Other Applied Mathematics Commons^™

Invariance Of Chsh Parameters When Projecting Weakly Signaling Distribution Into A No Signaling Subspace, Aaditya Paudel

LSU New Orleans Theses and Dissertations

The seminal 1935 paper by Einstein, Podolsky, and Rosen (EPR) sparked a fundamental debate in quantum mechanics about the completeness of physical reality through the EPR paradox. They questioned local realism by suggesting that particles could exhibit instantaneous correlations across any distance, challenging classical physics. Bell's theorem (1964) argued that no local hidden variable theory could replicate quantum predictions, introducing Bell's inequalities and their experimental tests. These tests, particularly through violations of Bell's inequalities, confirmed quantum predictions of non-local correlations that local realism could not account for. Quantum theory, while supporting such correlations, adheres to the no-signaling principle to prevent …

General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr

LSU New Orleans Theses and Dissertations

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation …

Mathematical Formulation Of Fusion Energy Magnetohydrodynamics, Nikolaos I. Xiros

LSU New Orleans Theses and Dissertations

Chapter 1 presents the basic principles of Controlled Thermonuclear Fusion, and the approaches to achieve nuclear fusion on Earth. Furthermore, the basic components of the Tokamak, the reactor which will house the fusion reaction, are analyzed. Finally, the chapter ends with a discussion on how the present thesis is related to the Controlled Thermonuclear Fusion. Chapter 2 introduces briefly the basic concepts of the Electromagnetic and Magnetohydrodynamic theories as well as MHD turbulence. Chapter 3 presents a first glance in OpenFOAM CFD library. Chapter 4 introduces the Orszag-Tang vortex flow, which is a benchmark test case for MHD numerical models. …

Underwater Acoustic Signal Analysis Toolkit, Kirk Bienvenu Jr

LSU New Orleans Theses and Dissertations

This project started early in the summer of 2016 when it became evident there was a need for an effective and efficient signal analysis toolkit for the Littoral Acoustic Demonstration Center Gulf Ecological Monitoring and Modeling (LADC-GEMM) Research Consortium. LADC-GEMM collected underwater acoustic data in the northern Gulf of Mexico during the summer of 2015 using Environmental Acoustic Recording Systems (EARS) buoys. Much of the visualization of data was handled through short scripts and executed through terminal commands, each time requiring the data to be loaded into memory and parameters to be fed through arguments. The vision was to develop …

Blow-Up Of Solutions To The Generalized Inviscid Proudman-Johnson Equation, Alejandro Sarria

LSU New Orleans Theses and Dissertations

The generalized inviscid Proudman-Johnson equation serves as a model for n-dimensional incompressible Euler flow, gas dynamics, high-frequency waves in shallow waters, and orientation of waves in a massive director field of a nematic liquid crystal. Furthermore, the equation also serves as a tool for studying the role that the natural fluid processes of convection and stretching play in the formation of spontaneous singularities, or of their absence.

In this work, we study blow-up, and blow-up properties, in solutions to the generalized, inviscid Proudman-Johnson equation endowed with periodic or Dirichlet boundary conditions. More particularly,regularity of solutions in an Lp setting will …