Mathematics
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Mathematics Theses [11]
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[20140109] Quantitative Ktheory and spin Chern numbers [dataset]
We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this is two symmetry classes, that of general unitary matrices and ... 
[20131217] Principal angles and approximation for quaternionic projections [dataset]
We extend Jordan's notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two orthogonal projections in the matrices over the real, complex or quaternionic field (or ... 
[20131202] Estimating norms of commutators
\begin{abstract} We find estimates on the norm of a commutator of the form $[f(x),y]$ in terms of the norm of $[x,y]$, assuming that $x$ and $y$ are bounded linear operators on Hilbert space, with $x$ normal and with ... 
[20131202] Estimating norms of commutators [dataset]
\begin{abstract} We find estimates on the norm of a commutator of the form $[f(x),y]$ in terms of the norm of $[x,y]$, assuming that $x$ and $y$ are bounded linear operators on Hilbert space, with $x$ normal and with ... 
[20131125] Computing a logarithm of a unitary matrix with general spectrum [dataset]
\begin{abstract} We analyze an algorithm for computing a skewHermitian logarithm of a unitary matrix, and also skewHermitian approximate logarithms for nearly unitary matrices. This algorithm is very easy to implement ... 
[20130130] Numerical simulation of traffic flow using a hydrodynamic model
We examine the solution to the system of partial differential equations for the transport and continuity equations. The model for our system of equations closely resembles the PayneWhitham model for traffic flow. The ... 
[20130130] Terrestrial and extraterrestrial radiation sources that move faster than light
Maxwell's equations establish that patterns of electric charges and currents can be animated to travel faster than the speed of light in vacuo and that these superluminal distribution patterns emit tightly focused ... 
[20120828] Viscous flow past plates
I devise a numerical method of high order in space (FDMHS) to simulate flow past a finite plate and a semiinfinite plate. The method solves the incompressible NavierStokes equation in the stream functionvorticity formulation. ... 
[20120827] Numerical and Analytical Studies of Electromagnetic Waves: Hermite Methods, Supercontinuum Generation, and Multiple Poles in the SEM
The dissertation consists of three parts: Hermite methods, scattering from a lossless sphere, and analysis of supercontinuum generation. Hermite methods are a new class of arbitrary order algorithms to solve partial ... 
[20120705] Arithmetic jet spaces and modular forms
In this thesis, we would look into the theory of arithmetic jet spaces and its application in modular forms. The arithmetic jet spaces can be thought of as an analogue of jet spaces in differential algebra. In the case of ... 
[20120323] Longtime behavior of GinzburgLandau systems far from equilibrium
Using singularperturbation techniques, we study the stability of modulated structures generated by driving GinzburgLandau systems far from equilibrium. We show that, far from equilibrium, the steadystate behavior is ... 
[20120323] Effects of thermal spread on the space charge limit of an electron beam
An asymptotic analysis is carried out to calculate the effects of a small thermal spread in the injection energy of an electron beam on its space charge limit. It is found that the space charge limit is lowered proportionally ... 
[20120323] Non relativistic KapitzaDirac scattering
We use techniques of singular perturbation theory to investigate the scattering of nonrelativistic charged particles by a standing light wave (KapitzaDirac scattering). Unlike previous treatments, we give explicit results ... 
[20120323] Caustics and virtual cathodes in electron beams
A simplified model is discussed that captures the basic physics of the phenomenon of oscillatory virtual cathodes in electron beams. A monoenergetic nonrelativistic onedimensional electron beam is injected through a ... 
[20120323] Space charge limit instabilities in electron beams
The method of characteristics and multiplescaling perturbation techniques are used to study the spacecharge instability of electron beams. It is found that the stable oscillating state (virtual cathode) created when the ... 
[20120323] Acousticwave nonlinearity in stimulated Brillouin scattering
Stimulated Brillouin scattering is investigated here under conditions characterized by high optical pump intensity. Calculations are carried out at 1.3 and 3.8 /jm with pump intensities equal to approximately three times ... 
[20120322] AN EFFICIENT SPECTRAL METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS WITH RATIONAL FUNCTION COEFFICIENTS
We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, ... 
[20120322] Optimized preparation of quantum states by conditional measurements
We introduce a general strategy for preparation of arbitrary quantum states via optimal control of repeated conditional measurements. The effectiveness of this strategy in generating finite Fockstate superpositions with ... 
[20120322] The Approximate Functional Formula for the Theta Function and Diophantine Gauss Sums
By introducing the discrete curvature of the polygonal line, and by exploiting the similarity of segments of the line, for small w, to Cornu spirals (Cspirals), we prove the precise renormalization formula. This formula, ... 
[20120322] Invertibility of current density from nearfield electromagnetic data
The problem of determining a current density confined to a volume from measurements of the magnetic and electric fields it produces exterior to that volume is known to have nonunique solutions. Despite the nonuniqueness ...