Digital Commons Network^™

Pressure Versus Impulse Graph For Blast-Induced Traumatic Brain Injury And Correlation To Observable Blast Injuries, Barbara Rutter

Doctoral Dissertations

"With the increased use of explosive devices in combat, blast induced traumatic brain injury (bTBI) has become one of the signature wounds in current conflicts. Animal studies have been conducted to understand the mechanisms in the brain and a pressure versus time graph has been produced. However, the role of impulse in bTBIs has not been thoroughly investigated for animals or human beings.

This research proposes a new method of presenting bTBI data by using a pressure versus impulse (P-I) graph. P-I graphs have been found useful in presenting lung lethality regions and building damage thresholds. To present the animal …

Decoupling Methods For The Time-Dependent Navier-Stokes-Darcy Interface Model, Changxin Qiu

Doctoral Dissertations

"In this research, several decoupling methods are developed and analyzed for approximating the solution of time-dependent Navier-Stokes-Darcy (NS-Darcy) interface problems. This research on decoupling methods is motivated to efficiently solve the complex Stokes-Darcy or NS-Darcy type models, which arise from many interesting real world problems involved with or even dominated by the coupled porous media flow and free flow. We first discuss a semi-implicit, multi-step non-iterative domain decomposition (NIDDM) to solve a coupled unsteady NS-Darcy system with Beavers-Joseph-Saffman-Jones (BJSJ) interface condition and obtain optimal error estimates. Second, a parallel NIDDM is developed to solve unsteady NS-Darcy model with Beavers-Joseph (BJ) …

New Reproducing Kernel Hilbert Spaces On Plane Regions, Their Properties, And Applications To Partial Differential Equations, Jabar S. Hassan

Doctoral Dissertations

"We introduce new reproducing kernel Hilbert spaces W₂^(m,n) (D) on unbounded plane regions D. We study linear non-homogeneous hyperbolic partial differential equation problems on D with solutions in various reproducing kernel Hilbert spaces. We establish existence and uniqueness results for such solutions under appropriate hypotheses on the driver. Stability of solutions with respect to the driver is analyzed and local uniform approximation results are obtained which depend on the density of nodes. The local uniform approximation results required a careful determination of the reproducing kernel Hilbert spaces on which the elementary …

Modeling Of Hiv, Sir And Sis Epidemics On Time Scales And Oscillation Theory, Gülşah Yeni

Doctoral Dissertations

"We study higher dimensional systems of first order dynamic equations on time scales together with their applications. In particular, we focus on epidemic models such as HIV (Human Immunodeficiency Virus), SIS (Susceptible-Infected-Susceptible) and SIR (Susceptible-Infected-Recovered).

First, we generalize the early studied continuous three dimensional linear model of drug therapy for HIV-1 decline on time scales in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. We compare these models to explore the impact of the theory of time scales. After fitting the models to the data collected at a clinical …

Dendrites Or Lambda-Dendroids As Generalized Inverse Limits, Faruq Abdullah Mena

Doctoral Dissertations

"This research centers on the study of generalized inverse limits. We show that all members of an infinite family of inverse limit spaces are homeomorphics to one particularly complicated inverse limit space known as "The Monster". Further, properties of factor spaces and graphs of bonding functions which are preserved in generalized inverse limit spaces with upper semi-continuous bonding functions with appropriate restrictions are investigated. Some of the properties are locally connectedness, hereditary decomposability, hereditary indecomposability, hereditary unicoherence, arc-likeness, and tree-likeness. The theorems are illustrated by several examples"--Abstract, page iv.