Open Access. Powered by Scholars. Published by Universities.®

Digital Commons Network™

Open Access. Powered by Scholars. Published by Universities.®

LSU Doctoral Dissertations

Discipline
Keyword
Publication Year

Articles 91 - 120 of 2328

Full-Text Articles in Entire DC Network

Johann Georg Hamann And The Liberal Project, Jesse D. Ansley Jan 2025

Johann Georg Hamann And The Liberal Project, Jesse D. Ansley

LSU Doctoral Dissertations

This dissertation examines the political thought of Johann Georg Hamann, his relationship to liberalism, and the importance to modern concerns for consensus formation and intercultural dialogue. This contributes to the line of literature sparked by Isaiah Berlin debating the political legacy of Hamann and its relation to the development of modern politics. Berlin labels Hamann an anti-rationalist whose current developed into the ideology of the Nazi party. My work supports the countervailing arguments that Hamann’s work is importantly different from the Romantics he inspired and even more so from the Nazis. By examining two complete works and a number of …


Nanofabrication Of Tetraphenyl Porphyrin Surface Assemblies Linked With Tin Tetrachloride: A Scanning Probe Microscopy Investigation, Quynh Do Dec 2024

Nanofabrication Of Tetraphenyl Porphyrin Surface Assemblies Linked With Tin Tetrachloride: A Scanning Probe Microscopy Investigation, Quynh Do

LSU Doctoral Dissertations

Scanning probe microscopy (SPM) and colloidal lithography methods were used to study the covalent coupling of porphyrins to surfaces. In this dissertation, experimental methods for SPM operation, techniques, and applications are described. Measurement of tip-sample interactions between a sharp tip and surface is translated into digital image data maps with x-, y-, and z-data. Colloidal lithography can be used to fabricate test platforms for AFM studies. The periodicity and arrangement of the designed nanostructures is determined by the size of the colloidal particles used for surface masks. Data processing is required to obtain images and topography information from raw AFM …


Understanding Mechanisms For Coastal Marsh Sustainability In A Changing Climate, Ashley R. Booth Nov 2024

Understanding Mechanisms For Coastal Marsh Sustainability In A Changing Climate, Ashley R. Booth

LSU Doctoral Dissertations

In the Chenier Plain of Louisiana and Texas, coastal marshes are subject to high rates of relative sea level rise (RSLR), restricted sedimentation, and declining elevation attributed to subsidence and decades of intensive management. These marshes were created via mineral sedimentation but now largely accrete via organic matter accumulation. This organic matter accumulation (OMA) – or the balance between plant productivity and decomposition – is essential for maintaining elevation and thus long-term sustainability. However, management for elevation is complicated by a poor understanding of how abiotic factors like flooding and salinity impact processes driving OMA and elevation. To better understand …


Development Of Machine Learning-Based Tool For Prediction Of Long-Term Field Performance Of Asphalt Concrete Overlays In A Hot And Humid Climate, Elise Mansour Nov 2024

Development Of Machine Learning-Based Tool For Prediction Of Long-Term Field Performance Of Asphalt Concrete Overlays In A Hot And Humid Climate, Elise Mansour

LSU Doctoral Dissertations

The performance of pavement plays a critical role in Maintenance, Rehabilitation and Reconstruction (MR&R) for highway agencies. Reliable and accurate estimation of pavement performance can be instrumental in prioritization of the limited resources and funding for highway agencies. The latter requires robust prediction models that can handle large-scale, real-world data and can forecast pavement performance in the long run. Unfortunately, the traditional performance prediction models have raised concerns regarding their efficiency and accuracy. It is because these models were based on a limited number of explanatory variables, were not up-to-date and were designed for forecasting short-term (up to five years) …


Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou Nov 2024

Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou

LSU Doctoral Dissertations

Stochastic differential equations (SDEs) are essential for modeling systems influenced by both deterministic dynamics and random fluctuations, with applications in a wide variety of disciplines. This thesis develops a Bayesian framework for nonparametric learning in SDEs, addressing key challenges in inference, particularly when dealing with complex systems and incomplete data. The thesis begins by establishing a theoretical foundation in optimization over Hilbert spaces, including a generalized representer theorem to address infinite-dimensional optimization problems encountered in nonparametric inference. Building on this, we introduce a Bayesian framework with shrinkage priors to learn drift functions from high-frequency data. Bayesian approach incorporates low-cost sparse …


Coloring Trivalent Graphs: A Defect Tft Approach, Amit Kumar Oct 2024

Coloring Trivalent Graphs: A Defect Tft Approach, Amit Kumar

LSU Doctoral Dissertations

We show that the combinatorial matter of graph coloring is, in fact, quantum in the sense of satisfying the sum over all the possible intermediate state properties of a path integral. In our case, the topological field theory (TFT) with defects gives meaning to it. This TFT has the property that when evaluated on a planar trivalent graph, it provides the number of Tait-Coloring of it. Defects can be considered as a generalization of groups. With the Klein-four group as a 1-defect condition, we reinterpret graph coloring as sections of a certain bundle, distinguishing a coloring (global-sections) from a coloring …


Effects Of Longitudinal Training Walls On Two-Dimensional Flow Structure, Sediment Transport, And Bed Aggredation Using Numerical Methods And Sediment Core Analyses In Grand River, Michigan, Sumaiya Tul Siddique Oct 2024

Effects Of Longitudinal Training Walls On Two-Dimensional Flow Structure, Sediment Transport, And Bed Aggredation Using Numerical Methods And Sediment Core Analyses In Grand River, Michigan, Sumaiya Tul Siddique

LSU Doctoral Dissertations

Longitudinal training walls (LTWs) are structures oriented parallelly with the main flow and separate the channel into two sub-channels. One channel acts as the main navigational channel and the other is considered a secondary side channel. The long-term effects of the LTWs on morphodynamics and deposition remain poorly understood. This study investigated the long-term effects of the LTWs on flow, sediment transport and long-term deposition of the Grand River using numerical approaches and sediment core analysis. The effects of LTWs on 2D flow dynamics and sediment transport were investigated by using numerical approaches. The long-term deposition under the influence of …


The Role Of Siamese In G2 Checkpoint Regulation In Arabidopsis Thaliana, Martha A. Schwall Oct 2024

The Role Of Siamese In G2 Checkpoint Regulation In Arabidopsis Thaliana, Martha A. Schwall

LSU Doctoral Dissertations

Cyclin-cyclin dependent kinase (Cyclin-CDK) pairs regulate progression through the checkpoints of the cell cycle. They bind with some specificity and must be bound to for their regulative properties to be active. The presence of cyclin-CDKs is conserved throughout eukaryotes, while differences in specifics exist between yeast, animals, and plants. In Arabidopsis, SIAMESE (SIM) is a CDK inhibitor that restricts progression through mitosis. Overexpression of SIM is required for endoreplication in Arabidopsis trichomes, and overexpression of SIM results in increased endoreplication in leaf epidermal cells. SIM is expressed at high levels in the root elongation zone, where it plays a …


Exploring Pre-Service Teachers' Experiences With Emerging Technologies In Secondary Education: A Phenomenological Study, Richelle M. Decuir Oct 2024

Exploring Pre-Service Teachers' Experiences With Emerging Technologies In Secondary Education: A Phenomenological Study, Richelle M. Decuir

LSU Doctoral Dissertations

This research was an investigation of the role of emerging technologies in preparing pre-service teachers to engage with secondary learners effectively. A phenomenological approach was utilized to explore how instructional design models and constructivist learning theories shape technology training in two Southeastern public universities. The research was focused on pre-service teachers' experiences developing digital competencies, integrating instructional design, and utilizing emerging technologies in educational settings. Data was collected through semi-structured interviews and demographic surveys to understand the participants’ perspectives comprehensively. The study findings revealed that while pre-service teachers recognize the value of technology in enhancing student engagement and supporting personalized …


Enhancing Writing By Increasing Metacognitive Skills Through Socratic Seminars In A High Poverty Middle School Social Studies Classroom: An Intrinsic Case Study, Kirsten Hickingbottom Oct 2024

Enhancing Writing By Increasing Metacognitive Skills Through Socratic Seminars In A High Poverty Middle School Social Studies Classroom: An Intrinsic Case Study, Kirsten Hickingbottom

LSU Doctoral Dissertations

The purpose of this intrinsic case study was to better understand the role metacognitive skills play within classroom settings to increase students’ writing through Socratic Seminars. A predominant question guided this study: Can improving student metacognition through the repetitive use of questioning techniques in Socratic Seminars lead to improved writing skills? This question, along with four additional research questions guided the research. There is a need for more activities that promote metacognition due to its correlation with academic achievement, critical thinking skills, problem-solving abilities, and perceived self-efficacy (Keus, 2020). The significance of this study was to examine a method of …


Modern Lakeshore Processes And Historic Lake And Glacial Changes In Taylor Valley, Antarctica, Michael Stanley Stone Oct 2024

Modern Lakeshore Processes And Historic Lake And Glacial Changes In Taylor Valley, Antarctica, Michael Stanley Stone

LSU Doctoral Dissertations

Taylor Valley, which opens to the Ross Sea, is one of several ice-free valleys comprising the McMurdo Dry Valleys, Antarctica. The valley is home to several close-basin, perennially ice-covered lakes, whose lake levels largely reflect a balance between meltwater inputs and lake ice ablation; both being driven by climate. A dynamic environment exists where the lake ice covers meet the lakeshore, with the ice grounding to the substrate throughout the cold and dark of winter, and melting to form a perimeter of thin-to-no ice around the lake during the summer. These marginal freeze-thaw regions are known as moats. Here, physical, …


Multiscale & Multiphysics Model Of Damage In Lithium-Ion Batteries, Edris Akbari Oct 2024

Multiscale & Multiphysics Model Of Damage In Lithium-Ion Batteries, Edris Akbari

LSU Doctoral Dissertations

The demand for safer and more reliable lithium-ion batteries (LIBs) in electric vehicles has increased significantly, especially in addressing mechanical failures like internal short circuits (ISCs), which can lead to thermal runaway. This research investigates the mechanical behavior and damage mechanisms in lithium-ion pouch cells through a multiscale and multiphysics approach, focusing on Lithium Nickel Manganese Cobalt Oxide (NMC) and Lithium Iron Phosphate (LFP) batteries.

The study involved quasi-static and dynamic mechanical tests, including indentation and high-speed penetration, to evaluate stress-strain responses and fracture behaviors. Anisotropic mechanical properties were measured for individual battery components (anode, cathode, separator, and shell) using …


Examination Of Musical Sophistication And Working Memory Correlates In High School Students, Abby South Oct 2024

Examination Of Musical Sophistication And Working Memory Correlates In High School Students, Abby South

LSU Doctoral Dissertations

Abstract

The purpose of this study was to examine the relationship between musical engagement and cognitive ability in high school students. While musicians’ brains have long been of interest to those who study experience-dependent neuroplasticity, a lack of adolescent data grossly limits our understanding of the relationship between music training and observed neuroplastic changes in the brain. Advances in psychometric testing and brain imaging reveal relationships among musical expertise, changes in brain function, structure, and connectivity, and enhanced cognitive ability, but categorical groupings of dichotomously defined musicians and non-musicians prevent nuanced understanding of these complex relationships. In this study, 83 …


Effect Of Electronegativity On Environmentally Persistent Free Radical (Epfr) Formation, Persistence, And Toxicity On Transition Metal Oxides, Syed Monjur Ahmed Oct 2024

Effect Of Electronegativity On Environmentally Persistent Free Radical (Epfr) Formation, Persistence, And Toxicity On Transition Metal Oxides, Syed Monjur Ahmed

LSU Doctoral Dissertations

Environmentally persistent free radicals (EPFRs) are a group of emerging environmental pollutants. Owing to their resonance structures, EPFRs have significantly higher lifetimes than typical free radicals, and can induce the formation of reactive oxygen species (ROS) known to cause pulmonary and cardiovascular dysfunction. EPFRs form by the adsorption of organic precursors on a transition metal oxide (TMO) surface and exhibit enough stability to cause negative health and environmental effects. While aromatic and substituted aromatic precursors form EPFRs on TMO surface at elevated temperatures and numerous substituted organics are ubiquitous in various industrial processes and household products, studies have largely overlooked …


Coastal Sedimentary Records Of Extreme Events And Human Activity: Examples From Hurricanes And Microplastics, Nicholas T. Culligan Aug 2024

Coastal Sedimentary Records Of Extreme Events And Human Activity: Examples From Hurricanes And Microplastics, Nicholas T. Culligan

LSU Doctoral Dissertations

Coastal regions are uniquely vulnerable to a myriad of natural and anthropogenically caused stresses such as hurricane strikes and chronic microplastic pollution. Both hurricanes and microplastics have major negative effects on global coastlines and are forecast to become more damaging in the future. However, current model trends are based on limited modern data and may not provide an accurate or comprehensive view of the future. Therefore, this dissertation investigates coastal stratigraphic records to determine long-term past trends of these presses and pulses so that researchers, stakeholders, and policy makers can use them to enact strategies to mitigate damages from worsening …


Creating A Wholistic Manufacturing Score To Highlight The Effects Of Hidden Inefficiencies In Automated Manufacturing Caused By Soft Dedication And Preventative Maintenance Failures, Oded Tal Aug 2024

Creating A Wholistic Manufacturing Score To Highlight The Effects Of Hidden Inefficiencies In Automated Manufacturing Caused By Soft Dedication And Preventative Maintenance Failures, Oded Tal

LSU Doctoral Dissertations

The semiconductor industry is one of the most advanced manufacturing sectors, operating at an unparalleled scale and complexity. A new manufacturing facility costs between $500 million and $15 billion, and the industry's investment in automation is unmatched. However, the intricate and cyclical nature of semiconductor manufacturing creates very complex manufacturing facilities where the boundaries between planning and real-time operations often blur.

For the industry to keep improving, there is a need to create a new method that allows comparison among different manufacturing environments to uncover hidden losses that may be obscured by automation.

To better understand these hidden losses, the …


A Coarse-Grained Molecular Dynamics Study Of Gas Hydrate Formation And Dissociation, Meisam Adibifard Aug 2024

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

LSU Doctoral Dissertations

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


Constraining Giant Planet Occurrence Rates With The Multi-Band Imaging Survey For High-Alpha Planets (Mishaps) Observations Of 47 Tucanae, Alison Crisp Jul 2024

Constraining Giant Planet Occurrence Rates With The Multi-Band Imaging Survey For High-Alpha Planets (Mishaps) Observations Of 47 Tucanae, Alison Crisp

LSU Doctoral Dissertations

Though the confirmed exoplanet population has now reached over 5,500 planets, we still have a plethora of unanswered questions, e.g., regarding their formation mechanisms, true demographics, occurrence rates, and habitability. One remaining question is whether hot Jupiters formed in situ or migrated to their current orbits, so close to their host stars that their periods are 10 days or less. This question can potentially be answered by probing the effects of elemental abundances on hot Jupiter occurrence rates. These rates have been found to correlate with metallicity, but the specific elements responsible for the correlation have largely been unresolved. The …


Synthesis Of Portions Of An Acinetobacter Baumannii Lipooligosaccharide (Los), Brandon Conrad Jul 2024

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

LSU Doctoral Dissertations

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


Quantum Classical Algorithm For Solving The Hubbard Model Via Dynamical Mean-Field Theory, Anshumitra Baul Jul 2024

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

LSU Doctoral Dissertations

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


Novel Approaches To The Activation Of Chalcogenoglycosides For O-Glycosylation, Tiffany Duong Jul 2024

Novel Approaches To The Activation Of Chalcogenoglycosides For O-Glycosylation, Tiffany Duong

LSU Doctoral Dissertations

Carbohydrates are integral to various biological processes such as cell signaling, function and regulation. Carbohydrates also play critical roles in various disease and metastatic pathways. This has garnered considerable attention to the field of glycoscience, however, the study of carbohydrate-containing compounds remains a challenge due to the difficulty in obtaining pure samples from natural sources. As a result, the biological evaluation of carbohydrates relies on synthetic chemistry to produce pure compounds in significant quantities. However, the synthesis of carbohydrates present their own challenges owing to the complexity in controlling stereochemistry and regiochemistry. The most significant of these challenges is controlling …


Diving Deeper Into Supercuspidal Representations, Prerna Agarwal Jul 2024

Diving Deeper Into Supercuspidal Representations, Prerna Agarwal

LSU Doctoral Dissertations

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


Investigation Of Solvation Structures And Dynamics Of Li-Ion Battery Electrolytes And Amides In Water: An Infrared Spectroscopy, Electrochemical And Computational Study, Ernest O. Nachaki Jul 2024

Investigation Of Solvation Structures And Dynamics Of Li-Ion Battery Electrolytes And Amides In Water: An Infrared Spectroscopy, Electrochemical And Computational Study, Ernest O. Nachaki

LSU Doctoral Dissertations

The investigation of solvation structures and dynamics in lithium-ion battery electrolytes and amides in water has significant implications for both fundamental science and practical applications. Understanding the solvation dynamics of lithium electrolytes can lead to the development of safer and more efficient LIBs. The study of hydrogen bond dynamics of N-alkyl substituted amides has important implications for the development of thermos-responsive polymers used in biomedical applications. By understanding how N-alkyl substitutions affect the hydration structure and dynamics of amides, this research can inform the design of polymers with tailored properties for drug delivery, tissue engineering, and other medical applications. This …


Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, Zachary Jermain Jul 2024

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

LSU Doctoral Dissertations

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


Topics In Photonic Quantum Technology: Polarization Entanglement Dynamics In Optical Fibers And Low-Light Imaging., Pratik J. Barge Jul 2024

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

LSU Doctoral Dissertations

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


Riesz Particle Markov Chain Monte Carlo Methods, Xiongming Dai Jul 2024

Riesz Particle Markov Chain Monte Carlo Methods, Xiongming Dai

LSU Doctoral Dissertations

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


Advances In Stereoselective Glycosylation: Electron-Withdrawing Groups, Benzyne-Mediated Stereoinversion, And Visible-Light Photochemistry For 1,2-Cis O-Glycosylation, Erik Giovanni Alvarez Valenzuela Jul 2024

Advances In Stereoselective Glycosylation: Electron-Withdrawing Groups, Benzyne-Mediated Stereoinversion, And Visible-Light Photochemistry For 1,2-Cis O-Glycosylation, Erik Giovanni Alvarez Valenzuela

LSU Doctoral Dissertations

The symbiotic relationship between humans and their microbiota is essential for health, with imbalances in the complex microbiota ecosystem linked to a variety of disorders ranging from neurodegenerative to gastrointestinal diseases. Bacteria within the human microbiota, comprising over 1000 known species, are densely and diversely coated with oligosaccharides crucial for functions like cell recognition, communication, signaling, adhesion, proliferation, and pathogenic inhibition. However, studying the structure-activity relationships of these sugars which are also secreted by bacteria is challenging due to difficulties in obtaining homogenous samples from natural sources.

Chemical synthesis offers a solution by enabling the production of well-defined oligosaccharides in …


Elementary Science Teachers' Experiences: A Case Study On The Use Of Science+Cyber Curriculum, Laurie Salvail Jul 2024

Elementary Science Teachers' Experiences: A Case Study On The Use Of Science+Cyber Curriculum, Laurie Salvail

LSU Doctoral Dissertations

The field of science education in the United States has undergone a major reform since 2015. A little more than twelve years ago, work began on constructing a framework for elementary, middle, and high school science education. This framework emphasized the shift from science being merely a memorization of facts to experiences that include science and engineering practices applied through crosscutting concepts and focused on core ideas in the field of science. With new standards teachers also have to overcome a) not having adequate time available to devote to science instruction b) lack of updated instructional materials aligned to the …


Investigations And Characterization Of Loud Transient Noise In Advanced Ligo Detectors, Shania Nichols Jul 2024

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

LSU Doctoral Dissertations

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

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


Higher Order Operator Splitting Schemes With Complex Coefficients And Applications, Arun Banjara Jul 2024

Higher Order Operator Splitting Schemes With Complex Coefficients And Applications, Arun Banjara

LSU Doctoral Dissertations

The goal of this dissertation is to apply the concept of Lie generators for linear semigroups induced by nonlinear flows, originally developed by J. R. Dorroh and J. W. Neuberger in the 1990’s [15], to approximate solutions of initial value problems like

x′(t) = F(x(t)), x(0) = x0, (1)

where F = (F1,··· ,FN), and Fi : RN ⊃ Ω -> RN. The method, sometimes referred to as ``Bernard Koopman’s Global Linearization Method,” traces its origins back to the works of Sophus Lie in the 1890’s [30], Gerhard Kowalewski in …