Browsing Mathematics by Title
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[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 ... 
[20130905] 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 SasakiEinstein metrics have positive Ricci curvature, and since positive Sasakian ... 
[20120201] 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 ... 
[20140214] 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 ... 
[20140915] Sasakian geometry on lens space bundles over Riemann surfaces
we compute the cohomology of the join of a 3 manifold with the sphere and we see the dependence of this cohomology on one of the parameters. 
[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 ... 
[20150901] Spatial Decay of Rotating Waves and Restrictions on Finite Disks.
In this thesis, we consider the system of reactiondiffusion equations and the behavior of the solution of such a system. The focus is to concentrate on solutions which decay at infinity. Under suitable assumptions, we ... 
[20160825] Standard Closure Operations on Several Rings of Dimension One
There are numerous results regarding the cardinality of the set of star and semistar operations on a domain R. However the cardinality of the set of such operations has only just begun to be examined in the nondomain ... 
[20140712] Star Operations and Numerical Semigroup Rings
We aim to classify the star and semistar operations on conductive numerical semigroup rings which are of the form $k + x^n k[[x]]$. By classifying the star and semistar operations on conductive numerical semigroup rings ... 
[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, ... 
[20150128] Strongly Nonlinear Phenomena and Singularities in Optical, Hydrodynamic and Biological Systems
Singularity formation is an inherent feature of equations in nonlinear physics, in many situations such as in selffocusing of light nonlinearity is essential part of the model and physical events cannot be captured ... 
[20160201] Studies of Coherent Synchrotron Radiation with the Discontinuous Galerkin Method
In this thesis, we present methods for integrating Maxwell's equations in FrenetSerret coordinates in several settings using discontinuous Galerkin (DG) finite element method codes in 1D, 2D, and 3D. We apply these routines ... 
[20130905] A Study of the Pressure Term in the NavierStokes 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 ... 
[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 ... 
[20160825] Toroidal Matrix Links: Local Matrix Homotopies and Soft Tori
In this document we solve some local connectivity problems in matrix representations of the form C(T^N) > M_n and C(T^N) > M_n < C([1, 1]^N) using the so called toroidal matrix links, which can be interpreted as ... 
[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 ... 
[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. ... 
[20120201] 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 ... 
[20130905] Wellposedness and Illposedness of the Nonlinear Beam Equation
The dissertation consists of two parts, Wellposedness and illposedness 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 ...