Physical Sciences and Mathematics Commons^™

Reducibility Of Schrödinger Operators On Multilayer Graphs, Jorge Villalobos Alvarado

LSU Doctoral Dissertations

A local defect in an atomic structure can engender embedded eigenvalues when the associated Schrödinger operator is either block reducible or Fermi reducible, and having multilayer structures appears to be typically necessary for obtaining such types of reducibility. Discrete and quantum graph models are commonly used in this context as they often capture the relevant features of the physical system in consideration.

This dissertation lays out the framework for studying different types of multilayer discrete and quantum graphs that enjoy block or Fermi reducibility. Schrödinger operators with both electric and magnetic potentials are considered. We go on to construct a …

Finite Monodromy And Artin Representations, Emma Lien

LSU Doctoral Dissertations

Artin representations, which are complex representations of finite Galois groups, appear in many contexts in number theory. The Langlands program predicts that Galois representations like these should arise from automorphic representations and many examples of this correspondence have been found such as in the proof of Fermat's Last Theorem. This dissertation aims to make an analysis of explicitly computable examples of Artin representations from both sides of this correspondence. On the automorphic side, certain weight 1 modular forms have been shown to be related to Artin representations and an explicit analysis of their Fourier coefficients allows us to identify the …

The Modular Generalized Springer Correspondence For The Symplectic Group, Joseph Dorta

LSU Doctoral Dissertations

The Modular Generalized Springer Correspondence (MGSC), as developed by Achar, Juteau, Henderson, and Riche, stands as a significant extension of the early groundwork laid by Lusztig's Springer Correspondence in characteristic zero which provided crucial insights into the representation theory of finite groups of Lie type. Building upon Lusztig's work, a generalized version of the Springer Correspondence was later formulated to encompass broader contexts.

In the realm of modular representation theory, Juteau's efforts gave rise to the Modular Springer Correspondence, offering a framework to explore the interplay between algebraic geometry and representation theory in positive characteristic. Achar, Juteau, Henderson, and Riche …

Analytic Wavefront Sets Of Spherical Distributions On The De Sitter Space, Iswarya Sitiraju

LSU Doctoral Dissertations

In this work, we determine the wavefront set of certain eigendistributions of the Laplace-Beltrami operator on the de Sitter space. Let G′ = O_1,n(R) be the Lorentz group, and let H′ = O_1,n−1(R) ⊂ G′ be its subset. The de Sitter space dSⁿ is a one-sheeted hyperboloid in R^1,n isomorphic to G′/H′. A spherical distribution is an H′-invariant eigendistribution of the Laplace-Beltrami operator on dSⁿ. The space of spherical distributions with eigenvalue λ, denoted by D_λ^H'(dSⁿ), has dimension 2. We construct a basis for the space of …

Thermal Frontal Polymerization – Applications In Coatings And Composites, Maria Martinez

LSU Doctoral Dissertations

Thermal frontal polymerization has long been used as a method to cure composites and coatings. However, this is the first time these applications have been used without the use of a catalyst, for the case of composites and coatings.

Chapter 2 discusses how to optimize cure-on-demand, thin layer coatings, using frontal polymerization. Previously, for the use of curing thin layer coating using thermal FP, it was known to just make the formulation viscous enough, as this would prevent premature quenching caused by heat loss. It was discovered that for a given layer thickness, a minimum viscosity and initiator concentration were …

Subroups Of Coxeter Groups And Stallings Foldings, Jake A. Murphy

LSU Doctoral Dissertations

For each finitely generated subgroup of a Coxeter group, we define a cell complex called a completion. We show that these completions characterizes the index and normality of the subgroup. We construct a completion corresponding to the intersection of two subgroups and use this construction to characterize malnormality of subgroups of right-angled Coxeter groups. Finally, we show that if a completion of a subgroup is finite, then the subgroup is quasiconvex. Using this, we show that certain reflection subgroups of a Coxeter are quasiconvex.

Applied Depositional Geosystems Of The Coos Bay Basin, Oregon: Organic Geochemistry, Maturation, Paleoenvironmental Reconstruction And Biostratigraphy Of The Coaledo Delta During The Middle Eocene Climatic Optimum (Meco), Allison K. Barbato

LSU Doctoral Dissertations

The Coos Bay Basin on the southwestern coast of Oregon is a forearc basin that contains exceptionally preserved Eocene to Miocene, tidal to wave-dominated, shallow deltaic to deep marine sediments of the Coaledo Delta. Coastal depositional environments are known to host source, reservoir, and seal rocks. Climate, topographic relief, and geographical position all play an important role in regional vegetation development and oceanic setting. This study assesses 84 outcrop and 12 core samples from Coos Bay for their organic geochemical characteristics and microfossil assemblage to provide source rock characterization information, organofacies descriptions, environmental reconstructions, and age control.

Results indicate the …

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 …

Characterizing And Mitigating Transient Noise In Ligo Observatories For Gravitational Wave Detection, Jane Glanzer

LSU Doctoral Dissertations

The existence of gravitational waves is predicted by Albert Einstein's Theory of General Relativity. Commonly referred to as "ripples in spacetime", these waves are generated by some of the most violent and energetic processes in the universe. Despite their theoretical prediction over a century ago, it wasn't until 2015 that the Advanced LIGO (aLIGO) interferometers in Hanford, WA and Livingston, LA directly detected gravitational waves for the first time, confirming Einstein's theory and ushering in a new era of astrophysics.

Detecting gravitational waves requires incredible precision. Because of the extreme sensitivity required, it is possible for the gravitational wave data …

The Homotopy Cardinality Of The Representation Category, Justin Murray

LSU Doctoral Dissertations

Given a Legendrian knot in (R^3, ker(dz − ydx)) one can assign a combinatorial invariants called ruling polynomials. These invariants have been shown to recover not only a (normalized) count of augmentations but are also closely related to a categorical count of augmentations in the form of the homotopy cardinality of the augmentation category. In this article, we prove that that the homotopy cardinality of the n-dimensional represen- tation category is a multiple of the n-colored ruling polynomial. Along the way, we establish that two n-dimensional representations are equivalent in the representation category if they are “conjugate homotopic”. We also …

Surface And Bulk Properties Of Multi-Component Metal Alloys, Frank A. Mckay Iii

LSU Doctoral Dissertations

While HEAs have been studied extensively for their material properties, their potential as catalysts remains widely unexplored. To explore the feasibility of CoCrFeNi as a catalyst for the hydrogen evolution reaction, the results of X-ray photoelectron spectroscopy (XPS) and high-resolution electron energy loss spectroscopy (HREELS) experiments are compared to electrochemical experiments and theoretical calculations. XPS shows that this surface forms passive oxides with a propensity of Cr > Fe > Co, with no evidence of Ni oxidation. From comparison to calculations, it is shown that the electrochemical activity is enhanced in a partially oxidized state. The lack of Ni oxidation suggests that …

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 …

Auslander-Reiten Triangles On A Bounded Derived Category Of Constructible Complexes, Vishnu Prasad Sivaprasad

LSU Doctoral Dissertations

In this dissertation, concepts from homological algebra are used to study the existence of Auslander-Reiten triangles.

Auslander-Reiten triangles are closely related to representable functors, and the main theorem characterizes the existence of representable functors in a specific bounded derived category of constructible complexes.

Under certain boundedness conditions, a specific bounded derived category is shown to have Auslander-Reiten triangles.

Attochemistry Regulation Of Charge Migration, Aderonke Folorunso

LSU Doctoral Dissertations

Charge migration (CM) is a coherent attosecond process that involves the movement of localized holes across a molecule. This phenomenon is potentially useful to understand the fundamental principles of photochemistry, such as light harvesting. The first part of this dissertation discusses the molecular modes of attosecond charge migration. In this work, we used first-principles calculations to investigate the modes of charge migration (CM) in halogenated hydrocarbon chains at attosecond timescales. We have simulated the creation of a localized hole on the halogen atom using constrained density functional theory (DFT) and then tracked its subsequent dynamics with time-dependent DFT (TDDFT). Our …

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 …

Extended Defects And Linear Junctions At The Surfaces Of Topological Insulators, Eklavya Thareja

LSU Doctoral Dissertations

Topological Insulators (TIs) have emerged as promising candidates for spintronics and quantum computing applications. Two properties that underlie these applications are the locking of spin and momentum of the surface electrons and topological protection of surface states. While the existence of gapless surface states is guaranteed by topology, as long as time-reversal symmetry is intact, other properties of the surface states are still tunable. Spin-momentum locking makes these states immune to scattering from non-magnetic point impurities. However, extended defects can scatter the states even with electrostatic potential. We show that a line defect with magnetic and electrostatic potential scattering hosts …

Controlling Guest Binding To Transition Metal Hosts Via Redox Stimuli, Jasmine S. Sanford

LSU Doctoral Dissertations

Several metal complexes were investigated as potential hosts to execute controllable host- guest interactions using a redox stimulus. Previously, our group has synthesized new Cu^II m-xylylenebis(pyridyltriazole) (m-xpt) hosts and their redox properties were analyzed. In Chapter 2, we take advantage of the Cu^II host’s ability to perform redox to investigate its interaction with chloride guest ions. This study was executed with two main Cu-xpt hosts: [Cu₂(m- xpt)₂(NO₃)₂](PF₆)₂ and [Cu₂(m-xpt)₂Cl₂]Cl₂. The host-guest interaction was analyzed with additions …

Design, Synthesis And Post Functionalization Of Bodipy Dyes For Use As Chemo Sensors., Caroline Njeri Ndung'u

LSU Doctoral Dissertations

An overview of BODIPYs history, basic structure, electronic properties is described. Additionally, their attribute of tenability in their photophysical and electronic properties has been discussed. Lastly, their application in the biomedical field as bio imaging, labeling, chemo sensors and photosensitizers are also discussed. In Chapter 2, a library of meso- Pyridyl and meso pyridinium BODIPY dyes was designed, synthesis and comparison on their photophysical, electrochemical and cytotoxic studies done. From this study chlorine atoms at the 2, 6 positions was shown to enhance their relative fluorescence quantum yields in different organic solvents and water. In chapter 3, 8(meso)-pyridyl-BODIPYs with a …

Computational Investigations Of Polymer Electrolytes In Aqueous Solutions, Hishara Keshani Gallage Dona

LSU Doctoral Dissertations

Polymer electrolyte membranes, an intriguing category of soft materials, are characterized by polymer backbones tethered with negatively or positively charged functional groups, finding applications from biological macromolecules to electrochemical separations in fuel cells. This dissertation focuses on computational investigations of polymer electrolytes in aqueous solutions using polypeptoids and ion exchange membranes. Polypeptoids, highly tailorable peptidomimetic polymers lacking backbone hydrogen bonding or chirality, were used as model systems. Micelles formed from these polypeptoid polymers exhibited electrostatic repulsion, which competes with charge-sodium interactions, adding complexity to predicting micelle shapes. This research refined the design strategy, enhancing micelle shape and structure through precise …

Deciphering The Role Of Molecular Interactions On The Interfacial Structure Of Aqueous And Non-Aqueous Interfaces, Dodangodage Ishara Indunil Senadheera, D I. Senadheera

LSU Doctoral Dissertations

The study focused on "Deciphering the role of molecular interactions on the interfacial structure of aqueous and non-aqueous interfaces" holds immense significance in diverse scientific and industrial domains. Our primary objective is to unravel the intricate web of molecular interactions occurring at the boundaries between aqueous and non-aqueous phases. The research presented here spans a wide scope, encompassing applications in microelectromechanical systems in the semiconductor industry, energy-efficient membranes for electrochemical separations, and renewable energy storage systems. Molecular dynamics simulations were conducted in collaboration with experimental studies, specifically atomic force microscopy, to achieve insights at the molecular level.The first project centered …

Cationic Frontal Polymerization: Front Kinetics, Effects Of Additives, And Applications, Brecklyn R. Groce

LSU Doctoral Dissertations

Cationic frontal polymerization broadens the potential application of frontal polymerization by allowing for use of monomers such as epoxies and vinyl ethers. In this work, the effects of monomer and initiator composition and additives including fillers on front kinetics, along with applications of cationic frontal polymerization were investigated.

Using a radical-induced cationic frontal polymerization (RICFP) method with a superacid generating salt and a thermal radical initiator, the addition of vinyl ethers to epoxy formulations was studied, where an increase of front velocity was seen with increase of divinyl ether to epoxy ratio. Other aspects of vinyl ether systems, such as …

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 …

Optimizing Large-Capacity Key-Value Systems For Efficient Data Management, Kefei Wang

LSU Doctoral Dissertations

In today's Internet services, key-value system is playing a crucial and indispensable role, and has attracted extensive research in both academia and industry. During the past years, we have witnessed an unprecedented quick development of both memory-based and flash-based key-value systems. With the rapid evolution of memory and storage technologies, we are seeing both challenges and research opportunities.

In this dissertation, we focus on understanding and optimizing the efficiency of large-capacity, high-speed key-value systems from the perspective of both software and hardware to meet the ever-growing performance expectations. We first propose a multi-tier mapping structure, called Cascade Mapping, exploring the …

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 …

Nonlinear Optical Studies At Surfaces And Interfaces, Mojgan Dehghani

LSU Doctoral Dissertations

Nonlinear optical studies have revealed that surfaces and interfaces possess unique optical properties due to the lack of inversion symmetry. These properties are significantly different from those of the bulk material. Second harmonic generation (SHG), a second-order nonlinear optical phenomenon, has emerged as a surface-specific technique to study these unique properties. The powerful selection rule allows generation of second harmonic light only in the bulk of noncentrosymmetric media and the regions with broken inversion symmetry, including surfaces and interfaces. The generated second harmonic provides significant information on the electronic and structural properties of the microscopic surface layer at the boundary …

First-Principles Simulations Of Attosecond Transient X-Ray Absorption, Min Chen

LSU Doctoral Dissertations

The first part of this dissertation presents calculations of the extinction spec- tra of gold-silver/silver-gold core-shell nanospheres. The goal of this projectsis to get a deeper understanding of surface plasmonic resonance in metal nanospheres with core-shell geometry. Here, we used the finite-difference time-domain (FDTD) method and total-field/scattered-field (TFSF) framework to compute the extinction spectra of nanoparticles to determine the geometry of gold-silver/silver-gold core-shell nanoparticles. This supported experimental work on monitoring the growth dynamics of colloidal gold- silver/silver-gold core-shell nanoparticles using in situ second harmonic generation (SHG) and extinction spectroscopy.

The second and main project involved simulating attosecond transient spectra for …

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 …

Phase Transitions And Magnetocaloric Effects In Metastable Phases Of Intermetallic Compounds, Tej Bahadur Poudel Chhetri

LSU Doctoral Dissertations

The interplay between spin and lattice degrees of freedom in magnetic materials often results in interesting magnetoresponsive effects. The magnetocaloric effect is one such magnetothermal phenomenon that may be utilized in energy-efficient magnetic cooling systems. This effect becomes more prominent near a coupling of magnetic and structural transitions, i.e., magnetostructural transitions (MSTs). This dissertation investigates phase transitions (magnetic and structural) in metastable phases of MnNiGe- and MnCoGe-based compounds generated through high-pressure synthesis/annealing and thermal quenching techniques and assesses their magnetocaloric effects.

First, the effects of doping, hydrostatic pressure, and thermal quenching on phase transitions and related magnetocaloric effects in Mn …