Physical Sciences and Mathematics Commons^™

Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Autonomous Shipwreck Detection & Mapping, William Ard

LSU Master's Theses

This thesis presents the development and testing of Bruce, a low-cost hybrid Remote Operated Vehicle (ROV) / Autonomous Underwater Vehicle (AUV) system for the optical survey of marine archaeological sites, as well as a novel sonar image augmentation strategy for semantic segmentation of shipwrecks. This approach takes side-scan sonar and bathymetry data collected using an EdgeTech 2205 AUV sensor integrated with an Harris Iver3, and generates augmented image data to be used for the semantic segmentation of shipwrecks. It is shown that, due to the feature enhancement capabilities of the proposed shipwreck detection strategy, correctly identified areas have a 15% …

Can Gulf Ribbed Mussels Enhance Coastal Restoration Projects In A Future With Climate Change?, Skylar Liner

LSU Master's Theses

Living shorelines present one restoration approach using biotic elements (via ecosystem engineers) to stabilize shorelines and increase valuable habitat. Gulf ribbed mussels (Geukensia granosissima) are important ecosystem engineers within brackish and salt marshes in the northern Gulf of Mexico, and can increase nutrient availability, enhance marsh vegetation production, and potentially improve shoreline stability. It is unknown whether mussels will maintain these functions as future climate change predicts increases in temperature and water level, which may exceed the mussel’s tolerance. A field survey conducted during the summer of 2022 identified the daily maximum temperature at the marsh surface, where mussels naturally …

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 …

Multiplication Operators By White Noise Delta Functions And Associated Differential Equations, Luigi Accardi, Un Cig Ji, Kimiaki Saitô

Journal of Stochastic Analysis

No abstract provided.

Random Variables With Overlapping Number And Weyl Algebras Ii, Ruma Dutta, Gabriela Popa, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

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 …

Experiments And Data Analysis For Modulated Phase Gratings In X-Rays, Sydney B. Carr

LSU Master's Theses

Purpose: Modulated Phase Grating (MPG) interferometry has been shown in theory and simulations to produce observable fringes on a clinical detector without requiring fluence absorbing analyzer. In this work, we will experimentally show that the MPG X-ray system produces observable fringes and multi-modal X-ray images.

Motivation:Nearly 1 in 8 women in the US will develop invasive breast cancer in their lifetime, accounting for approximately 40,000 deaths each year [1-2]. In order to pursue the best treatment option available, cancer itself must be adequately imaged and staged, based on size and level of metastasis, on the order of Stage I-IV. …

Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Atmospheric Impacts From The 2010 Deepwater Horizon Oil Spill, Charles Philip Johnson

LSU Master's Theses

Although the ecological devastations induced by an oil spill are well studied, the hydrometeorological impacts from a long-term slick have gone unnoticed. The ocean-surface alterations stemming from the lasting oil footprint increase solar radiation absorption which in turn alters the surface pressure and moisture gradients and wind speeds thereby influencing precipitation surrounding the oil spill. Revealing the potential impacts from these could better aid in the safety of crews cleaning spills and provide a better understanding of how humans alter the landscape. This thesis examines the changes in local hydrometeorology brought on by the 2010 summer Deepwater Horizon (DWH) oil …

Errata: Continuous Lattices And Domains, Jimmie D. Lawson

Seminar on Continuity in Semilattices

No abstract provided.

Symmetric Functions Algebras (Sfa) Ii: Induced Matrices, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Optimal Control Problems For Stochastic Processes With Absorbing Regime, Yaacov Kopeliovich

Journal of Stochastic Analysis

No abstract provided.

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 …

20-Year Assessment Of Total Suspended Sediment (Tss) Variability In Barataria Bay From Modis Ocean Color Using A Combination Of Adaptive Semi-Analytical And Neural Network Algorithms, Bijaylaxmi Sahoo

LSU Master's Theses

Barataria Bay, a hydrologically dynamic basin in the northern Gulf of Mexico, exhibits a distinct spatio-temporal distribution of total suspended sediment (TSS). However, studies on sediment distribution are limited by availability of in-situ data as well as the limitation of ocean color algorithms for suspended sediments in shallow optically complex waters. Barataria Bay TSS concentration profile is complex, influenced in the upper basin by fresh water sources such as the Davis Pond Freshwater Diversion, and in the lower bay by the river plume and marine influence near the mouth of the bay. To efficiently study the sediment dynamics in the …

An Analysis Of Hurricane Laura's Storm Surge In Cameron Parish Using Synthetic Storm Tracks, Climatology, And Statistics, Cameron Goff

LSU Master's Theses

Cameron Parish is a large coastal parish in southwest Louisiana that has been impacted by several powerful tropical cyclones. In 2020, the strongest hurricane in recorded history to ever hit this region, Hurricane Laura, set a state record for the highest storm surge measurement at 6.34 meters. I examine the climatology of tropical cyclone landfalls in this parish, looking for trends in intensity and frequency with time. I then compare the extreme surge of Hurricane Laura with a dataset of 645 synthetic tropical cyclones generated and used by the Coastal Hazards System for Louisiana. Plots comparing various meteorological statistics to …

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 …

Quantifying Mud Settling Velocity As A Function Of Turbulence And Salinity In A Deltaic Estuary, Michael W. Mcdonell

LSU Master's Theses

Mud settling velocity is controlled by flocculation, which in turn strongly depends on turbulence and on the chemistry and biology of the water-sediment mixture. As a result, mud settling velocity can be poorly constrained in coastal areas and vary in space and time by orders of magnitude. Here we quantified mud settling velocity in Barataria Basin, a deltaic estuary in Louisiana (USA), using three independent methods: eddy covariance (one station for 200 days), floc cameras (4 stations at one time), and Rouse profile inversion (14 stations, replicated 10-30 times each). Eddy covariance indicates that settling velocity increases with turbulence, at …

Snow Distribution And Influence In Taylor Valley, Antarctica, Using Remote Sensing, Katherine Mcnulty, Peter Doran, Mark Salvatore, Suniti Karunatillake

LSU Master's Theses

The McMurdo Dry Valleys is the largest ice-free area in Antarctica, but seasonal snow covers the valley floors sporadically throughout the year. In this study, a model to estimate areal snow coverage from satellite imagery was created. An area-volume model was created to estimate the amount of snow water equivalent (SWE) from the snow area extracted from the imagery. Snow cover influences the total albedo, the hydrologic budget, and the soil moisture and soil temperature in Taylor Valley (TV). Quantifying snow precipitation in TV is challenging because snow redistributes with winds, sublimates, or melts within a short period. Previous estimates …

Gulf Sturgeon Mesohabitat Use And Movement In The Lower Pearl River Louisiana-Mississippi, Amanda Popovich

LSU Master's Theses

After spring migrations to natal rivers Gulf Sturgeon Acipenser oxyrinchus desotoi reside in freshwater holding areas prior to fall emigrations to nearby estuaries. Limited published information on the physical habitat characteristics of these holding areas is available, especially for juvenile fish in the western portion of the Gulf Sturgeon’s distribution. To further investigate freshwater occupancy and movement patterns, 32 acoustic receivers were deployed from late April to October of 2021 and 2022 in 1600-m reaches distributed throughout the lower Pearl River, Louisiana-Mississippi, the westernmost river within their distribution. Generalized linear mixed models and multi-state models were used to determine what …

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 …