Mathematics Commons^™

An Analysis Of Capillary Flow In Finite Length Interior Corners, Samuel Shaw Mohler

Dissertations and Theses

We analyze the mathematical robustness of slow massively parallel interior corner flows in low gravity environments. An interior corner provides a preferential orientation in low gravity environments. This is a luxury usually only found on earth. It also provides a passive pumping mechanism due to geometry of a conduit. The driving force for this flow is a pressure difference due to local surface curvature gradients. An alternative reasoning is that due to the geometrical constraints the interior corner surface energy is unbounded below. This results in the liquid wicking into corners indefinitely. Interior corner flow's main quantity of interest is …

Generalized Differential Calculus And Applications To Optimization, R. Blake Rector

Dissertations and Theses

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations …

A Parabolic Equation Analysis Of The Underwater Noise Radiated By Impact Pile Driving, Nathan Laws

Dissertations and Theses

Impact pile driving can produce extremely high underwater sound levels, which are of increasing environmental concern due to their deleterious effects on marine wildlife. Prediction of underwater sound levels is important to the assessment and mitigation of the environmental impacts caused by pile driving. Current prediction methods are limited and do not account for the dynamic pile driving source, inhomogeneities in bathymetry and sediment, or physics-based sound wave propagation.

In this thesis, a computational model is presented that analyzes and predicts the underwater noise radiated by pile driving and is suitable for shallow, inhomogeneous environments and long propagation ranges. The …