Mathematics Dissertations
Recent Submissions

[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 ... 
[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, ... 
[20110702] Analysis of the organization and dynamics of proteins in cell membranes
Cells communicate with the outside world through membrane receptors that recognize one of many possible stimuli (hormones, antibodies, peptides) in the extracellular environment and translate this information to intracellular ... 
[20100910] Contact homology of toric contact manifolds of Reeb type
We use contact homology to distinguish contact structures on various manifolds. We are primarily interested in contact manifolds which admit an action of Reeb type of a compact Lie group. In such situations it is well ... 
[20100909] Commutators and dyadic paraproducts on weighted Lebesgue spaces
We prove that the operator norm on weighted Lebesgue space L^2(w) of the commutators of the Hilbert, Riesz and Beurling transforms with a BMO function b depends quadratically on the A2 characteristic of the weight, as ... 
[20100909] Analysis of nonlinear Black Scholes models
The Black Scholes equation is a fundamental model for derivative pricing. Modifying its assumptions will lead to more realistic but mathematically more complicated models. This dissertation consists of analytical and ... 
[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 ... 
[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 ... 
[20090129] Modeling Arctic sea ice using the materialpoint method and an elasticdecohesive rheology
Sea ice has an important effect on global climate by reducing the heat transfer between the atmosphere and ocean and by reflecting incoming solar radiation. Additionally, sea ice can be an important navigational concern. ...