Physical Sciences and Mathematics Commons^™

Patterns And Processes Behind Secretive Marshbird Movement, Abundance, And Distribution Across Southeastern Louisiana, Leah Moran

LSU Doctoral Dissertations

Restoration and conservation of coastal Louisiana hinges on understanding the patterns and processes underlying habitat heterogeneity on the landscape and therefore the species that inhabits this region, including secretive marshbirds. Elusive in nature, this guild of birds has evolved under dynamic hydroperiods, and myriad plant communities present within wetlands. Only recently, however, has research focused on the role of hydrologic dynamics and vegetative structure and distribution on abundance, movement and detection of marshbirds, specifically within southeastern Louisiana. This study aimed to quantify the ecological patterns and processes, particularly hydrologic processes and landscape structure, driving breeding secretive marshbird movement, abundance and …

Quasistatic Peridynamics, Existence Of Unique Solution In The Presence Of Damage, Nuwanthi N. Samarawickrama

LSU Doctoral Dissertations

A mathematical model for damage propagation based on nonlocal potentials is developed within the framework of peridynamics. This model is applied to simulate damage evolution in cyclically loaded structures. By neglecting inertial effects, a well-posed quasistatic formulation for cyclic loading is obtained.\\ The resulting equation is expressed as a nonlocal and nonlinear integral operator that couples damage evolution to the deformation field.\\ This coupling occurs through the product of a damage factor and the derivative of a force potential. The damage factor ranges between zero and one, where one represents undamaged material and zero indicates complete damage.\\ It serves to …

Digital Forensics And Ai: Artifact Analysis And Using Ai In The Forensics Domain, Clinton Joel Walker

LSU Doctoral Dissertations

Digital Forensics (DF) is a field of forensic science focusing on the acquisition, authentication, and analysis of digital evidence while maintaining integrity of that data. DF analysts use forensic tools to parse large volumes of data for investigations and depend on them for identification of pertinent digital evidence in vast amounts of data. Keeping up with innovations and ever-expanding data volumes is a constant challenge for these investigators. The prevalence of Artificial Intelligence (AI) in everyday computing is rapidly expanding, with the use of Machine Learning (ML) and Large Language Models (LLM)s becoming increasingly commonplace. Innovations in technology bring new …

Towards Leveraging Social Media Data For Fostering Collaborations Among Non-Profits, Monazil Chowdhury

LSU Doctoral Dissertations

Nonprofit organizations serve a crucial role in tackling a wide range of significant social, environmental, and economic issues. But it is often hard to get a clear picture of their work because their information is spread out and it is difficult to see how they are collaborating. To address this issue we developed a web-based tool to collect scattered data—from a variety of sources, such as the IRS, social media, and the Census, into one easy-to-use resource. The tool begins by taking IRS records and geocoding each nonprofit’s physical address With its coordinates. It then retrieves census tract information from …

Quantitative Boundary Doubling Estimates For Elliptic Equations, Jack Dalberg

LSU Doctoral Dissertations

We present an approach for obtaining quantitative boundary doubling inequalities for elliptic equations with Neumann boundary conditions. Carleman estimates are used to prove three-ball inequalities, which are then used to prove quantitative doubling inequalities, with bootstrapping from the interior to the boundary. This approach is illustrated by its application to the Laplace eigenvalue problem with homogeneous Neumann boundary conditions, where sharp doubling inequalities are recovered.

When then consider a equation with non homogeneous Neumann boundary conditions. By following the approach, we are able to obtain potentially sharp results. Finally, we are able to get an improvement on previously obtained results …

Gain Threshold Optimization Using Fano Resonance, Alina Oktiabrskaia

LSU Doctoral Dissertations

The study of resonances in electromagnetics plays a critical role in the design of optical systems. This dissertation investigates the interaction between resonance and gain in optical structures to establish a universal principle for achieving ultra-low-threshold lasing. Through the analysis of geometric symmetries, material properties, and coupling mechanisms, this research develops prototype structures applicable to a wide range of optical and electromagnetic systems. A range of models is considered, starting from a simple onedimensional string-resonator system (based on the model of H. Lamb), then advancing to two- and three-dimensional waveguide models, and culminating with a realistic high-contrast model in open …

The Search For Magnetar Giant Flares In Archival Gamma-Ray Burst Data To Constrain Their Rates And Energetics, Aaron Trigg

LSU Doctoral Dissertations

Magnetar giant flares are rare, extremely bright bursts of gamma-rays from highly magnetized neutron stars. These events are difficult to identify because, at extragalactic distances, they can appear similar to other astrophysical phenomena. Only a handful have been confidently identified to date, limiting our understanding of their origin and physical properties. This dissertation focuses on expanding the sample of known events and enabling a more detailed characterization of their observational features. We report on two newly identified examples, GRB 180128A and GRB 231115A, that are consistent with a magnetar origin based on their spectral properties and association with nearby star-forming …

Investigation Of Subcellular Damage And Long-Term Non-Cancerous Cardiovascular Effects Following Whole-Body Photon Irradiation, Nousha Afshari

LSU Doctoral Dissertations

Current radiobiological models focus primarily on nuclear DNA damage and fail to fully explain radiation-induced noncancerous health effects. This dissertation investigates whether non-nuclear subcellular structures contribute to radiation-induced biological damage through experimental biomarker analysis and computational microdosimetry. The central hypothesis posits that whole-body photon irradiation results in subcellular non-nuclear damage, specifically increased circulating mitochondrial DNA concentrations, that correlates with radiation dose and long-term noncancerous effects such as cardiovascular disease.

Specific Aim 1 measured mitochondrial and nuclear DNA concentrations in banked blood samples from 72 Chinese rhesus macaques that previously received whole-body photon irradiation ($0-10$ Gy) from Cobalt-60 or LINAC sources. …

A Theory Of Fundamental Strata For Twisted Formal Connections, Sorawit Viwanthananut

LSU Doctoral Dissertations

Let $G$ be a complex reductive group. A fundamental stratum for $G$ is a triple $(x,r,\beta)$ where $x$ is a point in the Bruhat-Tits building of $G$, $r$ is a nonnegative real number called depth of the stratum, and $\beta$ is a semistable functional on the Moy-Prasad filtration of $\fg$ associated to $x$ at level $r$. Fundamental strata were first introduced to classify admissible representations of a $p$-adic reductive group. More recently, Bremer and Sage have shown that fundamental strata play an important role in the geometric Langlands program and developed a theory of fundamental strata for $G$-connections. In this …

Strichartz Estimates For Many Particle Dispersive Equations, Tristan Reynoso

LSU Doctoral Dissertations

Dispersive equations are useful for describing a wide variety of phenomena in which solutions disperse through the space as time progresses. These equations show up frequently in physics, especially when studying quantum mechanical and fluid related systems. The single particle variants of equations such as the Schr\"{o}dinger and Wave equations have been studied at great length throughout modern history. Over the last couple decades progress has been made toward extending single particle dispersive equations to cover their many body counterparts. Space-time Strichartz estimates for the homogenous $N$-particle Schr\"{o}dinger equation with small interacting potentials was recently established on both $\mathbb{R}^d$ and …

Investigating The Role Of Aerosols In Extreme Precipitation Events Along The Gulf Coast Of The U.S.A., Wenjia Cao

LSU Doctoral Dissertations

Atmospheric aerosols have been found to influence tropical cyclone (TC) and flood event development. In this study, the Weather Research and Forecasting model is applied to investigate specific microphysical impacts and aerosol sensitivity to heavy precipitation and TC events in the U.S. Gulf Coastal area. The Thompson aerosol-aware scheme with regular and adjusted aerosol concentration scenarios is used to quantify precipitation, wind field, horizontal/vertical structures, and track variations, by aerosol mixing ratio. In general, results for the three storms analyzed (the 2016 Baton Rouge, Louisiana, flood event (Chapter 2); Hurricane Harvey in 2017 (Chapter 3); and an idealized storm event …

Memory-Augmented Llm Agent For Predicting Locomotion Modes In Construction Activities, Ehsan Ahmadi

LSU Doctoral Dissertations

The construction industry faces significant challenges, including labor shortages, high physical demands, and safety risks, necessitating advanced assistive technologies like exoskeletons to enhance worker efficiency and reduce injuries. However, effective exoskeleton control in dynamic construction environments requires accurate locomotion prediction, a task complicated by the diversity of activities and reliance on supervised learning methods that struggle to generalize. This study investigates a multimodal approach to locomotion prediction, leveraging speech commands and visual data from smart glasses to enable adaptive and safe human-exoskeleton interaction. The research unfolds in two stages: the first develops a framework to evaluate the zero-shot capability and …

Multiparticle Quantum Plasmonics: Fundamentals And Applications, Mingyuan Hong

LSU Doctoral Dissertations

Quantum plasmonics explores the interaction between light and collective charge oscillations at metal-dielectric interfaces, enabling strong light confinement and enhanced quantum effects at the nanoscale. While traditional quantum optics has primarily focused on single-photon systems, an intermediate regime exists between classical and single-photon optics - multiparticle (or multiphoton) quantum optics. In this regime, classical light sources, when analyzed through techniques such as photon-number-resolving (PNR) detection and projective measurement, can reveal nontrivial quantum correlations. This thesis investigates how multiparticle quantum plasmonics harnesses these correlations to control quantum statistical properties, enhance coherence, and enable novel applications in quantum technologies.

In this thesis, …

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 …

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 …

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 …

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) …

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 …

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 …

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 …

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 …

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; …

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 …

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 …