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...
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...
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...
Biological invasions provide a unique opportunity to study the mechanisms that regulate community composition and ecosystem function. Invasive species that are also ecosystem engineers can substantially alter physical features in an environment, and this can lead to cascading effects on the biological community. Aquatic-terrestrial interface ecosystems are excellent systems to...
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...
This thesis consists of three subsequent parts addressing the applications of stochastic
processes to the analysis and solutions of parabolic equations with discontinuous coefficients
that are of mathematical interest.
The first two parts consist of three manuscripts, in which we analyze solutions
of Fickian convection dispersion equations with discontinuous coefficients...
We develop several a-priori and a-posteriori error estimates for two-grid finite element discretization of coupled elliptic and parabolic systems with a set of parameters P. We present numerical results that verify the convergence order of the numerical schemes predicted by the a-priori estimates. We present numerical results that verify the...