Now showing items 12-28 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. ...
• #### [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 ...
• #### [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 ...
• #### [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 ...
• #### [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 ...
• #### [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 ...
• #### [2014-09-15]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.
• #### [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 ...
• #### [2014-07-12]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 ...
• #### [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, ...
• #### [2015-01-28]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 self-focusing of light nonlinearity is essential part of the model and physical events cannot be captured ...
• #### [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 ...
• #### [2013-01-30]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 ...
• #### [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 ...
• #### [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. ...
• #### [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 ...
• #### [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 ...

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