In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to 21st century problems. We also discuss the pre ...

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 repr ...

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 fe ...

In this report we consider the Debye model along with Maxwell's equations (Maxwell- Debye) to model electromagnetic wave propagation in dispersive media that exhibit orientational polarization. We construct and analyze ...

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. ...