Physical Sciences and Mathematics Commons^™

Errata: The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saito

Journal of Stochastic Analysis

No abstract provided.

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

LSU Doctoral Dissertations

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

Bernoulli Convolution Of The Depth Of Nodes In Recursive Trees With General Affinities, Toshio Nakata, Hosam Mahmoud

Journal of Stochastic Analysis

No abstract provided.

Stochastic Solutions For Hyperbolic Pde, Abdol-Reza Mansouri, Zachary Selk

Journal of Stochastic Analysis

No abstract provided.

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

LSU Doctoral Dissertations

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

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

LSU Doctoral Dissertations

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

Diving Deeper Into Supercuspidal Representations, Prerna Agarwal

LSU Doctoral Dissertations

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

Limit Theorems For Increments Of Branching Particle Systems With Linear Rates And Poisson Initial Condition, Alexander Kreinin, Vladimir V. Vinogradov

Journal of Stochastic Analysis

No abstract provided.

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

LSU Doctoral Dissertations

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

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

LSU Doctoral Dissertations

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

Riesz Particle Markov Chain Monte Carlo Methods, Xiongming Dai

LSU Doctoral Dissertations

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

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

LSU Doctoral Dissertations

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

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

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

LSU Doctoral Dissertations

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

Holomorphic Functional Calculus Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas

Journal of Stochastic Analysis

No abstract provided.

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

LSU Doctoral Dissertations

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

The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saitô

Journal of Stochastic Analysis

No abstract provided.

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

LSU Doctoral Dissertations

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

Optics Design And Fabrication For A Lung Interferometry-Radiography System, Rachael Lyn Blair

LSU Master's Theses

Purpose: High prevalence of lung diseases leads to many people worldwide needing spirometry and imaging testing. The typical imaging done uses chest radiography and/or low-dose CT. Lung tissue is difficult to visualize, making them substandard for monitoring lung disease progression. An improvement on these systems is x-ray interferometry which produces additional images that provide better visualization of changes in the lung tissue. The set-up of x-ray interferometry builds upon other imaging systems in that it includes diffraction gratings.

Materials: This thesis focused on implementing the fabrication processes to create diffraction gratings for a lung imager prototype that is currently under …

Decay Spectroscopy Of 134sb Using X-Array And Saturn, Graeme E. Morgan

LSU Doctoral Dissertations

The ground-state decay of ¹³⁴Sb is reported by the current evaluated nuclear data to be dominated by a 0^-→0⁺ first-forbidden Gamow-Teller transition to the ground state of ¹³⁴Te. In 2013, a recoil-ion time-of-flight (RI-TOF) spectroscopy measurement of ¹³⁴Sb with the Beta-decay Paul Trap (BPT) indicated that the ground-state feeding of ¹³⁴Te is weaker than reported. Simulation work of ¹³⁴Sb ground-state decays replicated the RI-TOF results with the addition of a theorised 5-MeV state that was fed with ~17% of the total β-decay strength. To search for higher energy states and transitions that …

Molybdenum Alkylidyne Complexes With Phenoxide Ligands For Alkyne Metathesis, Marvin L. Stewart Jr

LSU Doctoral Dissertations

Abstract

Alkyne metathesis is a powerful synthetic tool, which provides easy access to complex organic molecules in a single-step. It is a dynamic covalent reaction that scrambles alkynes, carbon-carbon triple bonds (C≡C). Molybdenum- or tungsten-alkylidyne (Mo≡C, W≡C) complexes are typically used as catalyst to cleave and reform alkyne bonds. Our goal has been to gain a deeper understanding of the intrinsic differences between functional ligands by the development of novel phenoxide ligands.

In chapter 2 we explore the detailed synthesis of novel phenoxide podand ligands in an effort to identify their mo-alkylidyne complexes. We were able to synthesize a variety …

The Lowest Discriminant Ideal Of Cayley-Hamilton Hopf Algebras, Zhongkai Mi

LSU Doctoral Dissertations

Discriminant ideals are defined for an algebra R with central subalgebra C and trace tr : R → C. They are indexed by positive integers and more general than discriminants. Usually R is required to be a finite module over C. Unlike the abundace of work on discriminants, there is hardly any literature on discriminant ideals. The levels of discriminant ideals relate to the sums of squares of dimensions of irreducible modules over maximal ideals of C containing these discriminant ideals. We study the lowest level when R is a Cayley-Hamilton Hopf algebra, i.e. C is also a Hopf subalgebra, …

Post-Modeling Adjustments And Delivered Dose Verification Of The 6fff Beam Model Commissioned For The Monaco Treatment Planning System, Grant C. Debevec

LSU Master's Theses

External beam radiation therapy has been shown to be an effective treatment method for tumors and abnormalities of the spine and vertebral region. Treating the spine using a stereotactic body radiation therapy (SBRT) technique can reduce toxicity to the spinal cord. The 6 MV flattening filter free (6FFF) beam model is currently used to plan and calculate dose for SBRT treatment plans, and the treatment plans are delivered using a linear accelerator (LINAC).

The commissioned beam model represents an invariant component of a LINAC. For volumetric modulated arc therapy (VMAT) treatment plans, the multileaf collimator (MLC) positions are changing throughout …

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 …

Estimating Crustal Thickness In Northwest Louisiana Using The Receiver Function Method, Delton Samuel

LSU Master's Theses

I aim to constrain the crustal thickness of the Sabine Block in the Sabine Uplift region of northwest Louisiana, using the frequency domain receiver function deconvolution technique followed by H-κ stacking. The passive margin on the southern edge of the North American continent experienced an active tectonic history, including the spreading events that led to the formation of the Gulf of Mexico. A previous study proposed the Sabine Block is a residual fragment of Proterozoic orogenic origin; however, its full extent and geometry are up for debate. It is now overlain by thick sedimentary sequences ranging from ~4-6 km deposited …

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 …

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.

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 …

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 …