Digital Commons Network^™

Brst Conserved Moments For Fluids, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

This note adds a missing proof for an assertion in the original paper Gauge Invariance and Repeated Time Isolated Solution Discontinuities.

The assertion is that under weak limits and within a constant energy isosurface, enstrophy is conserved up to losses due to viscous dissipation.

According to the BRST theory for quantum Yang-Mills fields, the conserved moments are exactly those with infinite vacuum expectation values. Application of the BRST theory to fluids is explored. The BRST restriction to the loop expansion (fixed space) is justified by the reqirement that a perturbative expansion can be constructed. In this case the theory predicts …

Mathematicly Rigorous Quantum General Relativity, I: Pure, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

A pure general relativity (quantum or classical) is one lacking in matter. Such a field has a Lorentzian space time geometry. A renormalization perturbative expansion, truncated to all finite orders, establishes both the quantum and the general relativity theory with full mathematical rigor.

Weak Solutions Of The Navier-Stokes Equation And Their Euler Limits, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

The existence of a weak solution of the incompressible isothermal Navier-Stokes equation with given initial conditions in the Sobolev space $\mathcal{H}_{-2}$ for energy fluctuations and in $\mathcal{H}_{-3}$ for enstrophy fluctuations is assumed. The existence is uniform with respect to the Euler limit of zero viscosity $\nu$. Thus, existence of weak solutions of the Euler equation with given initial conditions is established, and these Euler solutions are the zero viscosity limit of Navier-Stokes solutions, provided the Navier-Stokes solutions exist.

Mathematicly Rigorous Quantum General Relativity, I: Pure, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

A pure quantum general relativity field is one lacking in matter. Such a field has a Lorentzian space-time geometry. A renormalized perturbation expansion, truncated to all finite orders, establishes  the existence of pure quantum general relativity with full mathematical rigor

The Pure Yang-Mills Field. I: Eistence, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

Two pure Yang-Mills quantum gauge field theories are constructed, one based on short distance asymptotics and the other based on long distance asymptotics.

The construction is based on the axial gauge, ghost states, the BRST framework and Gribov extension of the Hamiltonian, with a loop expansion cutoff to all finite orders for the dynamics.

The construction is established by renormalized perturbation theory to all finite orders.

The construction depends on an assumed principle of a maximum rate of entropy production

The Pure Yang-Mills Field, \, Iia: The Axioms, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

A previously constructed pure Yang-Mills quantum gauge field theory is shown to satisfy all Osterwalder Schrader axioms.

Non-Smooth Solutions Of The Navier-Stokes Equation And Their Means, James Glimm, Jarret Petrillo

Department of Applied Mathematics & Statistics Faculty Publications

Non-smooth (finite time blowup) Leray-Hopf solutions of the incompressible Navier-Stokes equation are constructed. The initial data for blowup is characterized by nonzero energy related turbulent fluctuations. The construction occurs in a finite periodic cube T3. The mean value of a weak solution of the Navier-Stokes equation is identified as a smooth solution of the Navier-Stokes equation.

Scaling Laws, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

Scaling laws, accurate to all orders and for intermediate times, are constructed for Navier-Stokes and Euler fluids and for quantum Yang-Mills fields. A maximum entropy principle is assumed. A finite periodic spatial volume is assumed.

Conventional renormalization group scaling is accurate to all orders in a large time asymptotic limit, but it fails at intermediate times at less than leading order due to blowups and a possible resetting of the gauge group.

The extension to quantum general relativity is indicated.

The Pure Yang-Mills Field: Repeated Blowups, James Glimm, James G. Glimm

Department of Applied Mathematics & Statistics Faculty Publications

The temporal scaling of the quantum Yang-Mills solution is characterized by analytic solutions for a limited time interval, each ended by a discontinuity (blowup).

For general initial conditions, there will be a series of blowups and a possible resetting of the gauge group..

The principle of a maximum rate of entropy production is assumed. A finite periodic spatial volume is assumed.

The Boson Yang-Mills Field: The Loop Expansion, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

This paper demonstrates convergence of the loop expansion for Yang-Mills fields.

The loop construction of perturbation theory is based on the axial gauge, ghost states, the BRST framework and the Gribov extension of the Hamiltonian, with the loop expansion perturbatively renormalizable.

The construction is established by renormalized perturbation theory convergent to all finite orders.

Two distinct Yang-Mills theories are constructed, one based on short distance asymptotics and the other based on long distance asymptotics.

The construction depends on an assumed principle of a maximum rate of entropy production.

The paper has sufficient generality to include existence for all cases that …

The Pure Yang-Mills Field: Axioms And The Mass Gap, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

The infinite volume limit is constructed based on previously constructed finite volume pure Yang-Mills quantum gauge field theories. For this limit theory, Osterwalder-Schrader axioms are verified and the existence of a mass gap in the energy spectrum is proven.

Requirements for the Millennium Yang-Mills prize are fulfilled.

Prevention Beyond Deterrence, Benjamin A. Barsky

Faculty Scholarship

This Article reconceptualizes preventive justice—the public safety paradigm that seeks to prevent harm before it occurs. Scholars have long documented how cities have advanced this paradigm through largely punitive measures, notably variants of broken windows policing, which posit that aggressive misdemeanor enforcement deters more serious crime. Yet in the aftermath of the 2020 George Floyd protests, and as underscored recently in City of Grants Pass v. Johnson, these measures have faced a legitimacy crisis—prompting calls for nonpunitive responses to nonviolent incidents.

This Article establishes a preventive justice approach that advances health and safety without emphasizing crime deterrence. It draws on …

Privacy’S Autonomy Thicket: Disentangling Choice, Consent And Control, Jordan Francis, Woodrow Hartzog, Neil Richards

Faculty Scholarship

When it comes to talking about autonomy, privacy law could use a little clarity. Its discourse uses terms like “choice,” “consent,” and “control” to evoke autonomy, but these terms are too rarely defined and too often used interchangeably, even though they can mean very different things. The three terms have become entangled in a way that has become confusing and counterproductive. We call this problem “privacy’s autonomy thicket,” and it matters because it encourages talking past each other in policy debates, enabling the redefinition of these terms in misleading ways that produce weak and disempowering “notice and choice” regimes.

In …

Regulating Crisis Pregnancy Centers After Nifla And Dobbs: Controversies Over When Government Is Imposing An Orthodoxy About Abortion, Linda C. Mcclain

Faculty Scholarship

How does this broader sense of Barnette’s proscription of government from imposing “what shall be orthodox” implicate governmental restrictions on reproductive autonomy? Battles over reproductive freedom centrally implicate objections that government is unconstitutionally imposing a gender orthodoxy. Arguments for a right of personal autonomy embodying an antitotalitarian principle of liberty are arguments for a right to resist governmental imposition of an orthodoxy— for example, an idea about the natural or traditional role of women as mothers together with a view about how best to respect the sanctity of life. Rights to reproductive autonomy, grounded in personal autonomy and equality, …

Match Or Mismatch? : The Effects Of Fingerprint Evidence And Expert Testimony On Jury Decisions, Kassie N. Thallas

Dissertations

Fingerprint evidence is widely perceived as objective and reliable, yet is typically presented to jurors through expert testimony rather than directly evaluated. The present study examined how fingerprint match status and expert testimony influence juror decision-making. Participants (N = 225) read a mock criminal trial summary and were randomly assigned to one of five conditions. Four conditions were derived by crossing Expert Condition (fingerprint expert alone vs. conflicting experts) and Match Status (match vs. no match), with an additional control condition without fingerprint evidence. The participants made verdict decisions and rated the credibility, honesty and believability of the expert. The …

Investigation Of A Flux Compression Magnetic Nozzle For Pulsed Plasma Propulsion, Zachary K. White

Dissertations

A key part of any propulsion system is how the energy of the propellants is used for thrust. Because of the high temperatures of nuclear fusion plasma, traditional methods like guiding the propellant with walls are not feasible, so instead, electromagnetic forces must be used to avoid physical contact between the propellant and the vehicle. Usually, to do so the physical nozzle is replaced by a magnetic nozzle where the physical walls are replaced by magnetic fields. This thesis focuses on the direct imaging and probe measurements of a laser produced plasma expanding into a magnetic field as analogous event …

Exploring Detached Concern, A Dual-Process Emotional-Regulation Strategy, Among Intensive Care Nurses Providing End-Of-Life Care In The United States, Melissa Milton Miasek

Dissertations

Intensive care unit (ICU) nurses repeatedly provide end-of-life care (EoLC) and experience significant emotional distress, burnout, and moral distress that can lead to leaving the profession. Detached concern (DC), a dual-process emotional-regulation strategy which balances empathetic concern with emotional detachment, may support ICU nurses' emotional well-being; however, DC among nurses remains vastly understudied. This qualitative descriptive study gained deeper understanding of DC among ICU nurses providing EoLC in the United States. The study was guided by a conceptual model adapting Lampert and Glaser's dynamic DC process within Elfenbein's emotional regulation framework. The overarching research question explored ICU nurses' perspectives on …

Development Of An Analytic Method For Approximating Jet Formation From Hemispherical Shaped Charge Liners, Drew Champion Marable

Dissertations

This effort investigates and details the collapse and jet formation process of a constant wall thickness hemispherical shaped charge liner. Upon interaction with a detonation wave, liner elements are ejected and converge toward an assumed uniform collapse location. By conserving mass, momentum, and treating the liner as an incompressible perfect fluid, a novel set of equations to predict the characteristics of a layered jet is presented. The use of Gurney formulas to describe the initial collapse velocity of a liner enables a fully self-contained, analytic method for predicting jet properties originating from a hemispherical-lined shaped charge. A base theory describing …

A Hierarchical, Data-Driven Analytical Paradigm For Strategic Planning, Operational Decision-Making, And Resilience Enhancement In United States Electric Power Systems Under Extreme Demand Conditions, Anyama Hanson Tettey

Dissertations

Historical evidence indicates that the United States electric power grid continues to face persistent criticism for reliability challenges during peak demand conditions. Extreme ambient temperatures are a primary driver of such peaks, rendering the grid most vulnerable precisely when electricity demand is highest. These demand surges are largely driven by coincident operation of heating, ventilation, and air-conditioning systems across customer classes, a trend expected to intensify as sectors such as transportation increasingly rely on electrification. Efforts to mitigate demand related unreliability have traditionally focused on system-level demand forecasting and planning, typically at the scale of cities or entire utilities. However, …

Threatened To Testify : Juror Perceptions Of Coercive Eyewitness Interviews, Alexa A. Mecikalski

Dissertations

The effects of coercive investigative questioning techniques have been extensively studied in the context of suspect interrogations; however, few studies have evaluated outcomes related to coercive questioning of eyewitnesses. Therefore, the present study investigated mock juror perceptions of the use of interrogation tactics during eyewitness questioning. Participants read a trial summary and provided trial judgments (e.g., verdict, eyewitness credibility, perceived coerciveness of the interview) pertaining to a case in which an eyewitness is questioned using either (1) maximization tactics (e.g. high pressure questioning, threats), (2) minimization tactics (e.g., minimizing severity or consequences), or (3) no tactics (e.g., statement provided voluntarily). …

Thermodynamic Properties Of Cluster Outskirts, Leo Moraczewski

Dissertations

We present the temperature, density, entropy, and pressure profiles of the intracluster mediums of eight galaxy clusters observed out to the virial radius with complete azimuthal coverage by the Suzaku X-ray space telescope. Suzaku’s low background was vital to probing the lower x-ray surface brightness of cluster outskirts that could not be studied by X-ray telescopes such as Chandra and XMM-Newton which have a higher background level. The eight clusters being examined are the last observed out to the virial radius by Suzaku that have not had their properties published. As all eight clusters have complete azimuthal coverage, we also …

Rocket Injector Flowfield Characterization Through Local, Instantaneous Gas Composition Tracing Using Laser Induced Breakdown Spectroscopy, Michaela Renee Hemming

Dissertations

Laser induced breakdown spectroscopy (LIBS) was developed for applications in the characterization of rocket engine injectors to evaluate the instantaneous, local gas concentration, or local mixture ratio of the injector flowfield. In this work, LIBS was tested in steady flows of premixed methane and air to create the correlation of the LIBS spectral species ratios H/O ratio, followed by a steady non-premixed flow to extract the localized mixing and shape of the flow field, then a transient study was performed to measure the development of the flow of the reactants in a pentad impingement injector previously used in RDE tests. …

Thermal Analysis Of The Fiber Fuse Effect, John Seekins

Dissertations

The fiber fuse effect is a self-sustaining damage propagation mechanism that can occur in the core of optical fibers. Under sufficient levels of applied power, laser light is absorbed as heat in the fiber. This phenomenon is characterized by a brightly glowing spot in the fiber that propagates towards the source of laser light at about 1 𝑚/𝑠. A numerical simulation of the fiber fuse effect is developed that solves the transient heat equation with source terms in cylindrical coordinates utilizing an explicit finite difference discretization. For the first time in a simulation of this type, a radiation transport equation …

Diffusion Behavior Of Uranium Fission Products In A Centrifugal Nuclear Thermal Rocket, Mitchell Schroll

Dissertations

Centrifugal nuclear thermal rockets (CNTR) are an advanced concept engine first proposed in the 1950’s that would allow for specific impulses of up to 1800 seconds. A major difference in this engine is that the liquid fuel allows for fission products to move through the fuel layer and even exit out of the reactor completely. This dissertation seeks to answer the question, how does the migration of fission products within a centrifugal nuclear thermal rocket affect its operation and performance?” To accomplish this a reduced order model was developed to simulate and track the fission products generated during the firing …

The Parallel And Perpendicular Diffusion Of Energetic Particles In The Inner Heliosphere Using Nonlinear Theories And Observations, Nibuna Siranjeevi Madam Subashchandar

Dissertations

Energetic-particle transport in the near-Sun solar wind is strongly controlled by magnetic turbulence and its geometry. Using Parker Solar Probe observations from encounters E1--E19, we investigate parallel, perpendicular, and momentum diffusion coefficients for energetic protons in the inner heliosphere. The observed turbulence spectra are decomposed into slab and two-dimensional components using a composite turbulence model. The parallel diffusion coefficient is calculated using second-order quasi-linear theory, while the perpendicular diffusion coefficient is obtained from unified nonlinear transport theory. The results show that parallel diffusion increases with heliocentric distance but decreases with increasing turbulence amplitude, indicating enhanced pitch-angle scattering in stronger turbulence. …

Diffusion Of Excitons In Thin Films Of Quantum Dots, Dustin Roberts

Dissertations

Quantum dots are heavily used in modern devices, such as consumer television screens, lasers, medical sensors, solar cells, and quantum computing. Their tunability and photo-stability make them candidates for a variety of applications which formerly required either dyes or significant amounts of band structure engineering. Despite all of the current and active applications, there is a gap in the current literature with regards to how energy is transported through thin films of quantum dots, and what methods may be used to control transport direction and range. The goal of this dissertation is to help fill those gaps, towards the end …

Full-Wave Modeling Of Rf Waves In Fusion Plasmas With Finite Element Method: Progress In Past Decades And Its Future Role, Syun'ichi Shiraiwa, Nicola Bertelli, Eun-Hwa Kim

Faculty Publications

No abstract provided.

Prophetic Preaching As A Tool For Social Justice, Trevor A. O'Reggio

Faculty Publications

No abstract provided.

Lost In Instructions: Study Of Blind Users' Experiences With Diy Manuals And Ai-Rewritten Instructions For Assembly, Operation, And Troubleshooting Of Tangible Products, Monalika Padma Reddy, Aruna Balasubramanian, Jiawei Zhou, Xiaojun Bi, Iv Ramakrishnan, Vikas Ashok

Computer Science Faculty Publications

AI tools like ChatGPT and Be-My-AI are increasingly being used by blind individuals. Although prior work has explored their use in some Do-It-Yourself (DIY) tasks by blind individuals, little is known about how they use these tools and the available product-manual resources to assemble, operate, and troubleshoot physical/tangible products – tasks requiring spatial reasoning, structural understanding, and precise execution. We address this knowledge gap via an interview study and a usability study with blind participants, investigating how they leverage AI tools and product manuals for DIY tasks with physical products. Findings show that manuals are essential resources, but product-manual instructions …

Explainable Convolutional Neural Network Model Provides An Alternative Genome-Wide Association Perspective On Mutations In Sars-Cov-2, Parisa C. Hatami, Richard Annan, Luis Miranda, Jane L. Gorman, Mengjun Xie, Letu Qingge, Hong Qin

Computer Science Faculty Publications

Identifying informative genomic features in SARS-CoV-2 can help clarify patterns of viral evolution. In this study, we developed an explainable convolutional neural network (CNN) model to classify SARS-CoV-2 genomic sequences into the WHO-designated Variants of Concern (VOCs), Alpha, Beta, Gamma, Delta, and Omicron. Using a balanced dataset of genomes, the classification CNN achieved 99.96% accuracy on the held-out test set. To interpret the model’s predictions, we applied SHapley Additive exPlanations (SHAP) to estimate the contribution of each nucleotide position to VOC-label prediction and compared aggregated attributions with a chi-square GWAS baseline applied to the same categorical labels. SHAP prioritized several …