Apart from the traditional role of preventing progression from HIV to AIDS, antiretroviral drug therapy (ART) has an additional benefit of substantially reducing infectiousness, making them potentially an important strategy in the fight against HIV. Recent advances in drug therapy have also seen the use of antiretroviral drugs as a...
A central challenge for ecology is to understand the dynamic nature of species interactions. A classic approach to community ecology assumes that individuals within a species are functionally identical and that consumer-resource dynamics can be predicted solely by using species abundances. However, one species can consist of multiple functional groups,...
In this work we consider a mathematical and computational model for biofilm growth and nutrient utilization. In particular, we are interested in a model appropriate at a scale of interface. The model is a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs). One of these PDEs is subject...
Two-phase flows in microtechnology based devices are purposefully present in multiphase reactors, phase separators, analytical devices and others. Two-phase flows can also be an undesirable side effect occurring during operation due to phase transitions or, more commonly, introduction of surrounding air through equipment gaps and with process feed. In both...
Engineers have long been inspired by nature's flyers. Such animals navigate complex environments gracefully and efficiently by using a variety of evolutionary adaptations for high-performance flight. Biologists have discovered a variety of sensory adaptations that provide flow state feedback and allow flying animals to feel their way through flight. A...
Within this dissertation, we develop tools and techniques to demonstrate the feasibility of real-time optimization of a magnetohydrodynamics generator. To ease computational complexity, we work on the kinematic magnetohydrodynamic system, prescribing the fluid-flow and model the material response of the system through an updated Generalized Ohm’s law. We focus on...
Given an initial opinion matrix in which every member of a population gives an opinion score of all the members in a population, natural questions to ask could be regarding what happens to those opinions over time, both in forward time and in backward time. While what happens over time...
Modern scientific and engineering problems often require simulations with a level of resolution difficult to achieve in reasonable amounts of time—even in effectively parallelized programs. Therefore, applications that exploit high performance computing (HPC) systems have become invaluable in academia and industry over the past two decades. Addressing the questions that...
Emerging infectious diseases impact both human and wildlife populations. Infectious agents, in particular the aquatic fungus Batrachochytrium dendrobatidis (chytrid), have an influential role in driving global amphibian population declines. The emergence of the chytrid fungus has aspects of both geographic spread as well as climate shifts altering environmental conditions and...
This dissertation examines properties and representations of several isotropic Gaussian random fields in the unit ball in d-dimensional Euclidean space. First we consider Lévy's Brownian motion. We use an integral representation for the covariance function to find a new expansion for Lévy's Brownian motion as an infinite linear combination of...