ennis

LSU Doctoral Dissertations

The Boltzmann equation describes the time evolution of the density function in position-velocity space for a classical particle subjected to possible collisions by other particles in a diluted gas that expands in vacuum for a given initial distribution. While many authors have studied the probabilistic interpretation of the spatially homogeneous Boltzmann equation, there is a dearth of articles on the stochastic framework of the full (that is, spatially inhomogeneous) Boltzmann equation. In this thesis, we examine a stochastic process, developed by S. Albevario, B. Ruediger, and P. Sundar, whose law is a weak solution to a mollified Boltzmann equation. This …

Explicit Modularity And Moments For Certain Hypergeometric Character Sums, Brian Grove

LSU Doctoral Dissertations

A great deal of progress in number theory throughout history has been motivated by trying to solve equations. One of the most famous challenges is to show there are no positive integer solutions to $x^{n}+y^{n} = z^{n}$ for $n > 2$, posed by Fermat around 1637. Special cases, such as the $n = 3$ and $n = 4$ cases, can be established using various algebraic manipulations. However, a general solution was elusive until the late 1990s when the combined work of Wiles \cite{Wiles} and Taylor--Wiles \cite{TaylorWiles} give a full proof.

One of the key insights used in proving Fermat's conjecture involves …

The Boltzmann-Enskog Equation With Brownian Forcing, Aurora Wallace

LSU Doctoral Dissertations

Interacting particle systems (IPS) are used to rigorously derive partial differential equations modeling macroscopic behavior given by systems of stochastic differential equa- tions in physics, biology, and other sciences. These systems model the time evolution of n interacting particles with desired dynamics. In the n-system studied here, only two parti- cles may interact at a time (binary collisions). The particles are exchangeable; that is, the ordering of the particles does not play a role, and the interaction between the ith particle and the jth particle models an elastic collision. In this thesis, we use the method of inter- acting particle …

The Metaphysics Of Frank Herbert's Dune And God Emperor Of Dune: On Time And Language, Garrett J. Busshart

LSU Doctoral Dissertations

This dissertation studies the metaphysics of time and rhetoric in the science fiction novels Dune (1963) and God Emperor of Dune (1981) by Frank Herbert. The first chapter critiques the protagonist’s sense of temporality, an ideology in which the future consists of multiple possible choices while each decision of one forecloses a still larger set. Jean-Pierre Dupuy calls this a “supermarket” model of temporality, as if the future were a contingent-free menu of possibilities a subject is free to pick between. My assertion is that this sense of temporality—the Western norm—matches the protagonist’s, Paul Atreides’s, rhetoric. In disclosing Paul’s sense …

Induced-Minor-Closed Classes Of Matroids, James Dylan Douthitt

LSU Doctoral Dissertations

A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple GF(q)-representable matroids that can be built from projective geometries over GF(q) by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors and characterize the class by its forbidden induced minors, noting that the case when q=2 is distinctive. Additionally, we show that the class of GF(2)-chordal matroids coincides …

Infrared Laser Ablation Of Biomolecules From Formalin-Fixed Tissue, Blessing Chisom Egbejiogu

LSU Doctoral Dissertations

In the research described in this dissertation, a high-precision infrared laser ablation microsampling method was utilized for spatially resolved proteomic and lipidomic analyses of formalin fixed paraffin embedded (FFPE) tissue, a widely used archival sample in biomedical research. Despite its extensive use, FFPE tissue presents challenges for proteomic analysis due to protein cross-linking and modifications introduced during fixation, which can hinder extraction and identification. Developing a streamlined high-resolution method to recover biomolecules from FFPE samples is critical for advancing biomarker discovery, retrospective studies, and multi-omics research. To address these challenges, this study employs an infrared (IR) laser ablation microdissection system …

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 …

Johann Georg Hamann And The Liberal Project, Jesse D. Ansley

LSU Doctoral Dissertations

This dissertation examines the political thought of Johann Georg Hamann, his relationship to liberalism, and the importance to modern concerns for consensus formation and intercultural dialogue. This contributes to the line of literature sparked by Isaiah Berlin debating the political legacy of Hamann and its relation to the development of modern politics. Berlin labels Hamann an anti-rationalist whose current developed into the ideology of the Nazi party. My work supports the countervailing arguments that Hamann’s work is importantly different from the Romantics he inspired and even more so from the Nazis. By examining two complete works and a number of …