Now showing items 1-20 of 28

• #### [2009-01-29]Modeling Arctic sea ice using the material-point method and an elastic-decohesive 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. ...
• #### [2009-08-27]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 ...
• #### [2010-06-28]Two topics in particle accelerator beams: Vlasov-Maxwell 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 Vlasov-Maxwell system which was developed, together with a code, in collaboration with Bassi, Ellison and Warnock. The emphasis ...
• #### [2010-09-09]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 ...
• #### [2010-09-09]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 ...
• #### [2010-09-10]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 ...
• #### [2011-07-02]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 ...
• #### [2011-08-31]Steady states, non-steady evolution, pinch-off and post-pinch-off 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, ...
• #### [2012-02-01]Propagation of intense UV filaments and vortices. ﻿

The goal of this dissertation is to investigate the propagation of ultrashort high intensity UV laser pulses of order of nanoseconds in atmosphere. It is believed that they have a potential for stable and diffractionless ...
• #### [2012-02-01]Weighted estimates for dyadic operators with complexity ﻿

We extend the definitions of dyadic paraproduct, dual dyadic paraproduct and $t$-Haar multipliers to dyadic operators that depend on the complexity $(m,n)$, for $m$ and $n$ positive integers. We will use the ...
• #### [2012-07-05]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 ...
• #### [2012-08-27]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 ...
• #### [2012-08-28]Viscous flow past plates ﻿

I devise a numerical method of high order in space (FDMHS) to simulate flow past a finite plate and a semi-infinite plate. The method solves the incompressible Navier-Stokes equation in the stream function-vorticity formulation. ...
• #### [2013-01-30]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 ...
• #### [2013-09-05]Well-posedness and Ill-posedness of the Nonlinear Beam Equation ﻿

The dissertation consists of two parts, Well-posedness and ill-posedness for the nonlinear beam equation and Strichartz estimates of the beam equation on the domains. In the first part, we will work to introduce the ...
• #### [2013-09-05]Positive Sasakian Structures on Links of Weighted Complete Intersection Singularities ﻿

Links of isolated singularities defined by weighted homogeneous polynomials have a natural Sasakian structure. Since it is known that Sasaki-Einstein metrics have positive Ricci curvature, and since positive Sasakian ...
• #### [2013-09-05]A Study of the Pressure Term in the Navier-Stokes Equations ﻿

In this paper we consider the Cauchy problem for the 3D \NS equations for incompressible flows, and their solutions. We will discuss the results of a paper by Otto Kreiss and Jens Lorenz on the role of ...
• #### [2013-09-05]Arithmetic Deformation Classes Associated to Curves via p-Jet Spaces ﻿

We show that for certain curves over p-adic rings its first p-jet space admits the structure of a torsor under a line bundle.
• #### [2014-02-13]Modeling the Mechanical Response of Polycrystalline Thin Films ﻿

Microelectromechanical systems (MEMS) are part of every modern technological advance. Electrodeposited thin nickel (Ni) polycrystalline films in MEMS often show fiber texture resulting in transverse isotropic elastic ...
• #### [2014-02-14]Quantification of Stability in Systems of Nonlinear Ordinary Differential Equations ﻿

A common process in ODE theory is to linearize an ODE system about an equilibrium point to determine the local stability properties of its orbits. Less common are results that quantify the domain of stability in the original ...

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