Browsing Applied Mathematics by Issue Date
Now showing items 41-60 of 494
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Bohmian Trajectories of the Two-Electron Helium Atom
(University of Waterloo, 2008-01-17)We introduce the de Broglie-Bohm causal interpreation of quantum mechanics and compare it to the standard interpretation of quantum mechanics, the Copenhagen interpretation. We examine the possibility of experimentally ... -
Bandlimited functions, curved manifolds, and self-adjoint extensions of symmetric operators
(University of Waterloo, 2008-05-20)Sampling theory is an active field of research that spans a variety of disciplines from communication engineering to pure mathematics. Sampling theory provides the crucial connection between continuous and discrete ... -
Vacuum Energy in Expanding Spacetime and Superoscillation - Induced Resonance
(University of Waterloo, 2008-05-20)This thesis is divided into two parts. The first part is a study of the general problem of vacuum energy or so-called `zero point fluctuations' of a quantum field on expanding spacetimes and the interplay between the ... -
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 ... -
Gaining Information About a Quantum Channel Via Twirling
(University of Waterloo, 2008-07-31)Finding correctable encoding that protects against a quantum process is in general a difficult task. Two main obstacles are that an exponential number of experiments are needed to gain complete information about the quantum ... -
Inverse Problems and Self-similarity in Imaging
(University of Waterloo, 2008-08-06)This thesis examines the concept of image self-similarity and provides solutions to various associated inverse problems such as resolution enhancement and missing fractal codes. In general, many real-world inverse ... -
Optimal Dither and Noise Shaping in Image Processing
(University of Waterloo, 2008-08-20)Dithered quantization and noise shaping is well known in the audio community. The image processing community seems to be aware of this same theory only in bits and pieces, and frequently under conflicting terminology. ... -
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 ... -
Internet Congestion Control: Modeling and Stability Analysis
(University of Waterloo, 2008-08-27)The proliferation and universal adoption of the Internet has made it become the key information transport platform of our time. Congestion occurs when resource demands exceed the capacity, which results in poor performance ... -
Bifurcation analysis of a system of Morris-Lecar neurons with time delayed gap junctional coupling
(University of Waterloo, 2008-08-27)We consider a system of two identical Morris-Lecar neurons coupled via electrical coupling. We focus our study on the effects that the coupling strength, γ , and the coupling time delay, τ , cause on the dynamics of the ... -
Information flow at the quantum-classical boundary
(University of Waterloo, 2008-08-28)The theory of decoherence aims to explain how macroscopic quantum objects become effectively classical. Understanding this process could help in the search for the quantum theory underlying gravity, and suggest new schemes ... -
Unsteady Free Convection from Elliptic Tubes at Large Grashof Numbers
(University of Waterloo, 2008-09-11)This study solves the problem of unsteady free convection from an inclined heated tube both numerically and analytically. The tube is taken to have an elliptic cross-section having a constant heat flux applied to its ... -
Resolution Enhancement in Magnetic Resonance Imaging by Frequency Extrapolation
(University of Waterloo, 2008-12-16)This thesis focuses on spatial resolution enhancement of magnetic resonance imaging (MRI). In particular, it addresses methods of performing such enhancement in the Fourier domain. After a brief review of Fourier theory, ... -
WKB Analysis of Tunnel Coupling in a Simple Model of a Double Quantum Dot
(University of Waterloo, 2008-12-16)A simplified model of a double quantum dot is presented and analyzed, with applications to spin-qubit quantum computation. The ability to trap single electrons in semiconductor nanostructures has led to the proposal of ... -
Poincare Waves and Kelvin Waves in a Circular Lake
(University of Waterloo, 2009-01-28)When wind blows over a stratified lake an interface tilt is often generated, and internal waves usually appear after the wind stops. Internal waves in lakes are studied in many literatures, but most assume a hydrostatic ... -
Numerical Simulation of Surface Waves using Meshfree Methods
(University of Waterloo, 2009-04-27)Smoothed Particle Hydrodynamics (SPH) is a Lagrangian-based numerical method used for simulating problems in fluid and solid mechanics. In this thesis, a basic introduction to particle and Smoothed Particle (SP) approximations ... -
PID Control of Systems with Hysteresis
(University of Waterloo, 2009-04-29)Hysteresis is exhibited by many physical systems. Smart materials such as piezoelectrics, magnetostrictives and shape memory alloys possess useful properties, especially in the field of micropositioning, but the control ... -
Flow Separation on the β-plane
(University of Waterloo, 2009-05-15)In non-rotating fluids, boundary-layer separation occurs when the nearly inviscid flow just outside a viscous boundary-layer experiences an appreciable deceleration due to a region of adverse pressure gradient. The fluid ... -
A Study of Infectious Disease Models with Switching
(University of Waterloo, 2009-05-20)Infectious disease models with switching are constructed and investigated in detail. Modelling infectious diseases as switched systems, which are systems that combine continuous dynamics with discrete logic, allows for the ... -
A Mathematical Model of CA1 Hippocampal Neurons with Astrocytic Input
(University of Waterloo, 2009-06-22)Over time astrocytes have been thought to function in an auxiliary manner, providing neurons with metabolic and structural support. However, recent research suggests they may play a fundamental role in the generation and ...