Browsing Applied Mathematics by Issue Date
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Hydrodynamic Stability of Free Convection from an Inclined Elliptic Cylinder
(University of Waterloo, 2006)The steady problem of free convective heat transfer from an isothermal inclined elliptic cylinder and its stability is investigated. The cylinder is inclined at an arbitrary angle with the horizontal and immersed in an ... 
Stability of Hybrid Singularly Perturbed Systems with Time Delay
(University of Waterloo, 2006)Hybrid singularly perturbed systems (SPSs) with time delay are considered and exponential stability of these systems is investigated. This work mainly covers switched and impulsive switched delay SPSs . Multiple ... 
Hydrodynamic Modeling of Dielectric Response in Graphene and Carbon Nanotubes
(University of Waterloo, 2006)This thesis studies two important carbon structures, graphene and carbon nanotubes, with the purpose of understanding how their threedimensional electron density distribution affects the way fast ions interact with them. ... 
ErrorTolerant Coding and the Genetic Code
(University of Waterloo, 2006)The following thesis is a project in mathematical biology building upon the socalled "error minimization hypothesis" of the genetic code. After introducing the biological context of this hypothesis, I proceed to develop ... 
The SigmaDelta Modulator as a Chaotic Nonlinear Dynamical System
(University of Waterloo, 20070123)The sigmadelta modulator is a popular signal amplitude quantization error (or noise) shaper used in oversampling analoguetodigital and digitaltoanalogue converter systems. The shaping of the noise frequency spectrum ... 
Hydrodynamic Modelling of the Electronic Response of Carbon Nanotubes
(University of Waterloo, 20070208)The discovery of carbon nanotubes by Iijima in 1991 has created a torrent of new research activities. Research on carbon nanotubes ranges from studying their fundamental properties, such as their electron band structure ... 
Stability and Boundedness of Impulsive Systems with Time Delay
(University of Waterloo, 20070413)The stability and boundedness theories are developed for impulsive differential equations with time delay. Definitions, notations and fundamental theory are presented for delay differential systems with both fixed and ... 
Controller Gain Optimization for Position Control of an SMA Wire
(University of Waterloo, 20070517)There has been an increasing interest in the field of `smart structures' and `smart materials'. In constructing smart structures, a class of materials called smart materials are often used as sensors and actuators. An ... 
Nonlinear Effects on Stopping of Fast Moving Molecular Ions Through Solids
(University of Waterloo, 20070627)This thesis studies the nonlinear (Barkas) effects on stopping of fast moving molecular ions through solids. We model the solid target by a rigid lattice of positive ion cores surrounded by a gas of electrons. To model ... 
Distorted Wave Born Approximation For Inelastic Atomic Collision
(University of Waterloo, 20070717)An investigation of the problem of inelastic scattering process under the Coulomb Born approximation is given. Different approaches to calculate Coulomb wavefunctions in the momentum space representation are analyzed and ... 
Entire Solutions to Dirichlet Type Problems
(University of Waterloo, 20070802)In this thesis, we examined some Dirichlet type problems of the form: \begin{eqnarray*} \triangle u & = & 0\ {\rm in\ } \mathbb{R}^n \\ u & = & f\ {\rm on\ } \psi = 0, \end{eqnarray*} and we were particularly ... 
Determining relaxation times for porous media: Theory, measurement, and the inverse problem
(University of Waterloo, 20070803)This thesis provides an introduction to and analysis of the problem of determining nuclear magnetic resonance (NMR) relaxation times of porous media by using the socalled CarrPurcellMeiboomGill (CPMG) technique. We ... 
Exact and Perturbed FriedmannLemaitre Cosmologies
(University of Waterloo, 20070807)In this thesis we first apply the 1+3 covariant description of general relativity to analyze nfluid FriedmannLemaitre (FL) cosmologies; that is, homogeneous and isotropic cosmologies whose matterenergy content consists ... 
Spectral analysis of internal waves generated by tidetopography interaction
(University of Waterloo, 20070821)Internal waves in the deep ocean play a deciding role in processes such as climate change and nutrient cycles. Winds and tidal currents over topography feed energy into internal waves at large scales; through nonlinear ... 
Efficiencybased hprefinement for finite element methods
(University of Waterloo, 20070823)Two efficiencybased grid refinement strategies are investigated for adaptive finite element solution of partial differential equations. In each refinement step, the elements are ordered in terms of decreasing local ... 
The Effects of the Earth's Rotation on Internal Wave Nearresonant Triads and Weakly Nonlinear Models
(University of Waterloo, 20070824)This thesis investigates the effects of the earth's rotation on internal waves from two perspectives of nonlinear internal wave theory: nearresonant triads and weakly nonlinear models. We apply perturbation theory ... 
Annular Capillary Surfaces: Properties and Approximation Techniques
(University of Waterloo, 20070917)The capillary surface formed within a symmetric annular tube is analyzed. Assuming identical contact angles along each boundary, we consider surfaces u(x,y) that satisfy the capillary problem on an annular region. Several ... 
Hedging Contingent Claims in Markets with Jumps
(University of Waterloo, 20070925)Contrary to the BlackScholes paradigm, an optionpricing model which incorporates the possibility of jumps more accurately reflects the evolution of stocks in the real world. However, hedging a contingent claim in ... 
Analysis of Asymptotic Solutions for Cusp Problems in Capillarity
(University of Waterloo, 20070927)The capillary surface $u(x,y)$ near a cusp region satisfies the boundary value problem: \begin{eqnarray} \nabla \cdot \frac{\nabla u}{\sqrt{1+\left\nabla u \right^2}}&=&\kappa u \qquad \textrm{in }\left\{(x,y): ... 
RootLocus Theory for InfiniteDimensional Systems
(University of Waterloo, 20070927)In this thesis, the rootlocus theory for a class of diffusion systems is studied. The input and output boundary operators are colocated in the sense that their highest order derivatives occur at the same endpoint. It is ...