Physical Sciences and Mathematics Commons^™

All-Optical Probes Of Particle-Like Charge Migration Dynamics, Kyle A. Hamer

LSU Doctoral Dissertations

Particle-like charge migration (CM) is the coherent, back-and-forth motion of a positively-charged electron hole along the backbone of a molecule following a sudden ionization. CM in small molecules generally occurs on an Angstrom (10^-10 m) spatial scale and an attosecond (10^-18 s) timescale. I use time-dependent density-functional theory (TDDFT) to simulate CM modes in organic molecules, and to explore all-optical probes of this attosecond electron dynamics using high-harmonic spectroscopy (HHS). By leveraging my results from previous studies of two-center interferences in carbon dichalcogens, in which I separated the harmonic signal into contributions from individual Kohn-Sham orbitals, I first …

Modeling And Numerical Analysis Of The Cholesteric Landau-De Gennes Model, Andrew L. Hicks

LSU Doctoral Dissertations

This thesis gives an analysis of modeling and numerical issues in the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We derive various time-step restrictions for a (weighted) $L^2$ gradient flow scheme to be energy decreasing. Furthermore, we prove a mesh size restriction, for finite element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers that is not well-known in the LC literature, particularly when simulating cholesteric LCs that exhibit ``twist''. Furthermore, we perform a computational exploration of the model and present several numerical simulations in 3-D, on both slab geometries and spherical …

Investigating Gulf Coast Aquifer System: Stratigraphy Reconstruction, Inverse Modeling, And Groundwater Stress Assessment, Shuo Yang

LSU Doctoral Dissertations

The Mississippi Embayment aquifer system (MEAS) and the Coastal Lowlands aquifer system (CLAS) provide substantial groundwater resources for human activities in the U.S. Gulf Coastal Plain. However, the overexploitation has led to groundwater depletion in the MEAS and the CLAS, threatening sustainable groundwater use. Such concern highlights the crucial need for an advanced understanding of stratigraphy and groundwater in these aquifer systems, which is essential for effective regional groundwater management. This dissertation presents a comprehensive investigation of MEAS and CLAS in the Louisiana and southwestern Mississippi region, encompassing three fundamental dimensions: stratigraphy reconstruction, groundwater modeling, and groundwater stress assessments. A …

Performative Mixing For Immersive Audio, Brian A. Elizondo

LSU Doctoral Dissertations

Immersive multichannel audio can be produced with specialized setups of loudspeakers, often surrounding the audience. These setups can feature as few as four loudspeakers or more than 300. Performative mixing in these environments requires a bespoke solution offering intuitive gestural control. Beyond the usual faders for gain control, advancements in multichannel sound demand interfaces capable of quickly positioning sounds between channels. The Quad Cartesian Positioner is such a solution in the form of a Eurorack module for surround mixing for use in live or studio performances.

Diffusion/mixing methods for live multichannel immersive music often rely on the repurposing of hardware …

Influences On Participation In The National Flood Insurance Program’S Community Rating System In Coastal Counties In Louisiana, Mississippi, Alabama, And Florida, Jennifer E. Argote

LSU Doctoral Dissertations

The National Flood Insurance Program provides an incentive-based program, the Community Rating System (“CRS”), to encourage communities to improve their hazard mitigation protocols to better protect against and prevent flood-related hazards. This dissertation analyzes factors that influence participation and points scored within the CRS to gain an understanding of the conditions under which communities are willing and able to take advantage of an incentive-based flood hazard mitigation program. It also includes an analysis of survey responses from 41 coastal county floodplain and CRS managers to gauge their opinions on the CRS and how it can be improved to better serve …

Connecting The Optical Regime To The X-Ray In Neutron Star Low Mass X-Ray Binaries, Alexander B. Igl

LSU Doctoral Dissertations

Using Rossi X-Ray Timing Explorer and Otto Struve Telescope data of low mass X-ray binaries (LMXBs) Cyg X-2 and Sco X-1, the optical regime’s relationship to the X-ray was investigated through several angles. Discrete cross correlations using the optical and X-ray data revealed evidence of reprocessing in both datasets. These were more consistently present in Sco X-1, where both small and obvious features were seen at less than 4 s of optical lag. The size of these lags makes it likely that most of the reprocessing is taking place on the accretion disk. Parameterization of the Z tracks led to …

Entanglement In The Hawking Effect: From Astrophysical To Optical Black Holes, Dimitrios Kranas

LSU Doctoral Dissertations

The Hawking effect is an exciting physical prediction lying at the intersection of the two most successful theories of the past century, namely, Einstein’s theory of relativity and quantum mechanics. In this dissertation, we put special emphasis on the quantum aspects of the Hawking process encoded in the entanglement shared by the emitted fluxes of created quanta. In particular, we employ sharp tools from quantum information theory to quantify the entanglement produced by the Hawking effect throughout the black hole evaporation process. Our framework allows us to extend previous calculations of entanglement to a larger set of cases, for instance, …

Some New Techniques And Their Applications In The Theory Of Distributions, Kevin Kellinsky-Gonzalez

LSU Doctoral Dissertations

This dissertation is a compilation of three articles in the theory of distributions. Each essay focuses on a different technique or concept related to distributions.

The focus of the first essay is the concept of distributional point values. Distribu- tions are sometimes called generalized functions, as they share many similarities with ordi- nary functions, with some key differences. Distributional point values, among other things, demonstrate that distributions are even more akin to ordinary functions than one might think.

The second essay concentrates on two major topics in analysis, namely asymptotic expansions and the concept of moments. There are many variations …

Adaptive Quantum Information Processing In Non-Equilibrium Environments, Arshag Danageozian

LSU Doctoral Dissertations

Solid state and condensed matter systems, such as diamond impurities, superconductors, quantum dots, and ion traps, constitute important physical platforms for various applications in quantum information processing (QIP). However, it has consistently been shown that all such modern platforms suffer from non-equilibrium behavior on timescales that are relevant for many important QIP tasks. The causes range from intrinsic non-equilibrium dynamics (e.g. in diamond) to the presence of various impurities with their own internal dynamics (e.g. in superconductors and quantum dots) or variations in the control fields used to stabilize the quantum matter (e.g. in ion traps). When reserving degrees of …

Simulations Of Intruder-Free X-Ray Transient Absorption And Time-Resolved X-Ray Scattering For Probing Attosecond Electron Dynamics, Mengqi Yang

LSU Doctoral Dissertations

The motion of electrons plays a fundamental role in both physics and chemistry, and capturing such dynamics requires the ability to resolve changes at the attosecond timescale, which is enabled by the advent of ultrashort laser pulses. This dissertation aims to facilitate the interpretation of ultrafast electron dynamics and attosecond spectroscopy by real-time time-dependent density functional theory (RT-TDDFT) simulations. The first part of this dissertation focuses on improving the simulation of X-ray transient absorption spectra (XTAS) with Gaussian basis sets in RT-TDDFT by applying a filter to the transition dipole matrix. Due to the spatial limitation of atom-centered Gaussian functions, …

Sedimentary Processes And Instability On The Mississippi River Delta Front Near The Wreck Of The Ss Virginia, Nathan Figueredo

LSU Doctoral Dissertations

Multi-cores and piston cores were collected seaward of the Mississippi River Delta’s Southwest Pass at ~80 m water depth in 2017 to better understand sedimentary characteristics and processes on the Mississippi River Delta Front (MRDF) in the vicinity of the SS Virginia shipwreck, and to support marine archeological research. Core analyses were performed to inform our understanding of the dynamics of sediment motion in the study area through radionuclide activity (²¹⁰Pb and ¹³⁷Cs), volume frequency of grain size, bulk density, and fabric (X-Radiography). Sediment accumulation rates (SAR), calculated from multi-core ²¹⁰Pb activity are 0.22 - 0.29 …

A Menagerie Of Symmetry Testing Quantum Algorithms, Margarite Lynn Laborde

LSU Doctoral Dissertations

In Chapter 1, we establish the mathematical background used throughout this thesis. We review concepts from group and representation theory. We further establish fundamental concepts from quantum information. This will allow us to then define the different notions of symmetry necessary in the following chapters. In Chapter 2, we investigate Hamiltonian symmetries. We propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group. Furthermore, we show that this algorithm is that this algorithm is DQC1-Complete. Finally, we execute one of our symmetry-testing algorithms on existing quantum computers for simple examples. In Chapter 3, we …

Nanosecond Infrared Laser Ablation Dynamics, Achala Priyadarshani Deenamulla Kankanamalage

LSU Doctoral Dissertations

Laser ablation dynamics encompasses studies of fundamental physical processes of mid infrared laser ablation. Understanding the mechanisms of IR laser desorption and ionization can lead to improvements in laser ablation-based techniques and expansion of their applications. Control of material removal ensures both accuracy and precision of the laser ablation-based techniques. The laser ablation mechanism in the studied wavelength region, is a process of water vaporization and photothermal disruption of tissue. Glycerol was used as the ablation target to establish the methods. Experiments were first aimed at developing methods to monitor material removal during ablation using a 2.94 µm wavelength mid-IR …

Domain Specific Analysis Of Privacy Practices And Concerns In The Mobile Application Market, Fahimeh Ebrahimi Meymand

LSU Doctoral Dissertations

Mobile applications (apps) constantly demand access to sensitive user information in exchange for more personalized services. These-mostly unjustified-data collection tactics have raised major privacy concerns among mobile app users. Existing research on mobile app privacy aims to identify these concerns, expose apps with malicious data collection practices, assess the quality of apps' privacy policies, and propose automated solutions for privacy leak detection and prevention. However, existing solutions are generic, frequently missing the contextual characteristics of different application domains. To address these limitations, in this dissertation, we study privacy in the app store at a domain level. Our objective is to …

First-Order Algorithms For Nonlinear Structured Optimization, Miao Zhang

LSU Doctoral Dissertations

Nonlinear optimization is a critical branch in applied mathematics and has attracted wide attention due to its popularity in practical applications. In this work, we present two methods which use first-order information to solve two typical classes of nonlinear structured optimization problems.

For a class of unconstrained nonconvex composite optimization problems where the objective is the sum of a smooth but possibly nonconvex function and a convex but possibly nonsmooth function, we propose a unified proximal gradient method with extrapolation, which provides unified treatment to convex and nonconvex problems. The method achieves the best-known convergence rate for first-order methods when …

Finite Element Methods For Elliptic Optimal Control Problems With General Tracking, Seonghee Jeong

LSU Doctoral Dissertations

This dissertation concerns a linear-quadratic elliptic distributed optimal control problem with pointwise state constraints in two spatial dimensions, where the cost function tracks the state at points, curves and regions of a domain.

First we explore the elliptic optimal control problem subject to pointwise control constraints. This problem is reduced into a problem that only involves the control. The solution of the reduced problem is characterized by a variational inequality. Then we introduce the elliptic optimal control problem with general tracking and pointwise state constraints. Here we reformulate the optimal control problem into a problem that only involves the state, …

Matroid Generalizations Of Some Graph Results, Cameron Crenshaw

LSU Doctoral Dissertations

The edges of a graph have natural cyclic orderings. We investigate the matroids for which a similar cyclic ordering of the circuits is possible. A full characterization of the non-binary matroids with this property is given. Evidence of the difficulty of this problem for binary matroids is presented, along with a partial result for binary orderable matroids.

For a graph G, the ratio of |E(G)| to the minimum degree of G has a natural lower bound. For a matroid M that is representable over a finite field, we generalize this to a lower bound on …

Sl(2,Z) Representations And 2-Semiregular Modular Categories, Samuel Nathan Wilson

LSU Doctoral Dissertations

We address the open question of which representations of the modular group SL(2,Z) can be realized by a modular category. In order to investigate this problem, we introduce the concept of a symmetrizable representation of SL(2,Z) and show that this property is necessary for the representation to be realized. We then prove that all congruence representations of SL(2,Z) are symmetrizable. The proof involves constructing a symmetric basis, which greatly aids in further calculation. We apply this result to the reconstruction of modular category data from representations, as well as to the classification of semiregular categories, which are defined via an …

Accurately Valuing Blue Carbon Sequestration And Storage To Foster Coastal Conservation Via Evidence-Based Policymaking And Model Environmental Services Statute Methodologies, John Shelton Penton Jr

LSU Doctoral Dissertations

Blue carbon ecosystems, especially mangrove forests, provide one of nature’s most effective means for sequestering carbon from the atmosphere and storing it in subsurface soils. The six nearshore coastal morphologies found in tropical and subtropical regions each possess a conspicuous environmental signature that can be employed to accurately estimate and predict mangrove forests’ carbon storage in above-ground biomass, below-ground biomass, and the soils by system type. The consistent geomorphology and geophysical processes within each of these coastal environmental settings, that is, the wave and tidal forcings, the rate of coastal sediment accretions, nutrient load and limitations (e.g., nitrogen-to-phosphorus …

Beyond Machine Learning: An Fmri Domain Adaptation Model For Multi-Study Integration, Lauryn Michelle Burleigh

LSU Doctoral Dissertations

Traditional machine learning analyses are challenging with functional magnetic
resonance imaging (fMRI) data, not only because of the amount of data that needs to be
collected, adding a particular challenge for human fMRI research, but also due to the change in
hypothesis being addressed with various analytical techniques. Domain adaptation is a type of
transfer learning, a step beyond machine learning which allows for multiple related, but not
identical, data to contribute to a model, can be beneficial to overcome the limitation of data
needed but may address different hypothesis questions than anticipated given the analysis
computation. This dissertation assesses …

Baldcypress (Taxodium Distichum) And Their Growth And Development Under Abiotic Stressors Related To Restoration Efforts, George Washburn

LSU Doctoral Dissertations

Baldcypresss (Taxodium distichum (L.) Rich.) forests are crucial to the Southeast coastal region for the trees’ ecosystem services. Many organizations have been trying to restore the ghost and dead forests found throughout the Gulf region through restoration events. Baldcypress seedlings and saplings face several abiotic and biotic stressors, including but not limited to elevated levels of salinity, nutrients, temperature, and light intensity. These stressors can be the limiting factor in the success or failure of these massive planting efforts.

To assess which stressors were of most concern to the restoration efforts, we conducted common garden experiments with baldcypress seedlings …

Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*-Algebras, Khalid Bdarneh

LSU Doctoral Dissertations

In this thesis we consider the Toeplitz operators on the weighted Bergman spaces and their analytic continuation. We proved the commutativity of the $C^*-$algebras generated by the analytic continuation of Toeplitz operators with special class of symbols that are invariant under suitable subgroups of $SU(n,1)$, and we showed that commutative $C^*-$algebras with symbols invariant under compact subgroups of $SU(n,1)$ are completely characterized in terms of restriction to multiplicity free representations. Moreover, we extended the restriction principal to the analytic continuation case for suitable maximal abelian subgroups of the universal covering group $\widetilde{SU(n,1)}$, and we obtained the generalized Segal-Bargmann transform, where …

Stellar Binaries And Post-Merger Evolution: A Framework For Stellar Evolution And Nucleosynthesis In R Coronae Borealis Stars, Bradley Munson

LSU Doctoral Dissertations

We have developed a framework for simulating binary stars through all three relevant
timescales: the dynamical merger, thermal, and nuclear evolution. The framework begins by simulating a dynamical merger in a 3-dimensional hydrodynamics adaptive mesh refinement code, Octo-Tiger, and performing a spherical averaging calculation to map the post-merger remnant into the 1-dimensional stellar evolution code, MESA. In this work, we primarily utilize this framework for simulating double white dwarf mergers, which are believed to be the progenitor to R Coronae Borealis (RCB) stars. We evolve the post-merger in MESA and compare the computed surface abundances to those observed …

Visual Analytics And Modeling Of Materials Property Data, Diwas Bhattarai

LSU Doctoral Dissertations

Due to significant advancements in experimental and computational techniques, materials data are abundant. To facilitate data-driven research, it calls for a system for managing and sharing data and supporting a set of tools for effective data analysis and modeling. Generally, a given material property M can be considered as a multivariate data problem. The dimensions of M are the values of the property itself, the conditions (pressure P, temperature T, and multi-component composition X) that control the concerned property, and relevant metadata I (source, date).

Here we present a comprehensive database considering both experimental and computational sources …

Measurement Of Near-Threshold Proton Branching Ratios In 31s Important For Novae, Sudarsan Balakrishnan

LSU Doctoral Dissertations

Classical novae are stellar explosions that contribute to the nucleosynthesis of isotopes on the proton-rich side of the valley of stability up to ⁴⁰Ca. In ONe novae, the incompletely understood reaction rate of ³⁰P(p,γ)³¹S is known to strongly influence the production rate of several stable isotopes such as ³⁰Si, ³¹P, and ^32,33,34S. A precise measurement of this reaction rate has several potential implications towards matching astrophysical observables to the physical composition of the nova site -- the observed elemental abundance ratios of O/S and S/Al have been suggested as useful `thermometers' to gauge …

Application Of Distributed Fiber-Optic Sensing For Pressure Predictions And Multiphase Flow Characterization, Gerald Kelechi Ekechukwu

LSU Doctoral Dissertations

In the oil and gas industry, distributed fiber optics sensing (DFOS) has the potential to revolutionize well and reservoir surveillance applications. Using fiber optic sensors is becoming increasingly common because of its chemically passive and non-magnetic interference properties, the possibility of flexible installations that could be behind the casing, on the tubing, or run on wireline, as well as the potential for densely distributed measurements along the entire length of the fiber. The main objectives of my research are to develop and demonstrate novel signal processing and machine learning computational techniques and workflows on DFOS data for a variety of …

Estimation Of Economic Risk From Coastal Natural Hazards In Louisiana, Rubayet Bin Mostafiz

LSU Doctoral Dissertations

Louisiana, U.S.A., is among the most vulnerable areas globally to coastal natural hazards, with risk vulnerability likely increasing. The risks associated with non-tropical-cyclone hazards in Louisiana’s coastal zone have been understudied. This research enhances present and future (i.e., 2050) Louisiana risk assessment using locally-weighted, model-based hazard frequency/intensity and population projections.

Results suggest that property risks associated with extreme cold temperature and tornado are and will remain costlier than those for hail and lightning. Property risks of extreme cold temperature and hail are projected to decrease with the expected warming temperatures, with those of all four of these hazards peaking in …

Sers Platform For Single Fiber Endoscopic Probes, Debsmita Biswas

LSU Doctoral Dissertations

Molecular detection techniques have huge potential in clinical environments. In addition to many other molecular detection techniques, endoscopic Raman spectroscopy has great ability in terms of minimal invasiveness and real-time spectra acquisition. However, Raman Effect is low in sensitivity, limiting the application. Surface-Enhanced Raman Scattering (SERS), addresses this limitation. SERS brings rough nano-metallic surfaces in contact with specimen molecules which enormously enhances Raman signals. This provides Raman spectroscopy with immense capabilities for diverse fields of applications.

Generally, in clinical probe applications, the spectrometer is brought near the target molecules for detection. Typically, optical fibers are used to couple spectrometers to …

Compilation Optimizations To Enhance Resilience Of Big Data Programs And Quantum Processors, Travis D. Lecompte

LSU Doctoral Dissertations

Modern computers can experience a variety of transient errors due to the surrounding environment, known as soft faults. Although the frequency of these faults is low enough to not be noticeable on personal computers, they become a considerable concern during large-scale distributed computations or systems in more vulnerable environments like satellites. These faults occur as a bit flip of some value in a register, operation, or memory during execution. They surface as either program crashes, hangs, or silent data corruption (SDC), each of which can waste time, money, and resources. Hardware methods, such as shielding or error correcting memory (ECM), …

Polymer Mimetics For Soil Modeling And Detection Of Biomarkers, Md Ragib Hasan

LSU Doctoral Dissertations

The population of the world is increasing day by day and is expected to reach 9.8 billion by the year 2050. The ever-increasing demand for agricultural products is putting an unprecedented strain on the world's soils as the human population continues to expand. Soil degradation caused by over-farming and the agrochemicals (fertilizers, pesticides, etc.) used in agriculture is a growing problem, although its causes remain murky. In addition, little is understood about the molecular-level interactions of substances that are subsequently introduced to soils, such as agricultural chemicals (ACs). Therefore, it is expected that these constraints may be circumvented by the …