Browsing Mathematics by Title
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[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 ... 
[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 ... 
[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 ... 
[20110701] Optimal control problems, curves of pursuit
We study a class of problems known as pursuitevasion problems (PE). These problems can be understood as special cases of optimal control problems. After describing the two main principles to study optimal control ... 
[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 ... 
[20110207] Orthogonality and convergence of discrete Zernike polynomials
The Zernike polynomials are an inﬁnite set of orthogonal polynomials over the unit disk, which are rotationally invariant. They are frequently utilized in optics, opthal mology, and image recognition, among many other ... 
[20100903] Pell's Equation and nearly equilateral triangles
In this paper, we seek a family of triangles that have integer sides and integer area. We focus mainly on scalene triangles since it is impossible to have such triangles that are equilateral and isoceles triangles with ... 
[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 ... 
[20120322] PSEUDOSPECTRAL SOLUTION OF THE TWODIMENSIONAL NAVIER{STOKES EQUATIONS IN A DISK
An efficient and accurate algorithm for solving the twodimensional (2D) incompressible NavierStokes equations on a disk with noslip boundary conditions is described. The vorticity stream function formulation of these ... 
[20100909] Quantifying uncertainty in reliability block diagrams
Reliability analysis yields statistically derived technical system performance estimates. Traditional reliability analysis employs classical statistical techniques predicated upon asymptotic properties of large data sets. ... 
[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 ... 
[20120322] The Quaternions with an application to Rigid Body Dynamics
William Rowan Hamilton invented the quaternions in 1843, in his effort to construct hypercomplex numbers, or higher dimensional generalizations of the complex numbers. Failing to construct a generalization in three dimensions ... 
[20120322] A reducedorder partial differential equation model for dynamics of the flow in athermosyphon
Flow in a closed loop thermosyphon heated from below exhibits a sequence of bifurcations with increasing Grashof number. Using the NavierStokes equations in the Boussinesq approximation we have derived a model where, in ... 
[20090827] Shock formation properties of continuum and kinetic models
Continuum mechanics and kinetic theory are two mathematical theories with fundamentally different approaches to the same physical phenomenon. Continuum mechanics together with thermodynamics treat a substance (a gas or ... 
[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 ... 
[20100625] Spatial spread of infectious diseases
In this thesis we do a comparative study of diffusive models with nondiffusive models, looking at the effect movements in the form of simple diffusion have on the spreading of infectious diseases. This study is undertaken ... 
[20110831] Steady states, nonsteady evolution, pinchoff and postpinchoff of axisymmetric drops in Stokes flow
A good understanding of drop evolution and breakup is important in many applications. For instance, controlling the liquid droplet size is crucial in atomization processes such as fuel combustion and fertilizer application, ... 
[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 ... 
[20120322] Topology of cyclooctane energy landscape
Understanding energy landscapes is a major challenge in chemistry and biology. Although a wide variety of methods have been invented and applied to this problem, very little is understood about the actual mathematical ... 
[20100628] Two topics in particle accelerator beams: VlasovMaxwell treatment of coherent synchrotron radiation and topological treatment of spin polarization
This thesis has two parts. In the first part I present results from my studies of the VlasovMaxwell system which was developed, together with a code, in collaboration with Bassi, Ellison and Warnock. The emphasis ...