Browsing Applied Mathematics by Subject "Applied Mathematics"
Now showing items 21-40 of 149
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Construction of Optimal Tubular Networks in Arbitrary Regions in R^3
(University of Waterloo, 2015-08-10)In this thesis, we describe various algorithms for the construction of tubular networks in an arbitrary three-dimensional region that possesses a principal direction along which the cross-section varies. The region can be ... -
Contrasting classical and quantum theory in the context of quasi-probability
(University of Waterloo, 2008-08-22)Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined ... -
Control of Hysteresis in the Landau-Lifshitz Equation
(University of Waterloo, 2013-11-15)There are two main tools for determining the stability of nonlinear partial differential equations (PDEs): Lyapunov Theory and linearization. The former has the advantage of providing stability results for nonlinear ... -
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 ... -
A Covariant Natural Ultraviolet Cutoff in Inflationary Cosmology
(University of Waterloo, 2013-08-28)In the field of quantum gravity, it is widely expected that some form of a minimum length scale, or ultraviolet cutoff, exists in nature. Recently, a new natural ultraviolet cutoff that is fully covariant was proposed. In ... -
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 ... -
The Discontinuous Galerkin Method Applied to Problems in Electromagnetism
(University of Waterloo, 2012-04-23)The discontinuous Galerkin method (DGM) is applied to a number of problems in computational electromagnetics. This is achieved by obtaining numerical solutions to Maxwell's equations using the DGM. The aim of these ... -
The discontinuous Galerkin method on Cartesian grids with embedded geometries: spectrum analysis and implementation for Euler equations
(University of Waterloo, 2012-09-21)In this thesis, we analyze theoretical properties of the discontinuous Galerkin method (DGM) and propose novel approaches to implementation with the aim to increase its efficiency. First, we derive explicit expressions ... -
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 ... -
Dynamic Magnetic Resonance Elastography
(University of Waterloo, 2010-01-20)Magnetic Resonance Elastography (MRE) is a medical imaging technique used to generate a map of tissue elasticity. The resulting image is known as an elastogram, and gives a quantitative measure of stiffness in the examined ... -
Dynamical Systems Methods Applied to the Michaelis-Menten and Lindemann Mechanisms
(University of Waterloo, 2009-08-06)In the first part of this thesis, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear ... -
The Effect of Time-Varying Boundary Conditions on the Generation of Sum and Difference Frequency Tones in a Coaxial Loudspeaker
(University of Waterloo, 2009-06-22)A coaxial loudspeaker in which the woofer and tweeter oscillate at angular frequencies ω_1 and ω_2 respectively, is known to produce sum and difference frequencies ω_± = ω_1 ± ω_2. The generation of these can be attributed ... -
Effects of the Dielectric Environment on the Electrical Properties of Graphene
(University of Waterloo, 2013-08-30)This thesis provides the study of graphene’s electrostatic interaction with the substrate surrounding it. Mathematical models based on current experimental configurations of graphene field-effect transistors (FET) are ... -
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 ... -
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 ... -
Efficient Stockwell Transform with Applications to Image Processing
(University of Waterloo, 2011-05-20)Multiresolution analysis (MRA) has fairly recently become important, and even essential, to image processing and signal analysis, and is thus having a growing impact on image and signal related areas. As one of the most ... -
Energy Shaping for Systems with Two Degrees of Underactuation
(University of Waterloo, 2012-01-11)In this thesis we are going to study the energy shaping problem on controlled Lagrangian systems with degree of underactuation less than or equal to two. Energy shaping is a method of stabilization by designing a suitable ... -
Energy transport in saturated porous media
(University of Waterloo, 2011-04-29)The energy analysis of the wave motion in the Lamb’s problem for a poroelastic half-space in the framework of Biot’s theory is presented. The results for the energy velocity and quality factor of poroelastic waves are ... -
Entanglement Entropy in Quantum Gravity
(University of Waterloo, 2008-05-22)We study a proposed statistical explanation for the Bekenstein-Hawking entropy of a black hole in which entropy arises quantum-mechanically as a result of entanglement. Arguments for the identification of black hole entropy ... -
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 ...