Physical Sciences and Mathematics Commons^™

Large Deviations For Stochastic Navier-Stokes Equations With Nonlinear Viscosities, Ming Tao

LSU Doctoral Dissertations

In this work, a Wentzell-Freidlin type large deviation principle is established for the two-dimensional stochastic Navier-Stokes equations (SNSE's) with nonlinear viscosities. We fi_x000C_rst prove the existence and uniqueness of solutions to the two-dimensionalstochastic Navier-Stokes equations with nonlinear viscosities using the martingale problem argument and the method of monotonicity. By the results of Varadhan and Bryc, the large deviation principle (LDP) is equivalent to the Laplace-Varadhan principle (LVP) if the underlying space is Polish. Then using the stochastic control and weak convergence approach developed by Budhiraja and Dupuis, the Laplace-Varadhan principle for solutions of stochastic Navier-Stokesequations is obtained in appropriate function …

On Identifying Critical Nuggets Of Information During Classification Task, David Sathiaraj

LSU Doctoral Dissertations

In large databases, there may exist critical nuggets - small collections of records or instances that contain domain-specific important information. This information can be used for future decision making such as labeling of critical, unlabeled data records and improving classification results by reducing false positive and false negative errors. In recent years, data mining efforts have focussed on pattern and outlier detection methods. However, not much effort has been dedicated to finding critical nuggets within a data set. This work introduces the idea of critical nuggets, proposes an innovative domain-independent method to measure criticality, suggests a heuristic to reduce the …

Application Of Helmholtz/Hodge Decomposition To Finite Element Methods For Two-Dimensional Maxwell's Equations, Zhe Nan

LSU Doctoral Dissertations

In this work we apply the two-dimensional Helmholtz/Hodge decomposition to develop new finite element schemes for two-dimensional Maxwell's equations. We begin with the introduction of Maxwell's equations and a brief survey of finite element methods for Maxwell's equations. Then we review the related fundamentals in Chapter 2. In Chapter 3, we discuss the related vector function spaces and the Helmholtz/Hodge decomposition which are used in Chapter 4 and 5. The new results in this dissertation are presented in Chapter 4 and Chapter 5. In Chapter 4, we propose a new numerical approach for two-dimensional Maxwell's equations that is based on …

Reef Fish Demographics On Louisiana Artificial Reefs : The Effects Of Reef Size On Biomass Distribution And Foraging Dynamics, Kirsten A. Simonsen

LSU Doctoral Dissertations

Understanding the role that habitat plays in the life history of reef-associated fishes is particularly significant given the dramatic increase in the number of artificial reefs deployed in coastal ecosystems over the past 50 years. In the Gulf of Mexico, the oil and gas industry has added a significant amount of structure to the Louisiana continental shelf, creating the largest de facto artificial reef deployment area in the world. Noting their usefulness as fish habitat, the Louisiana Artificial Reef Program was established to convert decommissioned platforms into artificial reefs. However, very little quantitative information exists on how these habitats affect …

Oligomers Of Beta-L-Arabinosides Of Hydroxyproline : Synthesis Of The Carbohydrate Epitope Of The Art V 1 Allergen, Ning Xie

LSU Doctoral Dissertations

The pollen of mugwort is a major contributor to hay fever in Europe and North America. The chemical structure of Art v 1, the major allergen of mugwort, has been elucidated. A notable motif in Art v 1 – characterized by clusters of contiguous â-arabinosides of hydroxyproline – was found to be a key recognition element for antibodies generated in response to the natural protein. This dissertation details the chemical synthesis of oligomers of â-arabinosides of hydroxyproline and the search to establish the minimal carbohydrate epitope of Art v 1. The â-arabinoside motif, being a 1,2-cis glycoside, presents a considerable …

Molecular-Level Investigations Combining Nanoscale Lithography And Atomic Force Microscopy, Chamarra Karmelia Saner

LSU Doctoral Dissertations

In this dissertation, nanostructures of octadecyltrichlorosilane (OTS) and were prepared using particle lithography and evaluated using characterizations with atomic force microscopy (AFM). The nanostructures of OTS were used as a resist for patterning fibronectin, an extracellular matrix protein. Particle lithography provides a practical and reproducible approach to generate billions of nanostructures comprised of organic thin films or nanomaterials. A film of mesospheres can be applied as a surface mask to define the periodicity and size of nanopatterns using processes of self-assembly. A close-packed arrangement of mesospheres is produced spontaneously when monodisperse solutions of latex or silica are dried on a …

Complexity-Driven Properties Of The Intermetallic Compounds Gd₁₁₇Co₅₆Sn₁₁₂ And Ln₃₀Ru₄Sn₃₁ (Ln = Gd And Tb), Devin Charles Schmitt

LSU Doctoral Dissertations

Understanding the relationships between the structure of materials and their properties in extended solid systems is a necessity when intuitively designing functional materials. One of the most fundamental properties of a material is its ability to transport heat, which is linked to the lattice complexity of the material. Here, the single crystalline materials Gd117Co56Sn112 and Tb30Ru4Sn31 are grown to study the pronounced effect of a complexity-driven reduction of lattice thermal conductivity. The transport and magnetic properties of Gd117Co56Sn112 and Ln30Ru4Sn31 (Ln = Gd and Tb) are also presented and related to other systems. Tb30Ru4Sn31 is found to be a large …

Exploring The Learnability Of Numeric Datasets, Di Lin

LSU Doctoral Dissertations

When doing classification, it has often been observed that datasets may exhibit different levels of difficulty with respect to how accurately they can be classified. That is, there are some datasets which can be classified very accurately by many classification algorithms, and there also exist some other datasets that no classifier can classify them with high accuracy. Based on this observation, we try to address the following problems: a)what are the factors that make a dataset easy or difficult to be accurately classified? b) how to use such factors to predict the difficulties of unclassified datasets? and c) how to …

Finite Element Methods For Fourth Order Variational Inequalities, Yi Zhang

LSU Doctoral Dissertations

In this work we study finite element methods for fourth order variational inequalities. We begin with two model problems that lead to fourth order obstacle problems and a brief survey of finite element methods for these problems. Then we review the fundamental results including Sobolev spaces, existence and uniqueness results of variational inequalities, regularity results for biharmonic problems and fourth order obstacle problems, and finite element methods for the biharmonic problem. In Chapter 2 we also include three types of enriching operators which are useful in the convergence analysis. In Chapter 3 we study finite element methods for the displacement …

Studies Of Core-Shell Nanogumbos And Liposomal Ionogels, Ashleigh Renee' Wright

LSU Doctoral Dissertations

The work presented in this dissertation is a description of novel core-shell nanomaterials derived from a group of uniform materials based on organic salts (GUMBOS) and the synthesis and characterizations of novel liposomal ionogels (LIGs). These GUMBOS are an extension of ionic liquids (ILs) which are organic salts with melting points between 25 °C and 100 °C. Ionic liquids have high thermal stability, low vapor pressure, and tunable physiochemical and functional properties. All of the properties of ILs are controlled by the chosen cation and anion pair. Similarly to ILs, GUMBOS possess the same qualities; however, they have melting points …

Cyclic Block Copolypeptoids : Synthesis, Self-Assembly And Macroscopic Properties, Chang-Uk Lee

LSU Doctoral Dissertations

This dissertation presents the first experimental efforts for synthesizing a new class of peptidomimetic polymers, cyclic block copolypeptoids, studying their self-assembly in dilute solution, and examining their macroscopic properties. Cyclic poly(N-methyl-glycine)-b-poly(N-decyl-glycine) (PNMG-b-PNDG) diblock copolymers were synthesized via sequential, N-heterocyclic carbene (NHC)-mediated ring-opening polymerization of NCA monomers with controlled chain length and compositions. Cryo-TEM shows that PNMG105-b-PNDG10 copolymers in methanol (1 mg/mL) form spherical micelles that organize to form cylindrical micelles over time. The formation of cylindrical micelles is attributed to the crystallization of PNDG chains, as revealed by SAED and microDSC analyses. Cyclic PNMG100-b-PNDG10 copolymers form thermo-reversible, free-standing gels at …

The Ring Theory And The Representation Theory Of Quantum Schubert Cells, Joel Benjamin Geiger

LSU Doctoral Dissertations

In recent years the quantum Schubert cell algebras, introduced by Lusztig and De Concini--Kac, and Procesi, have garnered much interest as this versatile class of objects are furtive testing grounds for noncommutative algebraic geometry. We unify the two main approaches to analyzing the structure of the torus-invariant prime spectra of quantum Schubert cell algebras, a ring theoretic one via Cauchon's deleting derivations and a representation theoretic characterization of Yakimov via Demazure modules. As a result one can combine the strengths of the two approaches. In unifying the theories, we resolve two questions of Cauchon and Mériaux, one of which involves …

Luminescence Studies : Part I. Lanthanide Nanogumbos Part Ii. Near Infrared Photothermal Nanogumbos, Jonathan Carver Dumke

LSU Doctoral Dissertations

Group of Uniform Materials Based on Organic Salts (GUMBOS) are a class of molten salts that have been focused to be specifically tailored towards applications. Primitively, from Davy to Walden molten salts were desirable for organic synthesis due to the properties. GUMBOS have been synthesized into nanoparticles (nanoGUMBOS) by various methods to be used for lanthanide luminescence and hyperthermal cancer therapeutics. Lanthanide photochemistry has been frequently studied for its high luminescence intensity, narrow emission band, and stable luminescent lifetime decay. Aerosol-derived europium nanoGUMBOS were characterized using electron microscopy (39.5 ± 8.4 nm), XPS, and spectroscopic techniques. Spectroscopic measurements indicated intense …

A Characterization Of Almost All Minimal Not Nearly Planar Graphs, Kwang Ju Choi

LSU Doctoral Dissertations

In this dissertation, we study nearly planar graphs, that is, graphs that are edgeless or have an edge whose deletion results in a planar graph. We show that all but finitely many graphs that are not nearly planar and do not contain one particular graph have a well-understood structure based on large Möbius ladders.

Study On The Performance Of Tcp Over 10gbps High Speed Networks, Cheng Cui

LSU Doctoral Dissertations

Internet traffic is expected to grow phenomenally over the next five to ten years. To cope with such large traffic volumes, high-speed networks are expected to scale to capacities of terabits-per-second and beyond. Increasing the role of optics for packet forwarding and transmission inside the high-speed networks seems to be the most promising way to accomplish this capacity scaling. Unfortunately, unlike electronic memory, it remains a formidable challenge to build even a few dozen packets of integrated all-optical buffers. On the other hand, many high-speed networks depend on the TCP/IP protocol for reliability which is typically implemented in software and …

Detection Of Microorganisms Using Maldi And Ion Mobility Mass Spectrometry, Juaneka Monet Hayes

LSU Doctoral Dissertations

Matrix-assisted laser ablation desorption ionization MALDI and ion mobility (IM) MALDI mass spectrometry (MS) were used for the detection and identification of microorganisms. MALDI MS is an analytical tool that separates ions by their mass-to-charge ratio (m/z) and is routinely used for bioanalysis because of its sensitivity, selectivity, general applicability, and tolerance to impurities. Ion mobility is a gas phase technique that separates ions based on their charge and collision cross-section. In this research, MALDI-TOF MS and MALDI-IM-TOF MS analysis were conducted in parallel to assess the effectiveness of MALDI-IM-TOF MS for microorganism identification. Whole cell bacteria Escherichia coli strain …

Structural And Synthesis Studies Of The Pro¹⁴³ Region Skp1 In Dictyostelium Discoideum, Chamini V. Karunaratne

LSU Doctoral Dissertations

In Skp1 of Dictyostelium discoideum (Dd), Pro143 is located at the N-terminus of an α-helix with four consecutive Glu residues immediately following Pro. Preceeding Pro143 is a segment of random coil. The proline residue undergoes post-translational modifications: hydroxylation and glycosylation. A cytoplasmic prolyl hydroxylase (P4H1) delivers a hydroxyl group to Pro143 and N-acetylglucosamine transferase 1 (Gnt1) transfers GlcNAc from UDP to Hyp143 of Skp1. The installation of the first GlcNAc residue in Skp1 in Dictyostelium is important for the organism to differentiate into a fruiting body to disperse spores. We describe herein some structural and synthesis studies of the Pro143 …

Depositional History Of The Trinity-Tiger Shoals Region : A Transgressed Delta Complex Of The Middle Holocene Mississippi Delta, Clint Hoyt Edrington

LSU Doctoral Dissertations

The Holocene Mississippi River Delta is arguably the world’s most thoroughly researched deltaic system. However, much of this research has occurred predominantly within the present-day subaerial delta, whereas comparatively little research has been attempted downdip within the offshore, more difficult-to-reach parts. This study advances our understanding of the Holocene delta by examining deltaic sediments within the Trinity-Tiger Shoals Complex region, located ~ 30 – 40 km offshore of central Louisiana. Specifically, this study addresses two questions. Which delta complex prograded into this offshore region? Do the overlying transgressive deposits reflect that predicted by the prevailing transgressive depositional systems model? To …

Higher Algebraic K-Theory And Tangent Spaces To Chow Groups, Sen Yang

LSU Doctoral Dissertations

In this work, using higher algebraic K-theory, we provide an answer to the following question asked by Green-Griffiths in [13]: Can one define the Bloch-Gersten-Quillen sequence G_j on infinitesimal neighborhoods X_j so that Ker(G₁ &rarr G₀)= TG₀, Here TG₀ should be the Cousin resolution of TK_m(O_X) and X is any n-dimensional smooth projective variety over a field k, chark=0. Our main results are as follows. The existence of G_j is discussed in chapter 3, following [8] and [18]. The main theorems are theorem5.2.5, theorem 5.2.6 and theorem …

Numerical Investigations Of Holstein Phonons On The Periodic Anderson Model, Peng Zhang

LSU Doctoral Dissertations

In condensed matter physics, the idea of localized magnetic moments and the scattering of conduction electrons by those local moments are of central importance not only for explaining the transport of electrons at low temperature region but also for developing the related models and theories to extend our understanding of novel physics like non-conventional superconductor, quantum phase transition and non-Fermi liquid behavior. In the first chapter of this work, I will look back at the discovery of Kondo scattering, the introduction of Anderson impurity scenario, the extension to lattice version of the Anderson impurities, the periodic Anderson model, and how …

A Multi-Scale Investigation Of Nutrient Dynamics In The Lake Pontchartrain Estuary And Basin, Eric Daniel Roy

LSU Doctoral Dissertations

Humans are responsible for global-scale alteration of nitrogen (N) and phosphorus (P) biogeochemical cycles to support food production. Increases in N and P inputs into soils and waste-streams has resulted in excessive nutrient loading to surface waters, including the Mississippi River, leading to eutrophication. Here I investigated N and P dynamics occurring in the Lake Pontchartrain Estuary and Basin. I measured two biogeochemical processes using intact sediment core incubations and quantified their importance in the context of nutrient-rich Mississippi River flood diversions through the Bonnet Carré Spillway. I show that diffusion of nitrate-N into sediments accounts for a substantial magnitude …

Amplifying Conjugated Polymers For Fluorescent Chemosensing, Deepa Pangeni

LSU Doctoral Dissertations

Chemo- and biosensors based on fluorescent conjugated polymers benefit from greater detection sensitivity due to amplification of the electronic perturbations produced by analyte binding. This amplification stems from the exciton-transporting properties of conjugated polymers. In the conventional sensor design paradigm, excitons migrate from the bulk of the polymer to the analyte binding sites which can be either fluorescence quenching sites (turn-off sensors) or lower energy fluorophores (turn-on sensors). In this dissertation, we proposed an alternative design paradigm when analyte binding creates a higher energy gap site in the polymer backbone. In the case of isolated polymer chains in dilute solution, …

Scanning Probe Investigations Of The Surface Self-Assembly Of Organothiols And Organosilanes Using Nanoscale Lithography, Tian Tian

LSU Doctoral Dissertations

Particle lithography and scanning probe lithography were applied to study the kinetics and mechanisms of surface self-assembly processes. Organothiols on Au(111) and organosilane on Si(111) were chosen as model systems for investigations at the nanoscale using atomic force microscopy (AFM). Fundamental insight of structure/property interrelationships and understanding the properties of novel materials are critical for developments with molecular devices. Methods using an AFM probe for nanofabrication have been applied successfully to prepare sophisticated molecular architectures with high reproducibility and spatial precision. The established capabilities of AFM-based nanografting were reviewed for inscribing patterns of diverse composition, to generate complicated surface designs …

Magnetic Deflections Of Ultra-High Energy Cosmic Rays From Centaurus A, Azadeh Keivani

LSU Doctoral Dissertations

The origin and mass composition of ultra-high energy cosmic rays (UHECRs) are among the mysteries of particle astrophysics. Since UHECRs are mostly or entirely charged particles, they will be deflected in cosmic magnetic fields on their way to Earth. UHECR deflections in the Galactic magnetic fields (GMF) should be considered to identify their origin and nature.

The calculated Galactic magnetic deflections of UHECRs from a source strongly depend on the GMF model. I use the recent GMF model of Jansson and Farrar (JF12), a 35-parameter model which includes coherent, striated and random components and is constrained by WMAP7 Galactic synchrotron …

Coupling Between Spin, Lattice, And Charge At The Surface Of Complex Transition Metal Compounds, Guorong Li

LSU Doctoral Dissertations

Understanding and controlling the complexity that develops in complex transition metal compounds such as high-Tc superconductivity, "colossal" magnetoresistance in manganites, and heavy-fermion compounds, is one of the grand challenges of the 21st century. The exotic properties displayed by these compounds are closely related to the coexistence of nearly degenerate states, coupling simultaneously several active degrees of freedom such as the charge, lattice, orbital, and spin. In this work, we have focused on two systems, one is the newly discovered Fe-based superconducting compounds ((Ba, Ca)(Fe1-xCox)2As2, FeTe1-xSex) and the other one is the doped Ruddleden-Popper (RP) ruthenates (Sr3(Ru1-xMnx)2O7). The materials community was …

Toward The Advancement Of Tetraphosphine Ligand Synthesis For Homogeneous Bimetallic Catalysis, Marc Anthony Peterson

LSU Doctoral Dissertations

A tetraphosphine ligand rac-et,ph-P4 (Et2PCH2CH2(Ph)PCH2P(Ph)CH2CH2PEt2) is used for the formation of a highly active and regioselective bimetallic hydroformylation catalyst. The proposed active catalytic species in acetone, [Rh2H2(µ-CO)2(rac-et,ph- P4)]2+, is formed in situ under H2/CO pressure. This is one of the most impressive examples of cooperativity in homogeneous catalysis. The fragmentation of this catalyst by CO has been investigated and confirmed by in situ NMR spectroscopic studies. A new tetraphosphine ligand rac-et,ph-P4-Ph (et,ph-P4-Ph = Et2P(o-C6H4)P(Ph)CH2(Ph)P(o-C6H4)PEt2) has been synthesized to combat this fragmentation problem. However, the inability to successfully separate the meso and racemic diastereomers led to the attempted alteration of the …

Polymer Microsystems For The Enrichment Of Circulating Tumor Cells And Their Clinical Demonstration, Joyce W. Kamande

LSU Doctoral Dissertations

Cancer research is centered on the discovery of new biomarkers that could unlock the obscurities behind the mechanisms that cause cancer or those associated with its spread (i.e., metastatic disease). Circulating tumor cells (CTCs) have emerged as attractive biomarkers for the management of many cancer-related diseases due primarily to the ease of securing them from a simple blood draw. However, their rarity (~1 CTC per mL of whole blood) makes enrichment analytically challenging. Microfluidic systems are viewed as exquisite platforms for the clinical analysis of CTCs due to their ability to be used in an automated fashion, minimizing sample loss …

A Hybrid Framework Of Iterative Mapreduce And Mpi For Molecular Dynamics Applications, Shuju Bai

LSU Doctoral Dissertations

Developing platforms for large scale data processing has been a great interest to scientists. Hadoop is a widely used computational platform which is a fault-tolerant distributed system for data storage due to HDFS (Hadoop Distributed File System) and performs fault-tolerant distributed data processing in parallel due to MapReduce framework. It is quite often that actual computations require multiple MapReduce cycles, which needs chained MapReduce jobs. However, Design by Hadoop is poor in addressing problems with iterative structures. In many iterative problems, some invariant data is required by every MapReduce cycle. The same data is uploaded to Hadoop file system in …

On-The-Fly Tracing For Data-Centric Computing : Parallelization, Workflow And Applications, Lei Jiang

LSU Doctoral Dissertations

As data-centric computing becomes the trend in science and engineering, more and more hardware systems, as well as middleware frameworks, are emerging to handle the intensive computations associated with big data. At the programming level, it is crucial to have corresponding programming paradigms for dealing with big data. Although MapReduce is now a known programming model for data-centric computing where parallelization is completely replaced by partitioning the computing task through data, not all programs particularly those using statistical computing and data mining algorithms with interdependence can be re-factorized in such a fashion. On the other hand, many traditional automatic parallelization …

Microfluidics For The Analysis Of Integral Membrane Proteins: A Top-Down Approach, Katrina Nychole Battle

LSU Doctoral Dissertations

The development of fully automated and high-throughput systems for proteomics is now in demand because of the need to generate new protein-based disease biomarkers. Unfortunately, it is difficult to identify protein biomarkers that are low abundant when in the presence of highly abundant proteins, especially in complex biological samples like serum, cell lysates, and other biological fluids. Membrane proteins, which are in many cases of low abundance compared to cytosolic proteins, have various functions and can provide insight into the state of disease and serve as targets for new drugs making them attractive biomarker candidates. Traditionally, proteins are identified through …