Physical Sciences and Mathematics Commons^™

Method Of The Riemann-Hilbert Problem For The Solution Of The Helmholtz Equation In A Semi-Infinite Strip, Ashar Ghulam

LSU Doctoral Dissertations

In this dissertation, a new method is developed to study BVPs of the modified Helmholtz and Helmholtz equations in a semi-infinite strip subject to the Poincare type, impedance and higher order boundary conditions. The main machinery used here is the theory of Riemann Hilbert problems, the residue theory of complex variables and the theory of integral transforms. A special kind of interconnected Laplace transforms are introduced whose parameters are related through branch of a multi-valued function. In the chapter 1 a brief review of the unified transform method used to solve BVPs of linear and non-linear integrable PDEs in convex …

A Conditioned Gaussian-Poisson Model For Default Phenomena, Tyler Brannan

LSU Doctoral Dissertations

We introduce a new model to study the behavior of a portfolio of defaultable assets. We refer to this model as the Gaussian-Poisson model. It builds upon one-factor Gaussian copula models and Poisson models (specifically Cox processes). Our model utilizes a random variable Y along with probability measures ℙ^• and ℙ^†. The measures ℙ^• and ℙ^† will act as market pricing measures and are obtained via conditioning. The random variable Y will act as a default descriptor.

We provide the distribution of Y under both ℙ^• and ℙ^†. We use a conditional …

Theory And Utility Of The Three Isotope Fractionation Relationship, Justin Alan Hayles

LSU Doctoral Dissertations

The field of isotope geochemistry began with the study of oxygen isotope geothermometry, most famously for carbonates. Traditionally oxygen isotope studies are only concerned with the relationship between one rare isotope, oxygen-18, and the common isotope, oxygen-16. In these cases, the abundance of the third stable isotope, oxygen-17 is ignored because for almost all terrestrial processes the 17O-16O relationship roughly scales with the 18O-16O relationship through a fractionation processes and is thought to not provide any new information. However, the discovery of large “mass independent” isotope effects for ozone chemistry has driven a multitude of uses for triple isotope relationships. …

Evolution Semigroups For Well-Posed, Non-Autonomous Evolution Families, Austin Keith Scirratt

LSU Doctoral Dissertations

The goal of this dissertation is to expand Berhard Koopman's operator theoretic global linearization approach to the study of nonautonomous flows. Given a system with states x in a set \Omega (the state space), a map t\to \gamma(t,s,x) (t\geq s \geq 0) is called a global flow if it describes the time evolution of a system with the initial state x \in \Omega at time t \geq s \geq 0. Koopman's approach to the study of flows is to look at the dynamics of the observables of the states instead of studying the dynamics of the states directly. To do …

Biomedical Applications Of Thiol-Acrylate Polymers, Leah Alyce Garber

LSU Doctoral Dissertations

The development of biocompatible polymers using thiol-acrylate Michael addition reactions between not only acrylates and thiols but also between amines and acrylates were demonstrated. The synthesis of an in situ tertiary amine catalyst initiates the propagation steps of the polymerization process by subsequently reacting with trimethylolpropane tris (3-mercaptopropionate) (TMPTMP). A few notable characteristics of this reaction are tunable gel times, the capability of reaching high polymer conversion and suitable mechanical strength. With addition of hydroxyapatite to the polymeric phase and foaming, a porous bone composite was produced. Further osteogenisis and in vivo work using the PETA-co-TMPTMP (HA) composite material was …

Garbage Collection For General Graphs, Hari Krishnan

LSU Doctoral Dissertations

Garbage collection is moving from being a utility to a requirement of every modern programming language. With multi-core and distributed systems, most programs written recently are heavily multi-threaded and distributed. Distributed and multi-threaded programs are called concurrent programs. Manual memory management is cumbersome and difficult in concurrent programs. Concurrent programming is characterized by multiple independent processes/threads, communication between processes/threads, and uncertainty in the order of concurrent operations. The uncertainty in the order of operations makes manual memory management of concurrent programs difficult. A popular alternative to garbage collection in concurrent programs is to use smart pointers. Smart pointers can collect …

An Investigation Of Environmentally Persistent Free Radical (Epfr) Formation In Contaminated Soils Using Surrogate-Based Model Systems, Ugwumsinachi Godwin Nwosu

LSU Doctoral Dissertations

Environmentally persistent free radicals (EPFRs) have recently attracted attention due to their properties that detrimental to the health of living organisms. Earlier studies devoted to the formation of combustion generated particulate matter (PM) showed that EPFRs formed as a result of the association of aromatic chlorinated hydrocarbons with transition metal centers. Based on our previous studies, the amounts of EPFRs formed at Superfund soil sites contaminated with pentachlorophenol (PCP) are ~30 times higher compared to those formed at the neighboring uncontaminated soil sites, showing that EPFR formation is not confined to combustion generated particle. In order to design viable remediation …

Studies Of The Properties Of Designed Nanoparticles Using Atomic Force Microscopy, Steve Matthew Deese

LSU Doctoral Dissertations

The purpose of the research in this dissertation was to elucidate the intrinsic properties of how nanoparticles are different from bulk materials. This was done by mechanical and electronic studies of the properties of designed nanoparticles using advanced modes of atomic force microscopy. Information relating to the work functions, contact potential difference, Young’s Moduli, elasticity, and viscoelasticity can be investigated using state-of-the-art atomic force microscope (AFM) experiments. Subsurface imaging of polystyrene encapsulated cobalt nanoparticles was achieved for the first time using Force Modulation Microscopy (FMM) in conjunction with contact mode AFM. Previously prepared sample of polystyrene coated cobalt nanoparticles were …

Fundamental Studies Of Humic Acid's Influence On Pollutant Toxicity To Aquatic Organisms, Rachel Dawn Deese

LSU Doctoral Dissertations

The main purpose of the research presented in this dissertation was to further understand the intricate and convoluted interactions between natural organic material, biological entities, and pollutants. This was achieved by utilizing humic acids (HAs) from differing sources, chemically modified humic acid, two biological entities (model biomembranes and Artemia Franciscana), and three types of pollutants (cations, surfactants, and carbon nanotubes). Fluorescence spectroscopy and model biomembranes were used to measure the change in HA’s ability to interact with the biomembranes in the presence of cations. Three differently sourced HAs, chemical modified HAs, and a range of cations were studied to elucidate …

Global A Priori Estimates And Sharp Existence Results For Quasilinear Equations On Nonsmooth Domains., Karthik Adimurthi

LSU Doctoral Dissertations

This thesis deals obtaining global a priori estimates for quasilinear elliptic equations and sharp existence results for Quasilinear equations with gradient nonlinearity on the right. The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain global unweighted a priori estimates for very weak solutions below the natural exponent and weighted estimates at the natural exponent. The weights we consider are the well studied Muckenhoupt weights. Using the results obtained in Chapter 4, we obtain sharp existence result for quasilinear operators with gradient type nonlinearity on the right. We characterize the function …

Synthetic Efforts Towards The Synthesis Of Prostaglandin Pgf2a, Amy Marie Pollard

LSU Doctoral Dissertations

This dissertation describes strategies for synthesizing prostaglandin PGF2α. Our synthetic design creates the stereochemistry needed for the core and side chains of the target prostaglandin PGF2 alpha and PGF2 alpha synthase selective analogues while incorporating iodocyclization desymmetrization of acyclic dienes. A model system for 4-(iodomethyl)-6-methyl-1,3-dioxan-2-one was developed and synthesized for our target compound 4-(2-(benzyloxy)ethyl)-6-(iodomethyl)-5-vinyl-1,3-dioxan-2-one. Both compounds were successfully synthesized providing useful stereocenters for completing the synthesis of prostaglandin PGF2 alpha. Efforts toward total stereochemical control of PGF2α include the partial syntheses of bis-diethylanimedimethylsilane and of (4S,5S)-2-((1E,3E)-penta-1,3-dien-1-yl)-4,5-diphenyl-1,3-ditosyl-1,3,2-diazaborolidine.

Visible Light And Electron Transfer Chemistry For O-Glycosylation And Remote Hydroxylation, Mark Louis Spell

LSU Doctoral Dissertations

This dissertation focuses on the synthesis of dauer pheromone analogs for biological evaluation, the development of visible light promoted O-glycosylation methods and the development of an Ir(ppy)3 catalyzed C-H hydroxylation method. Chapter 1 describes the synthesis of dauer pheromone analogs. C.elegans is a small nematode that enters a dauer stage when encountering unfavorable environmental conditions. The dauer stage is initiated by the nematodes chemosensation of the dauer pheromone caused by the down regulation biochemical pathways TGF-â and IGF-1. These biochemical pathways are also seen in Homo Sapiens and play a role in a number of biological processes. Understanding how these …

Synthesis Of Functional Polypeptides And Development Of New Synthetic Strategies Toward Polypeptides, Jinbao Cao

LSU Doctoral Dissertations

The objective of this work is to develop a new synthetic strategy for synthesizing advanced functional polypeptides or polypeptides in general. Polypeptides are amino acids based polymers with appealing properties for different applications. One of the key challenges in polypeptide research is the synthesis of functional polypeptides under mild conditions. We developed a system based on ring-opening polymerization (ROP) of N-thiocarboxyanhydrosulfides (NTAs) to synthesize polypeptides with wide range of molecular weights under mild conditions. Owing to NTAs’ good stability, our system serves as an excellent alternative to the traditional ROP of N-carboxyanhydrides (NCA). In Chapter 1, the fundamental knowledge and …

A Novel Recurrent Convolutional Neural Network For Ocean And Weather Forecasting, Robert James Firth

LSU Doctoral Dissertations

Numerical weather prediction is a computationally expensive task that requires not only the numerical solution to a complex set of non-linear partial differential equations, but also the creation of a parameterization scheme to estimate sub-grid scale phenomenon. The proposed method is an alternative approach to developing a mesoscale meteorological model – a modified recurrent convolutional neural network that learns to simulate the solution to these equations. Along with an appropriate time integration scheme and learning algorithm, this method can be used to create multi-day forecasts for a large region. The learning method presented is an extended form of Backpropagation Through …

On Properties Of Matroid Connectivity, Simon Pfeil

LSU Doctoral Dissertations

Highly connected matroids are consistently useful in the analysis of matroid structure. Round matroids, in particular, were instrumental in the proof of Rota's conjecture. Chapter 2 concerns a class of matroids with similar properties to those of round matroids. We provide many useful characterizations of these matroids, and determine explicitly their regular members. Tutte proved that a 3-connected matroid with every element in a 3-element circuit and a 3-element cocircuit is either a whirl or the cycle matroid of a wheel. This result led to the proof of the 3-connected splitter theorem. More recently, Miller proved that matroids of sufficient …

Pesticide Partitioning In Louisiana Wetland Aand Ricefield Sediment, Brendan Michael Marsh

LSU Master's Theses

Pesticides are used globally and are often found within bodies of water. The EPA investigates the potential environmental impact through computer modeling in order to help mitigate some of the regulatory burden of pesticide fate investigation. Currently when pesticides enter a water body, the Exposure Analysis Modeling System (EXAMS) estimates partitioning depth as 5 cm and assumes equal distribution. This assumption was tested with a wide variety of pesticides with varying Koc ranges and water solubilities. Savillex 150 ml Teflon tubes were filled with wetland and ricefield sediments with fresh and seawater as the aqueous phase. The seven pesticides tested …

Fractal Shapes Generated By Iterated Function Systems, Mary Catherine Mckinley

LSU Master's Theses

This thesis explores the construction of shapes and, in particular, fractal-type shapes as fixed points of contractive iterated function systems as discussed in Michael Barnsley's 1988 book ``Fractals Everywhere." The purpose of the thesis is to serve as a resource for an undergraduate-level introduction to the beauty and core ideas of fractal geometry, especially with regard to visualizations of basic concepts and algorithms.

Option Volatility & Arbitrage Opportunities, Mikael Boffetti

LSU Master's Theses

This paper develops several methods to estimate a future volatility of a stock in order to correctly price corresponding stock options. The pricing model known as Black-Scholes-Merton is presented with a constant volatility parameter and compares it to stochastic volatility models. It mathematically describes the probability distribution of the underlying stock price changes implied by the models and the consequences. Arbitrage opportunities between stock options of various maturities or strike prices are explained from the volatility smile and volatility term structure.

A Contemporary Approach To A Classic Model: Exploring The Influence Of Local Interactions And Disturbance On Mangrove Forest Dynamics With A Spatially-Explicit Version Of Forman, Kieley Shannon Hurff

LSU Master's Theses

The mangrove forest gap dynamic model, FORMAN, was the first individual-based model (IBM) to simulate the long-term successional dynamics of three Caribbean mangrove species, Avicennia germinans, Laguncularia racemosa, and Rhizophora mangle. Assumptions under the spatially implicit approach of gap dynamic models limit their application to small-scale simulations. An expanded, spatially-explicit version of FORMAN was developed to allow for simulations of larger spatial grids, through the inclusion of localized soil conditions and neighborhood-based light resource competition. This expanded model was used to investigate the influence of localized interactions and disturbances of varying size on forest dynamics. A data-model comparison using field …

Evaluating Survival Of Released Ranched American Alligator In Coastal Louisiana, Kristy Durham Capelle

LSU Master's Theses

Since 1986, Louisiana’s American alligator (Alligator mississippiensis) ranching program has required the release of alligators produced from eggs collected from wild nests to maintain wild populations. This project assessed long-term harvest data (1991-2010s) to estimate survival of released alligators. First, wildlife and fishery harvest models and general inter-disciplinary survival models were evaluated to determine best fit to the data. Second, once the best fitting model was selected, release length, precipitation and temperature from release sites, and an index of hunter effort were added to investigate influences on survival estimates. Release length was included because over time the proportion and size …

Biomass Gasification For Electricity Generation: An Integrated Approach For Development Of Forest Residue-Based Projects In Rural India, Anand Mishra

LSU Doctoral Dissertations

Biomass gasification is generally regarded as a promising technology for various advanced application in energy production. Biomass is the only carbon-based sustainable option among the renewable energy sources. This study is focused on fostering biomass gasification for electricity generation sector in India. The study addresses four broad aspects of biomass gasification for electricity generation - feedstock properties and gasification technology, policy and regulatory framework governing the sector, financial evaluation of electricity generation from biomass gasification, and feedstock supply. The study is divided in four chapters, each of which addresses one aspect of electricity generation through biomass gasification. Based on literature, …

Dynamic Resonant Scattering Of Near-Monochromatic Fields, Gayan Shanaka Abeynanda

LSU Doctoral Dissertations

Certain universal features of photonic resonant scattering systems are encapsulated in a simple model which is a resonant modification of the famous Lamb Model for free vibrations of a nucleus in an extended medium. We analyze this "resonant Lamb model" to garner information on dynamic resonant scattering of near-monochromatic fields when an extended system is weakly coupled to a resonator. The transmitted field in a resonant scattering process consists of two distinct pathways: an initial pulse (direct transmission) and a tail of slow decay (resonant transmission). The resonant Lamb model incorporates a two-part scatterer attached to an infinite string with …

Riemann-Hilbert Formalism In The Study Of Crack Propagation In Domains With A Boundary, Aleksandr Smirnov

LSU Doctoral Dissertations

The Wiener-Hopf technique is a powerful tool for constructing analytic solutions for a wide range of problems in physics and engineering. The key step in its application is solution of the Riemann-Hilbert problem, which consists of finding a piece-wise analytic (vector-) function in the complex plane for a specified behavior of its discontinuities. In this dissertation, the applied theory of vector Riemann-Hilbert problems is reviewed. The analytical solution representing the problem on a Riemann surface, and a numerical solution that reduces the problem to singular integral equations, are considered, as well as a combination of the numerical and analytical techniques …

Structure And Dynamics Of Layered Transition Metal Compounds Driven By Broken Symmetry, Chen Chen

LSU Doctoral Dissertations

Correlated Electron Systems have attracted attention because of their complex phase diagrams that often contain several exotic phases that cannot be understood at all with traditional ideas. This is driven by the competition between many low-lying states, competing to be the ground state. That means by tuning parameters like temperature, pressure, magnetic _x000C_field, or doping concentration, one phase would be suppressed and another emerges. These phases are in such a delicate balance that they compete and interact with each other, and experimentally we can always find a way to alter this balance. In this work, two systems have been investigated: …

Dynamics Of Land Building And Ecological Succession In A Prograding Deltaic Floodplain, Wax Lake Delta, La, Usa, Azure Elizabeth Bevington

LSU Doctoral Dissertations

Deltas are globally important locations of diverse ecosystems, human settlement and economic activity that are threatened by reduced sediment delivery, accelerated sea level rise, and subsidence. In this dissertation I investigated a number of aspects of the ecosystem development over time within an actively prograding river dominated delta along the northern Gulf of Mexico coast. I outlined a conceptual model of deltaic floodplain wetland establishment and succession focused on the vegetated deltaic floodplain ecosystem, which includes subtidal, intertidal and supratidal zones. This was used to guide the experimental design and statistically driven hypothesis testing in order to ascertain the validity …

Thiol-Acrylate Polymerization Kinetics And Applications In Microfluidics, Michael Perrin Tullier

LSU Doctoral Dissertations

The reaction kinetics and some applications in the field of microfluidics for thiol-acrylate Michael addition polymerizations using multifunctional monomers have been researched and are presented here. The polymerization rate constants for base-catalyzed systems were found to increase with increasing thiol and acrylate functionality, which was attributed to the intramolecular interactions between functional groups. The nucleophile-initiated thiol-acrylate Michael addition polymerization kinetics were monitored via FTIR, and it was determined that the increase in the rate of reaction in these multifunctional systems was significantly less dramatic than the increase observed in monofunctional systems. While no radical polymerization was observed during most typical …

Synthesis And Characterization Of Polyhalogenated Boron Dipyrromethenes And Carboranylbisthiophene Oligomers, Ning Zhao

LSU Doctoral Dissertations

Chapter 1 of this dissertation shows a brief overview of fundamental concepts and classic synthetic routes of BODIPY dyes. The synthetic strategies and various application (e.g. PDT sensitizers and fluorescent indicators) of halogenated BODIPYs are also presented in this chapter. Chapters 2-4 describe the synthesis of three new polyhalogenated BODIPY platforms and their regioselective functionalization. Such new platforms provide new methodologies for producing both symmetric and asymmetric BODIPYs. Pd(0)-catalyzed cross-couplings and aromatic substitution reactions were applied to investigate the reactivity and regioselectivity of different halogen groups on the BODIPY platforms. The studies showed that the reactivity order of the halogens …

Design, Synthesis And Biological Applications Of Polypeptoids And Boron Dipyrromethenes, Sunting Xuan

LSU Doctoral Dissertations

The dissertation is about the design, synthesis and biological applications of polypeptoids and boron dipyrromethenes (BODIPYs). The dissertation is divided into seven chapters reporting various aspects of the background to my field of study and the results obtained during my PhD program. Chapter 1 is a concise overview of the fundamental concepts of polypeptoids and hydrogels, as well as their recent developments on synthetic strategies, property investigations, and biological applications in different fields. Chapter 2 presents the design, synthesis and potential application as tissue engineering scaffold of thermoreversible ABC polypeptoid hydrogels. A series of ABC copolypeptoids were synthesized and their …

Contemporary Organic Transformations Enabled By Novel Cationic Processes, Caitlan Elizabeth Ayala

LSU Doctoral Dissertations

This dissertation focuses on the development of synthetic methodologies in organic synthesis in two different areas. Chapter 1 discusses the more recent examples of transforming alcohols to their corresponding alkyl chlorides. The first area of our group’s research interest is the development of a mild chlorination method from unactivated alcohols, detailed in Chapter 2. Chapter 3 provides an insight into the history of oxyallyl cations, the basis of the second methodology development project in our laboratory. This chapter focuses on the traditional reactions that utilize these reactive intermediates, and it also showcases the concept of direct nucleophilic addition and the …

Comparison Of Advanced Radiotherapy Techniques For Post-Mastectomy Breast Cancer Patients, David Elward Heins

LSU Master's Theses

Purpose: To determine if bolus electron conformal therapy (BECT) combined with volumetric modulated arc therapy (VMAT) and flattening filter free volumetric modulated arc therapy (FFFVMAT (6x and 10x)) can maintain equal or better dose coverage than standard volumetric modulated arc therapy (VMAT) while reducing doses to organs at risk (OARs). Methods: BECT+VMAT, FFFVMAT (6x and 10x), and VMAT treatment plans were produced for ten post-mastectomy radiotherapy (PMRT) patients previously treated at our clinic. The treatment plans were created on a commercially available treatment planning system (TPS) and all completed treatment plans were reviewed and approved by a radiation oncologist. The …