Physical Sciences and Mathematics Commons^™

Improving Ventricular Catheter Design Through Computational Fluid Dynamics, Sofy Hefets Weisenberg

Masters Theses

Cerebrospinal fluid (CSF) shunts are fully implantable medical devices that are used to treat patients suffering from conditions characterized by elevated intracranial pressure, such as hydrocephalus. In cases of shunt failure or malfunction, patients are often required to endure one or more revision surgeries to replace all or part of the shunt. One of the primary causes of CSF shunt failure is obstruction of the ventricular catheter, a component of the shunt system implanted directly into the brain's ventricular system. This work aims to improve the design of ventricular catheters in order to reduce the incidence of catheter obstruction and …

Optical Sensors For The Analysis Of Alcohols In Fuels, Kendhl Kate Witt

Masters Theses

This thesis reports the development of optical sensors to analyze alcohols in fuel samples. One optical sensor enables the analysis of phenol in aviation fuels and cellulosic biofuels. It is critical to monitor the concentration of phenols in fuels because they increase the presence of solid oxidative deposits and lower the thermal stability of fuels. Preliminary studies of another optical sensor have been conducted to detect ethanol in E10 gasoline samples. Gasoline containing ethanol is widely available and used, but the exact percentage of ethanol is not specified and varies between samples and regions. Higher concentrations of ethanol in gasoline …

Non-Compact Solutions To Inverse Mean Curvature Flow In Hyperbolic Space, Brian Daniel Allen

Doctoral Dissertations

We investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over horospheres in Hyperbolic space and show long time existence of the flow as well as asymptotic convergence to horospheres. Along the way many important local estimates as well as global estimates are obtained. In addition, we develop a useful family of cutoff functions for IMCF as well as a non-compact ODE maximum principle at infinity which are integral tools used throughout the document.

Modeling Feral Hogs In Great Smoky Mountains National Park, Benjamin Anthony Levy

Doctoral Dissertations

Feral Hogs (Sus scrofa) are an invasive species that have occupied the Great Smoky Mountains National Park since the early 1900s. Recent studies have revitalized interest in the pest and have produced useful data. The Park has kept detailed records on mast abundance as well as every removal since 1980 including geographic location and disease sampling. Data obtained via Lidar includes both overstory as well as understory vegetation information. In this dissertation, three models were created and analyzed using the detailed data on vegetation, mast, and harvest history. The first model is discrete in time and space and …

Duality Of Scales, Michael Christopher Holloway

Doctoral Dissertations

We establish an interaction between the large scale and small scale using two types of maps from large scale spaces to small scale spaces. First we use slowly oscillating maps, which can be described as those having arbitrarily small variation at infinity. These lead to a Galois connection between certain collections of large scale structures and small scale structures on a given set. Slowly oscillating functions can also be used to define to the notion of a dual pair of scale structures on a space. A dual pair consists of a large and a small scale structure on a space …

Hankel Operators On The Drury-Arveson Space, James Allen Sunkes Iii

Doctoral Dissertations

The Drury-Arveson space, initially introduced in the proof of a generalization of von Neumann's inequality, has seen a lot of research due to its intrigue as a Hilbert space of analytic functions. This space has been studied in the context of Besov-Sobolev spaces, Hilbert spaces with complete Nevanlinna Pick kernels, and Hilbert modules. More recently, McCarthy and Shalit have studied the connections between the Drury-Arveson space and Hilbert spaces of Dirichlet series, and Davidson and Cloutare have established analogues of classic results of the ball algebra to the multiplier algebra for the Drury-Arveson Space.

The goal of this dissertation is …