Curve Tracking Control Under State Constraints And Uncertainties, Robert Kelly Sizemore

LSU Doctoral Dissertations

We study a class of steering control problems for free-moving particles tracking a curve in the plane and also in a three-dimensional environment, which are central problems in robotics. In the two-dimensional case, we provide adaptive controllers for curve tracking under unknown curvatures and control uncertainty. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature to form the augmented error dynamics. This nonlinear dependence puts our curvature identification objective outside the scope of existing adaptive tracking and parameter identification results that were limited to cases where the unknown parameters …

Non-Local Methods In Fracture Dynamics, Eyad Said

LSU Doctoral Dissertations

We first introduce a regularized model for free fracture propagation based on non-local potentials. We work within the small deformation setting and the model is developed within a state based peridynamic formulation. At each instant of the evolution we identify the softening zone where strains lie above the strength of the material. We show that deformation discontinuities associated with flaws larger than the length scale of non-locality $\delta$ can become unstable and grow. An explicit inequality is found that shows that the volume of the softening zone goes to zero linearly with the length scale of non-local interaction. This scaling …

Broadband Measurement And Reduction Of Quantum Radiation Pressure Noise In The Audio Band, Jonathan Daniel Cripe

LSU Doctoral Dissertations

One hundred years after Albert Einstein predicted the existence of gravitational waves in his general theory of relativity, the Laser Interferometer Gravitational-Wave Observatory (LIGO) made the first direct detection of gravitational waves. Since the first detection of gravitational waves from a binary black hole merger, LIGO has gone on to detect gravitational waves from multiple binary black hole mergers, and more recently from a binary neutron star merger in collaboration with telescopes around the world. The detection of gravitational waves has opened a new window to the universe and has launched the era of gravitational wave astronomy.

With the first …

An Evaluation Of The Utility Of A Mass-Weighted Frequency Distribution Of Sediment For Modeling Aeolian Transport Rates, Raihan Jamil

LSU Master's Theses

Predictions made by aeolian transport models often do not match well with measured data. The poor predictive capability of these models remains a fundamental problem in aeolian geomorphology. This study evaluates the effectiveness of the recently proposed mass-weighted frequency distribution (Edwards and Namikas 2015) and the apparent von Kármán parameter proposed by Li et al. (2010) to improve transport rate predictions. The evaluation consists of comparisons of predicted transport rates versus a large dataset of measured field and lab transport rates collected from the literature. The transport rate predictions are made both with and without recalibration of model empirical coefficients. …

Backstepping And Sequential Predictors For Control Systems, Jerome Avery Weston

LSU Doctoral Dissertations

We provide new methods in mathematical control theory for two significant classes of control systems with time delays, based on backstepping and sequential prediction. Our bounded backstepping results ensure global asymptotic stability for partially linear systems with an arbitrarily large number of integrators. We also build sequential predictors for time-varying linear systems with time-varying delays in the control, sampling in the control, and time-varying measurement delays. Our bounded backstepping results are novel because of their use of converging-input-converging-state conditions, which make it possible to solve feedback stabilization problems under input delays and under boundedness conditions on the feedback control. Our …

Invariant Of Noncommutative Algebras And Poisson Geometry, Bach Van Nguyen

LSU Doctoral Dissertations

In this dissertation, we describe the structure of discriminant of noncommutative algebras using the theory of Poisson quantization and ring theoretic properties of Poisson algebra. In particular, under appropriate conditions, we express the discriminant of specialization of K[q^{+-1}]-algebras as product of Poisson prime elements in some Poisson central subalgebra. In addition, we provide methods for computing noncommutative discriminant in various settings using results obtained for specialization of K[q^{+-1}]-algebras. Further, to demonstrate, we explicitly compute the discriminant of algebra of quantum matrices and quantum Schubert cell algebras specializing at roots of unity. This dissertation is part of the collaboration with Trampel …

Unavoidable Immersions And Intertwines Of Graphs, Matthew Christopher Barnes

LSU Doctoral Dissertations

The topological minor and the minor relations are well-studied binary relations on the class of graphs. A natural weakening of the topological minor relation is an immersion. An immersion of a graph H into a graph G is a map that injects the vertex set of H into the vertex set of G such that edges between vertices of H are represented by pairwise-edge-disjoint paths of G. In this dissertation, we present two results: the first giving a set of unavoidable immersions of large 3-edge-connected graphs and the second on immersion intertwines of infinite graphs. These results, along with …

Dimers On Cylinders Over Dynkin Diagrams And Cluster Algebras, Maitreyee Chandramohan Kulkarni

LSU Doctoral Dissertations

This dissertation describes a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well-studied case of dimer models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for Schubert cells in a symmetric Kac--Moody algebra give rise to dimer models on the cylinder over the corresponding Dynkin diagram. We also give an independent proof of a result of Buan, Iyama, Reiten and Smith that the corresponding superpotentials are rigid using the dimer model structure of the quivers.

New Platinum(Ii) And Rhenium(I) Complexes Of "Linear" Chelate Ligands Terminated With Pyridyl Or Imidazolyl N-Donor Groups, Himali Kokila Ranasinghe Pilana Vithanage

LSU Doctoral Dissertations

The overall goal of this dissertation research is to design, synthesize, and study new Pt(II) and Re(I) complexes relevant to biomedical applications. One of the projects involves the assessment of the interactions of bulky tridentate carrier ligands with a bound guanine nucleobase derivative (G) in platinum complexes, with a goal of developing chemistry potentially relevant to active anti-cancer Pt drugs. In another project, the fac-[Re^I(CO)₃]⁺ core is used to prepare novel Re(I) complexes with the purpose of developing new linking chemistry relevant to ^99mTc and ¹⁸⁷Re radiopharmaceuticals. This research explores …

Spectra Of Quantum Trees And Orthogonal Polynomials, Zhaoxia Wang

LSU Doctoral Dissertations

We investigate the spectrum of regular quantum-graph trees, where the edges are endowed with a Schr\"odinger operator with self-adjoint Robin vertex conditions. It is known that, for large eigenvalues, the Robin spectrum approaches the Neumann spectrum. In this research, we compute the lower Robin spectrum. The spectrum can be obtained from the roots of a sequence of orthogonal polynomials involving two variables. As the length of the quantum tree increases, the spectrum approaches a band-gap structure. We find that the lowest band tends to minus infinity as the Robin parameter increases, whereas the rest of the bands remain positive. Unexpectedly, …

Madden-Julian Oscillation Relationships With Cool Season Cyclogenesis, Daily Precipitation, And Cool Season Severe Weather Frequencies In The Gulf Of Mexico Region, Stephen Paul Caparotta

LSU Doctoral Dissertations

Tropical cyclone variability in the Gulf of Mexico (GoM) has been the focus of a considerable amount of research. Variability on both interannual scales, related to the El Niño-Southern Oscillation (ENSO), and on subseasonal scales, related to the Madden-Julian Oscillation (MJO), is well documented. By contrast, very little research exists on the relationships between the MJO and cool season, non-tropical cyclones in the GoM.

The MJO influence on cool season (October-March) cyclogenesis in the GoM variability is explored here. Additionally, daily precipitation variability and cool season severe weather variability is examined for areas near and just inland of the GoM. …

Free-Radical Polymerization Of Acid-Containing Deep Eutectic Solvents, Kylee Fazende

LSU Doctoral Dissertations

The forefront of this study explored polymerization, specifically thermally-initiated, free-radical frontal polymerization of (meth)acrylic acid monomers while the monomers acted as a hydrogen bond donor of a deep eutectic solvent. These frontal polymerizations were shown to exhibit unusual front velocities and, in some cases, lower front temperatures than the frontal polymerization of the neat monomers or systems containing inert analogs in the place of the hydrogen bond acceptor of these monomer-containing deep eutectic solvents. The frontal polymerization will occur with a range of initiator concentrations including ones that were too low for the pure monomer systems to sustain a front. …

Accelerated Broadband Spectra And Attosecond Charge Migration Simulations Using Real-Time Time-Dependent Density Functional Theory, Adam S. Bruner

LSU Doctoral Dissertations

In this dissertation, the calculations of light-matter interactions offer insight into the structure and dynamical response of electrons in molecular systems. Such information is useful for characterizing molecules, electronic structure, photochemistry, photomaterials, and a host of other applications. In the first part of this work, simulations of broadband absorption spectra are accelerated by the use of Pad´e approximanants of Fourier Transforms and dipole decomposition. Electronic absorption spectra from valence and core levels are obtained using time-dependent methods and compared to results from established perturbative techniques. In addition, core level absorption spectra are calculated for a nickel porphyrin and shown to …

Development Of A Slab-Based Monte Carlo Proton Dose Algorithm With A Robust Material-Dependent Nuclear Halo Model, John Wesley Chapman Jr

LSU Doctoral Dissertations

Pencil beam algorithms (PBAs) are often utilized for dose calculation in proton therapy treatment planning because they are fast and accurate under most conditions. However, as discussed in Chapman et al (2017), the accuracy of a PBA can be limited under certain conditions because of two major assumptions: (1) the central-axis semi-infinite slab approximation; and, (2) the lack of material dependence in the nuclear halo model. To address these limitations, we transported individual protons using a class II condensed history Monte Carlo and added a novel energy loss method that scaled the nuclear halo equation in water to arbitrary geometry. …

Visualization And Quantification Of Cancer-Associated Enzymes With Fluorescent Small-Molecule Substrate Probes, Zhenhua Shen

LSU Doctoral Dissertations

Fluorescence imaging can be used both as a tool to diagnose diseases and guide treatment in clinical settings, and as a technique to monitor dynamic events or biological species in basic research. Therefore, there is a great need for the development of a multitude of fluorescent probes that can be incorporated with fluorescence imaging techniques to track and report endogenous enzymes with high specificity and selectivity. In contrast to always-on and targeted always-on fluorescent probes that continually emit light, activity-based substrate probes either emit low numbers of photons or are completely quenched. They can be converted to highly fluorescent reporters …

Templates For Representable Matroids, Kevin Manuel Grace

LSU Doctoral Dissertations

The matroid structure theory of Geelen, Gerards, and Whittle has led to a hypothesis that a highly connected member of a minor-closed class of matroids representable over a finite field is a mild modification (known as a perturbation) of a frame matroid, the dual of a frame matroid, or a matroid representable over a proper subfield. They introduced the notion of a template to describe these perturbations in more detail. In this dissertation, we determine these templates for various classes and use them to prove results about representability, extremal functions, and excluded minors.

Chapter 1 gives a brief introduction …

Investigation Of Structure And Dynamics Of Deep Eutectic Solvent Using Infrared Spectroscopy, Yaowen Cui

LSU Doctoral Dissertations

Deep Eutectic Solvents (DES) are liquid mixtures prepared from solids. As a new class of green solvents, DES not only share many properties with ionic liquids, such as low volatility, conductivity, tailorable constituents, but also have some advantages over ionic liquids, like easier preparation, safe and inexpensive materials, biodegradability, low toxicity, and excellent solubility. Because of those attractive properties, DES has been studied in many scientific and engineering fields. However, compared with the great number of studies of the application, many questions about structure and dynamics of DES are unanswered. To shed light on the mystery of solvent or solvation …

Spatial Trends And Variability Of Marsh Accretion Rates In Barataria Basin, Louisiana, Usa Using 210pb And 137cs Radiochemistry, Samuel Bryant Shrull

LSU Master's Theses

Coastal Louisiana is presently experiencing large amounts of coastal land loss with estimated rates exceeding 50 km² lost per year. In an attempt to mitigate or reverse land loss, billions of dollars are earmarked for restoration projects that promote land reclamation, habitat stabilization, and defending against saline intrusion. This study was performed in an effort to better understand spatial trends of accretion rates in Barataria Basin in coastal Louisiana. Data for this project came from twenty-five shallow cores extracted over a broad span of the entire basin, from freshwater to saline environments. Cores were processed for ¹³⁷Cs and …

Two Results In Drawing Graphs On Surfaces, Joshua E. Fallon

LSU Doctoral Dissertations

In this work we present results on crossing-critical graphs drawn on non-planar surfaces and results on edge-hamiltonicity of graphs on the Klein bottle. We first give an infinite family of graphs that are 2-crossing-critical on the projective plane. Using this result, we construct 2-crossing-critical graphs for each non-orientable surface. Next, we use 2-amalgamations to construct 2-crossing-critical graphs for each orientable surface other than the sphere. Finally, we contribute to the pursuit of characterizing 4-connected graphs that embed on the Klein bottle and fail to be edge-hamiltonian. We show that known 4-connected counterexamples to edge-hamiltonicity on the Klein bottle are hamiltonian …

Glyphosate In Soils: Retention, Transport, And Effect Of Phosphate, Joshua Padilla

LSU Master's Theses

Glyphosate [N-(phosphonomethyl) glycine)] (GPS) is currently the most commonly used herbicide worldwide, and is generally considered as immobile in soils. However, numerous reports of the environmental occurrence of the herbicide coupled with recent evidence of human toxicity require further investigation as to the behavior of GPS in the soil environment. The objectives of this study were to quantify GPS sorption and mobility in two Louisiana agricultural soils with varying physiochemical properties; Commerce silt loam and Sharkey clay. Results of batch sorption studies indicated a high affinity of both soils for solvated GPS, with 24-hour Freundlich partitioning coefficients of 158 and …

Joint Geodetic And Seismic Analysis Of Englacial And Subglacial Hydraulic Effects On Surface Crevassing Near A Seasonal, Glacier-Dammed Lake On Gornergletscher, Switzerland, Louis Stephen Garcia

LSU Master's Theses

Glacial outburst floods are difficult to predict and threaten human life. These events are characterized by rapid draining of glacier-dammed lakes via the sub/englacial hydraulic network to the proglacial stream. The glacier-dammed lake on Gornergletscher in Switzerland, which fills and drains each summer, provides an opportunity to study this hazard. For three drainages (2004, 2006, and 2007), icequakes (IQ) are tracked as well as on-ice GPS movement. The seasonal seismic networks had 8 – 24 three-component stations and apertures of about 300 – 400 m on the glacier surface. The seasonal GPS arrays contained 4 – 8 GPS antennae on …

Shifting Niche Space In Coastal Landscapes: Spatio-Temporal Patterns Driving Submerged Aquatic Vegetation Across The Northern Gulf Of Mexico, Kristin Elise Demarco

LSU Doctoral Dissertations

Identifying distributions of submerged aquatic vegetation (SAV) across the northern Gulf of Mexico (NGOM) coastal landscape necessitates describing ecological processes in estuarine gradients. SAV assemblages are ecological indicators of aquatic ecosystem health; spatial and temporal distributions are strongly correlated to environmental conditions. Many wildlife species, including waterfowl, are dependent on SAV and seeds in NGOM coastal marshes for food and habitat. To understand SAV distributions at multiple spatial and temporal scales a multi-tiered project was designed to collect SAV presence, species assemblage, and cover data, and cores to describe seed food. The first tier sampled inter-annually in the growing seasons …

Micropaleontological Record Of A Preserved, Late Pleistocene Bald Cypress Forest On The Northern Gulf Of Mexico Inner Shelf, Jonathan Thien Truong

LSU Master's Theses

A cluster of previously buried Taxodium distichum stumps are exposed and preserved in growth position at the bottom of a trough on the inner Gulf of Mexico (GOM) continental shelf in 18 m water depth and 13 km offshore Orange Beach, AL. Radiocarbon ages from wood and optically stimulated luminescence (OSL) dating of sediments suggest a Marine Isotope Stage (MIS) 3 age, or older. This study builds on the previous work of Gonzalez (2018) and Obeclz (2017). Five biofacies were identified in vibracore collected in 2015 and 2016: 1) the Holocene Mississippi-Alabama-Florida (MAFLA) sand sheet, 2) a Holocene interbedded sand …

Mixed Categories Of Sheaves On Toric Varieties, Sean Michael Taylor

LSU Doctoral Dissertations

In [BGS96], Beilinson, Ginzburg, and Soergel introduced the notion of mixed categories. This idea often underlies many interesting "Koszul dualities." In this paper, we produce a mixed derived category of constructible complexes (in the sense of [BGS96]) for any toric variety associated to a fan. Furthermore, we show that it comes equipped with a t-structure whose heart is a mixed version of the category of perverse sheaves. In chapters 2 and 3, we provide the necessary background. Chapter 2 concerns the categorical preliminaries, while chapter 3 gives the background geometry. This concerns both some basics of toric varieties as well …

Investigating Trace Metal Sequestration Of Reducing Environments In Modern And Ancient Settings, Adam Charles Turner

LSU Doctoral Dissertations

The incorporation of trace metals into a variety of reducing sediments are important proxies for the oxic state of the water mass in which the sediments form. While much work has been done interpreting these proxies, questions remain on the exact processes and products in which trace metal proxies form. This work employs bulk geochemical techniques to investigate circulation in the Late Pennsylvanian North American Midcontinent Sea (NAMS), and then uses sequential extractions to further understand the chemical phases in which trace metals are incorporated. Sequential extractions are then used to further investigate how trace metals are sequestered in modern …

Endorectal Digital Prostate Tomosynthesis, Joseph Robert Steiner

LSU Doctoral Dissertations

Several areas of prostate cancer (PCa) management, such as imaging permanent brachytherapy implants or small, aggressive lesions, benefit from high image resolution. Current PCa imaging methods can have inadequate resolution for imaging these areas. Endorectal digital prostate tomosynthesis (endoDPT), an imaging method that combines an external x-ray source and an endorectal x-ray sensor, can produce three-dimensional images of the prostate region that have high image resolution compared to typical methods. This high resolution may improve PCa management and increase positive outcomes in affected men.

This dissertation presents the initial development of endoDPT, including system design, image quality assessment, and examples …

Single And Multiparameter Estimation Using Multimode Interferometry And Single Photons, Margarite L. Laborde

Honors Theses

No abstract provided.

Stratigraphic Reconstruction Of A Late Pleistocene Bald Cypress Forest Discovered On The Northern Gulf Of Mexico Continental Shelf, Suyapa Michell Gonzalez Rodriguez

LSU Master's Theses

A previously buried bald cypress forest (Taxodium distichum) was discovered on the continental shelf, offshore of Orange Beach, Alabama, USA, in ~20 m water depth. The forest was exhumed by Hurricane Ivan in 2004, and is now exposed as stumps in life position in a trough located in the northern Gulf of Mexico continental shelf seafloor. We are investigating the local stratigraphy, paleo-landscape, and mode of forest preservation of this unique site. In August 2015 and July 2016, submersible vibracores (18 in total) were collected. Core analysis included: bulk density and imaging via Geotek multi sensor core logger, …

Investigating Uranium Incorporation In Modern Carbonates By Sequential Extraction: Applied To The Permian - Triassic Boundary In Lung Cam, Vietnam, Christopher Michael Wray

LSU Master's Theses

The Uranium (U) isotopic system can be used to model the extent of global-scale ocean anoxia by utilizing the 238U/235U ratios as a paleo-redox indicator (δ238U). While recent studies have shown promise with the use of this novel proxy, variability is seen in modern carbonate sediment samples suggesting that more work is needed in order to understand elemental U uptake during early marine diagenesis. This thesis utilizes a sequential extraction methodology in order to understand the distribution of authigenic U within carbonate sediments.

This thesis consists of four parts, (1) an evaluation and modification of a sequential extraction methodology for …

Assessment Of Mercury Content In Louisiana's Freshwater Fish And Its Association To Se Concentrations, Alexander David Reyes-Avila

LSU Master's Theses

Ample evidence has demonstrated the neurotoxic properties of organic Hg to humans. However, recent studies have proposed the protective effects of Se against organic Hg detected in marine fish. Louisiana’s freshwater bodies are exploited by recreational anglers that enjoy fishing as recreational activity and food source. Thus, testing of Hg in Louisiana was resumed in 2017 to update the state advisories. However, before drawing conclusions based solely on organic Hg, it might be useful to see how much Se is present in freshwater fish. The main objective of this study was to determine the Se:Hg molar ratio in Louisiana’s freshwater …