In this study, a heterogeneous flow model is proposed based on a non-overlapping domain decomposition method. The model combines potential flow and incompressible viscous flow. Both flow domains contain a free surface boundary.
The heterogeneous domain decomposition method is formulated following the Dirichlet-Neumann method. Both an implicit scheme and an...
Malaria is a vector-borne disease that has affected humans and other animals for a long time and which has shown high prevalence among different populations. During the beginning of the 20th century, Sir Ronald Ross and George Macdonald developed a model that represents the spread of malaria through the interaction...
In this work we will analyze branching Brownian motion on a finite interval with oneabsorbing and one reflecting boundary, having constant drift rate toward the absorbingboundary. Similar processes have been considered by Kesten ([12]), and more recently byHarris, Hesse, and Kyprianou ([11]). The current offering is motivated largely by the...
This thesis studies connections between disorder type in tree polymers and the branching random walk and presents an application to swarm site-selection. Chapter two extends results on tree polymers in the infinite volume limit to critical strong disorder. Almost sure (a.s.) convergence in the infinite volume limit is obtained for...
Microplastics (<5mm diameter) are present in a considerable number of marine and aquatic species. Understanding which species, the global spatial distribution, and what quantities of microplastics are present is extremely important for understanding the potential impacts they could have on recreationally important organisms and for the assessment of risk. We...
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...
The feedbacks between hydrology and biogeochemical cycling of nitrogen (N) are of critical importance to global bioavailable N budgets. Human activities are dramatically increasing the amount of bioavailable N in the biosphere, which is causing increasingly frequent and severe impacts on ecosystems and human welfare. Streams are important features in...
The goal of this research was to explore if an inkjet 3D printing technology, known as Multi Jet Fusion (MJF), could be used to fabricate magnetic polymer nanocomposites with systematically varied volume fractions of magnetic nanoparticles. Soft magnetic nanoparticles were chosen because of their applications in communications technologies and other...
In this dissertation we develop mathematical treatment for two important applications: (i) evolution of methane in coalbeds with the associated phenomena of adsorption, and (ii) formation of methane hydrates in seabed. We use simplified models for (i) and (ii) since we are more interested in qualitative properties of the solutions...