Browsing Applied Mathematics by Issue Date
Now showing items 21-40 of 493
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Improving Coarsening and Interpolation for Algebraic Multigrid
(University of Waterloo, 2006)Algebraic multigrid (AMG) is one of the most efficient algorithms for solving large sparse linear systems on unstructured grids. Classical coarsening schemes such as the standard Ruge-Stüben method [14] can lead ... -
Numerical Study of a Viscoelastic Model for Hydrocephalus
(University of Waterloo, 2006)Hydrocephalus is a clinical conditon where the brain tissue is deformed by the expanding ventricules. In this thesis, the mechanical deformation of a hydrocephalic brain is studied using a biomechanical model, where the ... -
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 ... -
Error-Tolerant Coding and the Genetic Code
(University of Waterloo, 2006)The following thesis is a project in mathematical biology building upon the so-called "error minimization hypothesis" of the genetic code. After introducing the biological context of this hypothesis, I proceed to develop ... -
The Sigma-Delta Modulator as a Chaotic Nonlinear Dynamical System
(University of Waterloo, 2007-01-23)The sigma-delta modulator is a popular signal amplitude quantization error (or noise) shaper used in oversampling analogue-to-digital and digital-to-analogue converter systems. The shaping of the noise frequency spectrum ... -
Hydrodynamic Modelling of the Electronic Response of Carbon Nanotubes
(University of Waterloo, 2007-02-08)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, 2007-04-13)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, 2007-05-17)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 ... -
Non-linear Effects on Stopping of Fast Moving Molecular Ions Through Solids
(University of Waterloo, 2007-06-27)This thesis studies the non-linear (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, 2007-07-17)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, 2007-08-02)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, 2007-08-03)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 so-called Carr-Purcell-Meiboom-Gill (CPMG) technique. We ... -
Exact and Perturbed Friedmann-Lemaitre Cosmologies
(University of Waterloo, 2007-08-07)In this thesis we first apply the 1+3 covariant description of general relativity to analyze n-fluid Friedmann-Lemaitre (FL) cosmologies; that is, homogeneous and isotropic cosmologies whose matter-energy content consists ... -
Spectral analysis of internal waves generated by tide-topography interaction
(University of Waterloo, 2007-08-21)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 ... -
Efficiency-based hp-refinement for finite element methods
(University of Waterloo, 2007-08-23)Two efficiency-based 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 Near-resonant Triads and Weakly Nonlinear Models
(University of Waterloo, 2007-08-24)This thesis investigates the effects of the earth's rotation on internal waves from two perspectives of nonlinear internal wave theory: near-resonant triads and weakly nonlinear models. We apply perturbation theory ... -
Annular Capillary Surfaces: Properties and Approximation Techniques
(University of Waterloo, 2007-09-17)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, 2007-09-25)Contrary to the Black-Scholes paradigm, an option-pricing 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, 2007-09-27)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): ... -
Root-Locus Theory for Infinite-Dimensional Systems
(University of Waterloo, 2007-09-27)In this thesis, the root-locus theory for a class of diffusion systems is studied. The input and output boundary operators are co-located in the sense that their highest order derivatives occur at the same endpoint. It is ...