http://hdl.handle.net/1957/13737 2013-05-19T13:17:54Z 2013-05-19T13:17:54Z Gelbaum, Zachary A. http://hdl.handle.net/1957/38592 2013-05-15T23:04:11Z 2013-04-17T00:00:00Z

Some results in probability from the functional analytic viewpoint Gelbaum, Zachary A. This dissertation presents some results from various areas of probability theory, the unifying theme being the use of functional analytic intuition and techniques. We first give a result regarding the existence of certain stochastic integral representations for Banach space valued Gaussian random variables. Next we give a spectral geometric construction of Gaussian random fields over various manifolds that generalize classical fractional Brownian motion. Lastly we present a result describing the limiting distribution for the largest eigenvalue of a product of two random matrices from the β-Laguerre ensemble. Graduation date: 2013

2013-04-17T00:00:00Z Bokil, V. A. Gibson, N. L. http://hdl.handle.net/1957/38475 2013-05-07T16:11:22Z 2013-05-06T00:00:00Z

Convergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media Bokil, V. A.; Gibson, N. L. We present discrete energy decay results for the Yee scheme applied to Maxwell's equations in Debye and Lorentz dispersive media. These estimates provide stability conditions for the Yee scheme in the corresponding media. In particular, we show that the stability conditions are the same as those for the Yee scheme in a nondispersive dielectric. However, energy decay for the Maxwell-Debye and Maxwell-Lorentz models indicate that the Yee schemes are dissipative. The energy decay results are then used to prove the convergence of the Yee schemes for the dispersive models. We also show that the Yee schemes preserve the Gauss divergence laws on its discrete mesh. Numerical simulations are provided to justify the theoretical results.

2013-05-06T00:00:00Z Cooper, Julia M. http://hdl.handle.net/1957/38394 2013-04-30T15:41:59Z 1989-05-18T00:00:00Z

Time dependent wavemaker problem for linear waves Cooper, Julia M. The classical two-dimensional wavemaker problem is formulated for linear waves. Two conformal mappings are applied to the mathematical formulation to transform the wavemaker problem into a unit disk. It is then shown that this technique cannot produce in practice a numerical representation of the fluid motion throughout time for any position in the wavemaker channel. An analytic solution to the classical wavemaker problem is developed and then solved numerically. This solution contibutes information about the fluid motion for all time and for any position in the wavemaker channel. In addition to this problem, a related initial value problem is solved theoretically and then numerically. This results in the surface wave and fluid motion being described for all time and all positions in a two dimensional, semi-infinite channel. Graduation date: 1990

1989-05-18T00:00:00Z Wichitsongkram, Noppadon http://hdl.handle.net/1957/38186 2013-04-15T23:09:52Z 2013-03-13T00:00:00Z

Representations of fractional Brownian motion Wichitsongkram, Noppadon Integral representations provide a useful framework of study and simulation of fractional Browian motion, which has been used in modeling of many natural situations. In this thesis we extend an integral representation of fractional Brownian motion that is supported on a bounded interval of ℝ to integral representation that is supported on bounded subset of ℝ[superscript d]. These in turn can be used to give new series representations of fractional Brownian motion. Graduation date: 2013

2013-03-13T00:00:00Z