Browsing Applied Mathematics by Type "Doctoral Thesis"
Now showing items 21-40 of 154
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A Critical Examination of Two Specific Approaches Used to Characterize Medical Images: i) Projection-based Descriptors for Image Retrieval and ii) Estimating Fractal Dimensions of Discrete Sets
(University of Waterloo, 2022-08-31)In this thesis we provide a critical examination of two methods which are used to characterize medical images. Accordingly, this thesis is split into two main parts. First, we take a look at the problem of designing ... -
The de Broglie-Bohm Causal Interpretation of Quantum Mechanics and its Application to some Simple Systems
(University of Waterloo, 2003)The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued ... -
Decentralized contact tracing protocols and a risk analysis approach to pandemic control
(University of Waterloo, 2022-12-23)Non-pharmaceutical interventions (NPIs) can protect against pandemic pathogens, but they depend on behaviour change, and so can impose costs on quality of life and civil liberties. With careful system design and risk ... -
Decoupling of Information Propagation from Energy Propagation
(University of Waterloo, 2016-08-31)Information and energy are concepts central to our understanding of nature. Their relevance, in physics, ranges from fundamental physics, e.g., in black hole physics, all the way to future quantum computing technology. ... -
Detecting and distinguishing transitions in ecological systems: model and data-driven approaches
(University of Waterloo, 2020-01-22)There exists a plethora of systems that have the capacity to undergo sudden transitions that result in a significantly different state or dynamic. Consider the collapse of fisheries, outbreak of disease or transition to a ... -
Development and Application of Models and Diagnostics for Geophysical Fluid Flows
(University of Waterloo, 2019-01-07)This thesis presents the development and application of numerical tools for simulating and diagnosing quasi-geostrophic fluid systems. In this thesis we present a new numerical model called SPIQG that is pseudo-spectral ... -
Dimensionality Reduction of the Chemical Master Equation
(University of Waterloo, 2019-01-11)The dynamics of biochemical systems show significant variability when the reactant populations are small. Standard approaches via deterministic modeling exclude such variability. A well established stochastic model, the ... -
Direct Numerical Simulation of Salt Fingering Gravity Currents and Double-Diffusive Rayleigh-Taylor Instabilities
(University of Waterloo, 2017-01-18)Double-diffusion refers to a class of instabilities that develops when the density of a fluid depends on two components with different diffusivities. For example, when warm, salty water is layered over cool, fresh water, ... -
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 ... -
Discrete total variation in multiple spatial dimensions and its applications
(University of Waterloo, 2024-05-13)Total variation plays an important role in the analysis of stability and convergence of numerical solutions for one-dimensional scalar conservation laws. However, extending this approach to two or more spatial dimensions ... -
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 Dynamics of Inhomogeneous Cosmologies
(University of Waterloo, 2004)In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaître models. We focus on cosmologies with one spatial degree of freedom, whose matter content ... -
Effects of a Geostrophic Current on the Propagation and Generation of Internal Tides
(University of Waterloo, 2021-08-30)Internal tides (ITs) are ubiquitous in a stratified ocean where they are generated in response to tidal flows incident upon bottom topography. Along-shelf currents or boundary currents are ocean currents commonly observed ... -
The Effects of Confinement on Kelvin-Helmholtz Billows
(University of Waterloo, 2016-01-15)Turbulence is one of the most interesting and important, yet poorly understood, aspects of fluid mechanics. The transition from an unstable laminar flow to a fully turbulent flow can follow many paths depending on the ... -
The Effects of Extrinsic and Intrinsic Noise on a Tumour and a Proposed Metastasis Model
(University of Waterloo, 2015-11-30)Cancer is a ubiquitous disease that afflicts millions of people worldwide and we will undoubtedly encounter it at some point in our lives, whether it be random strangers on the news, or someone much closer. As such, research ... -
Efficient Finite-difference Methods for Sensitivity Analysis of Stiff Stochastic Discrete Models of Biochemical Systems
(University of Waterloo, 2017-12-07)In the study of Systems Biology it is necessary to simulate cellular processes and chemical reactions that comprise biochemical systems. This is achieved through a range of mathematical modeling approaches. Standard methods ... -
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 ... -
Emergence and Implications of Conservation Opinion Propagation in Dynamic Coupled Socio-Ecological Systems
(University of Waterloo, 2021-04-22)Human behaviour is rarely a static phenomenon. In life, individuals are presented with choices that define the trajectories they will experience days, weeks or months later. As an example consider farmer decision-making ... -
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 ...