Browsing Mathematics by Title
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[20120322] Delayinduced destabilization of entrainment of nerve impulses on ephaptically coupled nerve fibers
We study the effect of delay on the synchronization of two nerve impulses traveling along two ephaptically coupled, unmyelinated nerve fibers. The system is modeled as a pair of delaycoupled FitzhughNagumo equations. A ... 
[20090709] Development of scoring rubrics and preservice teachers’ ability to validate mathematical proofs
The basic aim of this exploratory research study was to determine if a specific instructional strategy, that of developing scoring rubrics within a collaborative classroom setting, could be used to improve preservice ... 
[20120322] Dynamical properties of forced shear layers in an annular geometry
Results of numerical simulations of a forced shear flow in an annular geometry are presented. The particular geometry used in this work reduces the effects of centrifugal and Coriolis forces. However, there are still a ... 
[20120323] Effects of thermal spread on the space charge limit of an electron beam
An asymptotic analysis is carried out to calculate the effects of a small thermal spread in the injection energy of an electron beam on its space charge limit. It is found that the space charge limit is lowered proportionally ... 
[20120322] AN EFFICIENT SPECTRAL METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS WITH RATIONAL FUNCTION COEFFICIENTS
We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, ... 
[20131202] Estimating norms of commutators
\begin{abstract} We find estimates on the norm of a commutator of the form $[f(x),y]$ in terms of the norm of $[x,y]$, assuming that $x$ and $y$ are bounded linear operators on Hilbert space, with $x$ normal and with ... 
[20131202] Estimating norms of commutators [dataset]
\begin{abstract} We find estimates on the norm of a commutator of the form $[f(x),y]$ in terms of the norm of $[x,y]$, assuming that $x$ and $y$ are bounded linear operators on Hilbert space, with $x$ normal and with ... 
[20120320] The FALCLoop web server for protein loop modeling
The FALCLoop web server provides an online interface for protein loop modeling by employing an ab initio loop modeling method called FALC (fragment assembly and analytical loop closure). The server may be used to construct ... 
[20090827] High performance damper optimization using computer simulation and design of experiments
Design of experiments has become an increasingly popular tool used by racing teams in professional motorsports. A race car has literally hundreds of adjustable parameters associated with it. Specialized racing engineers ... 
[20120322] Invertibility of current density from nearfield electromagnetic data
The problem of determining a current density confined to a volume from measurements of the magnetic and electric fields it produces exterior to that volume is known to have nonunique solutions. Despite the nonuniqueness ... 
[20120323] Longtime behavior of GinzburgLandau systems far from equilibrium
Using singularperturbation techniques, we study the stability of modulated structures generated by driving GinzburgLandau systems far from equilibrium. We show that, far from equilibrium, the steadystate behavior is ... 
[20100219] Maintaining pathogens with short infectivity in seasonally structured tick populations: relative importance of three transmission pathways
Infectivity periods of different tickborne pathogens in host species can vary widely, and the variation affects how the pathogens are maintained in tick populations. In addition to systemic and vertical transmission, ... 
[20090827] The mathematics of the epicycloid : a historical journey with a modern perspective
The role of the epicycloid in both historical and mathematical contexts was studied through readings and research. Throughout history, circles have been considered perfect and thus very important shapes. Because epicycloids ... 
[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. ... 
[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 ...