Physical Sciences and Mathematics Commons^™

On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai

Mathematical Sciences Undergraduate Honors Theses

In this paper, I will discuss a partial differential equation that has solutions that are discontinuous. This example motivates the need for distribution theory, which will provide an interpretation of what it means for a discontinuous function to be a “solution” to a PDE. Then I will give a detailed foundation of distributions, including the definition of the derivative of a distribution. Then I will introduce and give background on the Navier-Stokes equations. Following that, I will explain the Millennium Problem concerning global regularity for the Navier-Stokes equations and share mathematical results regarding weak solutions. Finally, I will go over …

Differential Elliptic Flow Analysis Of Hadrons With Different Wuark Content In Simulated Pp Collisions, Elhussein Osama

Theses and Dissertations

According to current physics theories, it is assumed that in the first microsecond after the big bang, the universe was in a state of matter called Quark-Gluon Plasma (QGP), where the fundamental consistent of matters (quarks and leptons), were highly energetic, and floating around freely. Searching for such phase of matter; as the possible earliest signatures after the big bang, and among many other interesting experimental measurements, the jet quenching and elliptic flow are the most important ones, in the heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) experiments.

The azimuthal anisotropy …

Positron Emission Tomography In Oncology And Environmental Science, Samantha Delaney

Dissertations, Theses, and Capstone Projects

The last half century has played witness to the onset of molecular imaging for the clinical assessment of physiological targets. While several medical imaging modalities allow for the visualization of the functional and anatomical properties of humans and living systems, few offer accurate quantitation and the ability to detect biochemical processes with low-administered drug mass doses. This limits how physicians and scientists may diagnose and treat medical issues, such as cancer, disease, and foreign agents.

A promising alternative to extant invasive procedures and suboptimal imaging modalities to assess the nature of a biological environment is the use of positron emission …

Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas

Dissertations, Theses, and Capstone Projects

This four-chapter dissertation studies the efficient discretization of continuous variable functions with tensor train representation. The first chapter describes all the methodology used to discretize functions and store them efficiently. In this section, the algorithm tensor renormalization group is explained for self-containment purposes. The second chapter centers around the XY model. Quantics tensor trains are used to describe the transfer matrix of the model and compute one and two-dimensional quantities. The one dimensional magnitudes are compared to analytical results with an agreement close to machine precision. As for two dimensions, the analytical results cannot be computed. However, the critical temperature …

Modeling And Dynamics Of Capillary Bridges, Moyosore Odunsi

Dissertations, Theses, and Capstone Projects

Capillary bridges are ubiquitous in nature and have important implications in processes like inkjet printing. They are an important area of study not only because of their industrial applications but because many of the questions in capillary bridge research are applicable to other systems. For example, they exhibit pinning and unpinning patterns that are similar to those in sliding droplets. The rules underlying this pinning are essential to predicting liquid shapes and understanding how contact lines move across surfaces. Many previous studies have focused on axisymmetric capillary bridges and neglected to model the tangential forces that arise due to asymmetry. …

Signal Processing Algorithms For Doppler Lidar Sensors, Samantha Grubb

Physics and Astronomy Honors Papers

Light detection and ranging (LiDAR) is a remote sensing technology that obtains relative distance and velocity measurements between a sensor and a defined target by using light transmitted and received from the target. FMCW Doppler LiDAR, a particular variant of LiDAR, functions by analyzing the frequency shift in the reflected light to determine the target's range and velocity. This technology plays a crucial role across various sectors including defense, aerospace, and automotive. This paper presents signal processing algorithms designed to optimize data obtained from Doppler LiDAR sensors. By applying various window functions to time domain data, the Signal-to-Noise Ratio (SNR) …

Evaluation Of An End-To-End Radiotherapy Treatment Planning Pipeline For Prostate Cancer, Mohammad Daniel El Basha, Court Laurence, Carlos Eduardo Cardenas, Julianne Pollard-Larkin, Steven Frank, David T. Fuentes, Falk Poenisch, Zhiqian H. Yu

Dissertations & Theses (Open Access)

Radiation treatment planning is a crucial and time-intensive process in radiation therapy. This planning involves carefully designing a treatment regimen tailored to a patient’s specific condition, including the type, location, and size of the tumor with reference to surrounding healthy tissues. For prostate cancer, this tumor may be either local, locally advanced with extracapsular involvement, or extend into the pelvic lymph node chain. Automating essential parts of this process would allow for the rapid development of effective treatment plans and better plan optimization to enhance tumor control for better outcomes.

The first objective of this work, to automate the treatment …

The Analysis Of Mechanical Exfoliation Of Graphene For Various Fabrication And Automation Techniques, Lance Yarbrough

Mechanical Engineering Undergraduate Honors Theses

Mechanical Exfoliation of Graphene is an often-overlooked portion of the fabrication of quantum devices, and to create more devices quickly, optimizing this process to generate better flakes is critical. In addition, it would be valuable to simulate test pulls quickly, to gain insight on flake quality of various materials and exfoliation conditions. Physical pulls of graphene at various temperatures, pull forces, and pull repetitions were analyzed and compared to the results of ANSYS simulations, solved for similar results. Using ANSYS’ ability to predict trends in exfoliations, flake thickness and coverage using stress and deflection analyses were investigated. Generally, both strongly …

Encapsulated 2d Materials And The Potential For 1d Electrical Contacts, Sarah Wittenburg

Physics Undergraduate Honors Theses

The utilization of two-dimensional materials and heterostructures, particularly graphene and hexagonal boron nitride, have garnered significant attention in the realm of nanoelectronics due to their unique properties and versatile functionalities. This study focuses on the synthesis and fabrication processes of monolayer graphene encapsulated between layers of hBN, aiming to explore the potential of these heterostructures for various electronic applications. The encapsulation of graphene within hBN layers not only enhances device performance but also shields graphene from environmental contaminants, ensuring long-term stability. Experimental techniques, including mechanical exfoliation and stamp-assisted transfer, are employed to construct three-layer stacks comprising hBN-graphene-hBN. The fabrication process …

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations & Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …

Divergence-Free Tensor Densities In Two Dimensions, Tyler Hansen

All Graduate Theses and Dissertations, Fall 2023 to Present

In physics, a common method for exploring the way a physical system changes over time is to look at the system’s energy. Roughly speaking, the energy in these systems are either motion-based (kinetic energy, a bullet in flight) or position-based (potential energy, a rock sitting at the top of a hill). The difference between the system’s total kinetic and potential energies is quantified by an expression called the Lagrangian. Using a special procedure, this Lagrangian is massaged to produce a group of equations called the Euler-Lagrange equations; if the initial configuration of the system is provided, the solution to these …

A Comprehensive Investigation Of The Influence Of Geometric Structure On The Shape Memory Performance Of Nafion, Jade Thomas

Physics Undergraduate Honors Theses

While perfluorosulfonic acid (PFSA) membranes have primarily been used in fuel cells due to their chemical, thermal, and mechanical stability, one PFSA, Nafion, boasts two unique characteristics: a broad glass transition (~55 °C to 130 °C) and a temperature-persistent electrostatic network. The combination of these two characteristics endows Nafion with exceptional shape memory properties – the ability of a material to morph and transform into pre-programmed shapes when exposed to an external stimulus – with enhanced permanent shape memorization, and a potentially near-infinite number of temporary shape memorization. This study focused on expanding the base of knowledge surrounding Nafion’s shape …

A Comprehensive Investigation Of The Influence Of Geometric Structure On The Shape Memory Performance Of Nafion, Jade Thomas

Mechanical Engineering Undergraduate Honors Theses

While perfluorosulfonic acid (PFSA) membranes have primarily been used in fuel cells due to their chemical, thermal, and mechanical stability, one PFSA, Nafion, boasts two unique characteristics: a broad glass transition (~55 °C to 130 °C) and a temperature-persistent electrostatic network. The combination of these two characteristics endows Nafion with exceptional shape memory properties – the ability of a material to morph and transform into pre-programmed shapes when exposed to an external stimulus – with enhanced permanent shape memorization, and a potentially near-infinite number of temporary shape memorization. This study focused on expanding the base of knowledge surrounding Nafion’s shape …

Improving The Scalability Of Neural Network Surface Code Decoders, Kevin Wu

Undergraduate Honors Theses

Quantum computers have recently gained significant recognition due to their ability to solve problems intractable to classical computers. However, due to difficulties in building actual quantum computers, they have large error rates. Thus, advancements in quantum error correction are urgently needed to improve both their reliability and scalability. Here, we first present a type of topological quantum error correction code called the surface code, and we discuss recent developments and challenges of creating neural network decoders for surface codes. In particular, the amount of training data needed to reach the performance of algorithmic decoders grows exponentially with the size of …

Classification Of Topological Defects In Cosmological Models, Abigail Swanson

Student Research Submissions

In nature, symmetries play an extremely significant role. Understanding the symmetries of a system can tell us important information and help us make predictions. However, these symmetries can break and form a new type of symmetry in the system. Most notably, this occurs when the system goes through a phase transition. Sometimes, a symmetry can break and produce a tear, known as a topological defect, in the system. These defects cannot be removed through a continuous transformation and can have major consequences on the system as a whole. It is helpful to know what type of defect is produced when …

Towards A Practical Method For Monitoring Kinetic Processes In Polymers With Low-Frequency Raman Spectroscopy, Robert Vito Chimenti

Theses and Dissertations

Unlike liquids and crystalline solids, glassy materials exist in a constant state of structural nonequilibrium. Therefore, a comprehensive understanding of material kinetics is critical for understanding the structure-property-processing relationships of polymeric materials. Amorphous materials universally display low-frequency Raman features related to the phonon density of states resulting in a broad disorder band for Raman shifts below 100 cm-1, which is related to the conformational entropy and the modulus. This disorder band is dominated by the Boson peak, a feature due to phonon scattering because of disorder and can be related to the transverse sound velocity of the material, and a …

The Black-To-White Hole Transition, Farshid Soltani

Electronic Thesis and Dissertation Repository

Classically, an isolated black hole is a stable gravitational object. If however semiclassical effects are taken into account, an isolated black hole can be shown to slowly radiate its mass away in a process called evaporation. At the end of the evaporation process, when the size of the horizon becomes Planckian, the quantum nature of the gravitational field can no longer be neglected and the dynamics of the horizon is governed by quantum gravity. The main objective of this thesis is the systematic investigation of a tentative scenario for the “end of the life” of a black hole: the black-to-white …

Luminescence And Structural Properties Of Silicon-Germanium Quantum Structures Fabricated By Ion Implantation, Matheus Coelho Adam

Electronic Thesis and Dissertation Repository

The advancement of semiconductor materials has played a crucial role in driving positive technological breakthroughs that impact humanity in numerous ways. The presence of defects significantly alters the physical properties of semiconductors, making their analysis essential in the fabrication of semiconductor devices. I presented a new method to quantify surface and near-surface defects in single crystal semiconductors. Epitaxially-grown silicon was measured by low energy electron diffraction (LEED) to obtain the surface Debye temperature (θ_D). The results showed the surface θ_D of bulk Si (001), 1.0 μm, and 0.6 μm Si on sapphire of 333 K, 299 K, …

All-Optical Probes Of Particle-Like Charge Migration Dynamics, Kyle A. Hamer

LSU Doctoral Dissertations

Particle-like charge migration (CM) is the coherent, back-and-forth motion of a positively-charged electron hole along the backbone of a molecule following a sudden ionization. CM in small molecules generally occurs on an Angstrom (10^-10 m) spatial scale and an attosecond (10^-18 s) timescale. I use time-dependent density-functional theory (TDDFT) to simulate CM modes in organic molecules, and to explore all-optical probes of this attosecond electron dynamics using high-harmonic spectroscopy (HHS). By leveraging my results from previous studies of two-center interferences in carbon dichalcogens, in which I separated the harmonic signal into contributions from individual Kohn-Sham orbitals, I first …

Post-Modeling Adjustments And Delivered Dose Verification Of The 6fff Beam Model Commissioned For The Monaco Treatment Planning System, Grant C. Debevec

LSU Master's Theses

External beam radiation therapy has been shown to be an effective treatment method for tumors and abnormalities of the spine and vertebral region. Treating the spine using a stereotactic body radiation therapy (SBRT) technique can reduce toxicity to the spinal cord. The 6 MV flattening filter free (6FFF) beam model is currently used to plan and calculate dose for SBRT treatment plans, and the treatment plans are delivered using a linear accelerator (LINAC).

The commissioned beam model represents an invariant component of a LINAC. For volumetric modulated arc therapy (VMAT) treatment plans, the multileaf collimator (MLC) positions are changing throughout …

Predicting Biomolecular Properties And Interactions Using Numerical, Statistical And Machine Learning Methods, Elyssa Sliheet

Mathematics Theses and Dissertations

We investigate machine learning and electrostatic methods to predict biophysical properties of proteins, such as solvation energy and protein ligand binding affinity, for the purpose of drug discovery/development. We focus on the Poisson-Boltzmann model and various high performance computing considerations such as parallelization schemes.

Generation, Dynamics, And Interaction Of Quartic Solitary Waves In Nonlinear Laser Systems, Sabrina Hetzel

Mathematics Theses and Dissertations

Solitons are self-reinforcing localized wave packets that have remarkable stability features that arise from the balanced competition of nonlinear and dispersive effects in the medium. Traditionally, the dominant order of dispersion has been the lowest (second), however in recent years, experimental and theoretical research has shown that high, even order dispersion may lead to novel applications. Here, the focus is on investigating the interplay of dominant quartic (fourth-order) dispersion and the self-phase modulation due to the nonlinear Kerr effect in laser systems. One big factor to consider for experimentalists working in laser systems is the effect of noise on the …

Low Cost Magnetometer Calibration And Distributed Simultaneous Multipoint Ionospheric Measurements From A Sounding Rocket Platform, Joshua W. Milford

Doctoral Dissertations and Master's Theses

Low-cost and low-size-weight-and-power (SWaP) magnetometers can provide greater accessibility for distributed simultaneous measurements in the ionosphere, either onboard sounding rockets or on CubeSats. The Space and Atmospheric Instrumentation Laboratory (SAIL) at Embry-Riddle Aeronautical University has launched a multitude of sounding rockets in recent history: one night-time mid-latitude rocket from Wallops Flight Facility in August 2022 and three mid-latitude rockets from White Sands Missile Range during the October 2023 annular solar eclipse. All rockets had a comprehensive suite of instruments for electrodynamics and neutral dynamics measurements. Among this suite was one science-grade three-axis fluxgate magnetometer (Billingsley TFM65VQS / TFM100G2) and up …

Modeling And Numerical Analysis Of The Cholesteric Landau-De Gennes Model, Andrew L. Hicks

LSU Doctoral Dissertations

This thesis gives an analysis of modeling and numerical issues in the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We derive various time-step restrictions for a (weighted) $L^2$ gradient flow scheme to be energy decreasing. Furthermore, we prove a mesh size restriction, for finite element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers that is not well-known in the LC literature, particularly when simulating cholesteric LCs that exhibit ``twist''. Furthermore, we perform a computational exploration of the model and present several numerical simulations in 3-D, on both slab geometries and spherical …

Investigation Of Gas Dynamics In Water And Oil-Based Muds Using Das, Dts, And Dss Measurements, Temitayo S. Adeyemi

LSU Master's Theses

Reliable prediction of gas migration velocity, void fraction, and length of gas-affected region in water and oil-based muds is essential for effective planning, control, and optimization of drilling operations. However, there is a gap in our understanding of gas behavior and dynamics in water and oil-based muds. This is a consequence of the use of experimental systems that are not representative of field-scale conditions. This study seeks to bridge the gap via the well-scale deployment of distributed fiber-optic sensors for real-time monitoring of gas behavior and dynamics in water and oil-based mud. The aforementioned parameters were estimated in real-time using …

Characterizing And Mitigating Transient Noise In Ligo Observatories For Gravitational Wave Detection, Jane Glanzer

LSU Doctoral Dissertations

The existence of gravitational waves is predicted by Albert Einstein's Theory of General Relativity. Commonly referred to as "ripples in spacetime", these waves are generated by some of the most violent and energetic processes in the universe. Despite their theoretical prediction over a century ago, it wasn't until 2015 that the Advanced LIGO (aLIGO) interferometers in Hanford, WA and Livingston, LA directly detected gravitational waves for the first time, confirming Einstein's theory and ushering in a new era of astrophysics.

Detecting gravitational waves requires incredible precision. Because of the extreme sensitivity required, it is possible for the gravitational wave data …

Quantum Chaos, Integrability, And Hydrodynamics In Nonequilibrium Quantum Matter, Javier Lopez Piqueres

Doctoral Dissertations

It is well-known that the Hilbert space of a quantum many-body system grows exponentially with the number of particles in the system. Drive the system out of equilibrium so that the degrees of freedom are now dynamic and the result is an extremely complicated problem. With that comes a vast landscape of new physics, which we are just recently starting to explore. In this proposal, we study the dynam- ics of two paradigmatic classes of quantum many-body systems: quantum chaotic and integrable systems. We leverage certain tools commonly employed in equilibrium many-body physics, as well as others tailored to the …

Spectroscopic End Point Detection With An Electron Beam Evaporator, Ryan Mcgraw

University Honors Theses

Spectroscopic end point detection is a common tool used for measuring slope changes in wavelength intensity. Using algorithms able to apply this concept, coatings will be able to be dynamically measured in real time and stopped at the appropriate level to ensure process uniformity. It is currently applied to reductive processes such as etching, where the surface will start to be eaten away, creating a plasma. When the entire amount of a material on a substrate has been eaten away, the plasma will change color as it is beginning to etch a different material. Using a spectrometer, this point where …

Development Of An Integrated Workflow For Nucleosome Modeling And Simulations, Ran Sun

Doctoral Dissertations

Nucleosomes are the building blocks of eukaryotic genomes and thus fundamental to to all genetic processes. Any protein or drug that binds DNA must either cooperate or compete with nucleosomes. Given that a nucleosome contains 147 base pairs of DNA, there are approximately 4^147 or 10^88 possible sequences for a single nucleosome. Exhaustive studies are not possible. However, genome wide association studies can identify individual nucleosomes of interest to a specific mechanism, and today's supercomputers enable comparative simulation studies of 10s to 100s of nucleosomes. The goal of this thesis is to develop and present and end-to-end workflow that serves …

The Interplay Of Spin, Charge, And Heat: From Metal/Insulator Heterostructures To Perovskite Bilayers, Sam M. Bleser

Electronic Theses and Dissertations

In this dissertation begin with an investigation of non-local spin transport in an amorphous germanium (a-Ge) sample via the inverse spin Hall effect (ISHE). In that study we show that commonly used techniques such as differential conductance and delta mode of a paired Keithley 6221/2182a for non-local resistance measurements can lead to false indicators of spin transport. Next, we turn out attention to a thickness dependent study in thermally-evaporated chromium (Cr) thin films on a bulk polycrystalline yttrium-iron-garnet (YIG) substrate. This project analyzed the spin transport in the Cr films versus thickness via the longitudinal spin Seebeck effect (LSSE). This …