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 …

Aspects Of Parity Breaking In Classical And Quantum Fluids, Dylan J. Reynolds

Dissertations, Theses, and Capstone Projects

Parity-breaking is ubiquitous across many scales of physics, from the rotation of galaxies at the largest of scales, to the cyclotron orbits of electrons at the microscopic scale. In describing the collective dynamics of many particle systems, parity breaking effects typically originate from some form of chirality, such as angular momentum, at the level of the constituent particles. External forces can also induce chiral motion, with the primary examples being the Lorentz and Coriolis forces.

The effects of parity breaking are perhaps most strikingly seen in active matter, systems of complex particles that tend to convert energy into some directed …

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 …

Oscillations Of Capillary Surfaces With Volume And Edge Effects, Dingqian Ding

All Dissertations

Capillary surfaces are defined by an interface endowed with surface tension that is partially supported by a solid substrate and are susceptible to oscillations reflecting a balance between fluid inertia and the restorative force of surface tension. The wave dynamics strongly depend upon volume change within the domain and edge effects through the boundary conditions applied at the contact-line formed at the liquid-gas-solid interface, while the spatial wave structure conforms to the geometry of the capillary surface. This dissertation develops mathematical models to address these effects for several canonical capillary surfaces, which are organized into two parts that are focused …

Blade Design And Validation Of Hydrokinetic Turbine To Harvest Water Current Energy, Setare Sadeqi

University of New Orleans Theses and Dissertations

The innovative aspect of this research lies in the careful integration of cutting-edge technologies throughout the entire process of designing, fabricating, and testing the carbon fiber propeller for the 3-bladed horizontal axis ocean current turbine (OCT). SolidWorks software played a pivotal role in the initial design phase, enabling a meticulous and precise modeling of the propeller's geometry. The utilization of SolidWorks allowed for a detailed exploration of various design parameters, ensuring that the propeller's structure and form were optimized for performance in ocean current conditions. Moving beyond the realm of virtual design, the choice of carbon fiber as the fabrication …

Towing Tank Trials Of Hydrokinetic Turbine Scale Model To Support Marine Energy System Verification, Shahab Rouhi

University of New Orleans Theses and Dissertations

In response to the escalating demand for sustainable energy solutions and the critical reevaluation of conventional fossil fuels due to environmental concerns, this dissertation embarks on a comprehensive exploration of hydrokinetic energy as a promising alternative. The study delves into the underexplored domain of hydrokinetic energy, leveraging innovative methodologies for effective utilization and harnessing, particularly through the development and investigation of hydrokinetic turbines.

In the realm of hydrokinetic energy conversion, our research has exclusively concentrated on horizontal-axis turbines, distinct from other turbine configurations. Noteworthy is the adaptation of a conventional horizontal-axis wind turbine for water currents, revealing enhanced performance through …

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 …

Modeling Thermosyphon And Heat Pipe Performance For Mold Cooling Applications, Dwaipayan Sarkar

Electronic Thesis and Dissertation Repository

Thermosyphons are enhanced heat transfer devices that can continuously transfer very large amounts of heat rapidly over long distances with small temperature differences. The high heat transfer rate is achieved through simultaneous boiling and condensation of the working fluid and the continuous heat transfer is achieved through recirculation of the working fluid in its liquid and vapor phase. A potentially important application of the thermosyphons has been towards reducing the cycle times of the mold cooling processes which would provide economic incentives to the automotive industry.

Different operational and geometrical parameters such as the input heating power, fill ratio (FR), …

Les-C Turbulence Models And Fluid Flow Modeling: Analysis And Application To Incompressible Turbulence And Fluid-Fluid Interaction, Kyle J. Schwiebert

Dissertations, Master's Theses and Master's Reports

In the first chapter of this dissertation, we give some background on the Navier-Stokes equations and turbulence modeling. The next two chapters in this dissertation focus on two important numerical difficulties arising in fluid flow modeling: poor mass-conservation and nonphysical oscillations. We investigate two different formulations of the Crank-Nicolson method for the Navier-Stokes equations. The most attractive implementation, second order accurate for both velocity and pressure, is shown to introduce non-physical oscillations. We then propose two options which are shown to avoid the poor behavior. Next, we show that grad-div stabilization, previously assumed to have no effect on the target …