Physical Sciences and Mathematics Commons^™

Perfectly Matched Layer Absorbing Boundary Conditions For The Discrete Velocity Boltzmann-Bgk Equation, Elena Craig

Mathematics & Statistics Theses & Dissertations

Perfectly Matched Layer (PML) absorbing boundary conditions were first proposed by Berenger in 1994 for the Maxwell's equations of electromagnetics. Since Hu first applied the method to Euler's equations in 1996, progress made in the application of PML to Computational Aeroacoustics (CAA) includes linearized Euler equations with non-uniform mean flow, non-linear Euler equations, flows with an arbitrary mean flow direction, and non-linear clavier-Stokes equations. Although Boltzmann-BGK methods have appeared in the literature and have been shown capable of simulating aeroacoustics phenomena, very little has been done to develop absorbing boundary conditions for these methods. The purpose of this work was …

An Extensible Mathematical Model Of Glucose Metabolism, Caleb L. Adams

Mathematics & Statistics Theses & Dissertations

The American Diabetes Association reports that diabetes is the fifth leading cause of death by disease in the United States. An estimated 23.6 million individuals, or seven percent of the population, have diabetes. Nearly one-third are unaware that they have the disease. The total of the direct and indirect medical costs associated with diabetes in 2007 was projected to be $174 billion, or approximately one out of every ten health care dollars.

One must understand the glucose regulatory system of the healthy body to understand diabetes. Blood glucose concentration returns to a constant level after eating and is maintained during …

A Least Squares Closure Approximation For Liquid Crystalline Polymers, Traci Ann Sievenpiper

Mathematics & Statistics Theses & Dissertations

An introduction to existing closure schemes for the Doi-Hess kinetic theory of liquid crystalline polymers is provided. A new closure scheme is devised based on a least squares fit of a linear combination of the Doi, Tsuji-Rey, Hinch-Leal I, and Hinch-Leal II closure schemes. The orientation tensor and rate-of-strain tensor are fit separately using data generated from the kinetic solution of the Smoluchowski equation. The known behavior of the kinetic solution and existing closure schemes at equilibrium is compared with that of the new closure scheme. The performance of the proposed closure scheme in simple shear flow for a variety …