Browsing Applied Mathematics by Title
Now showing items 228-247 of 499
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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 ... -
Invariant manifold theory for impulsive functional differential equations with applications
(University of Waterloo, 2019-07-03)The primary contribution of this thesis is a development of invariant manifold theory for impulsive functional differential equations. We begin with an in-depth analysis of linear systems, immersed in a nonautonomous ... -
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 ... -
An investigation of the use of gradients in imaging, including best approximation and the Structural Similarity image quality measure
(University of Waterloo, 2023-08-18)The L^2-based mean squared error (MSE) and its variations continue to be the most widely employed metrics in image processing. This is most probably due to the fact that (1) the MSE is simple to compute and (2) it possesses ... -
Investigations into quantum light-matter interactions, their approximations and applications
(University of Waterloo, 2021-01-26)Devoting some thought to the interactions between light and matter quickly conjure a myriad of different possibilities; different models for light and matter, different possible interaction Hamiltonians, different simplifying ... -
Iterated Function Systems with Place-Dependent Probabilities and the Inverse Problem of Measure Approximation Using Moments
(University of Waterloo, 2016-10-25)The study of iterated function systems has close ties with the subject of fractal-based analysis. One important application is the approximation of a target object by the fixed point of a contractive iterated function ... -
Jets, Vortices and Turbulence in Quasi-Geostrophic Magnetohydrodynamics
(University of Waterloo, 2022-07-28)In this thesis, we model the dynamics of the solar tachocline and the Earth's molten core using a shallow, rapidly rotating, and electrically conducting fluid on an f-plane. We explore the effects of a strong uniform ... -
Kalman Filter Based Sensor Placement For Burgers Equation
(University of Waterloo, 2019-06-03)The algorithm used for determining sensor placement in this thesis will be based on the Kalman filter. This filter is very famous and its application are numerous - some examples include aircraft navigation, finance and ... -
Kinetic Modeling of Pyruvate Recycling Pathways in Pancreatic β-Cells.
(University of Waterloo, 2012-09-26)A variety of signaling mechanisms are employed to maintain healthy levels of glucose in the blood stream. The hormone insulin is one of the primary regulators of glucose homeostasis. Insulin, which activates glucose ... -
Kinodynamic Planning with μ-Calculus Specifications
(University of Waterloo, 2018-09-19)Motion planning problems involve determining appropriate control inputs to guide a system towards a desired endpoint. Sampling-based motion planning was developed as a technique for discretizing the state space of systems ... -
Landowner Perceptions Of The Value Of Natural Forest And Natural Grassland In A Mosaic Ecosystem In Southern Brazil
(Springer, 2016-03-01)The forest-grassland mosaics of southern Brazil have been subject to many land use and policy changes over the decades. Like many grasslands around the world, the Campos grasslands are declining with few conservation efforts ... -
Large eddy simulations and subgrid scale motions in stratified turbulence
(University of Waterloo, 2015-03-18)Direct numerical and large eddy simulations (DNS $\&$ LES) of decaying and forced stratified turbulence are studied in this thesis. By defining a test filter scale $k_c$ in the horizontal and vertical directions separately, ... -
Late-lumping backstepping control of partial differential equations
(Elsevier, 2019-02)We consider in this paper three different partial differential equations (PDEs) that can be exponentially stabilized using backstepping controllers. For implementation, a finite-dimensional controller is generally needed. ... -
Light-Matter Interaction Models in Relativistic Quantum Information
(University of Waterloo, 2021-05-21)In this thesis, we study the interaction of a first-quantized atomic system with the quantum electromagnetic field within the context of relativistic quantum information (RQI). To that end, we examine common classes of ... -
Limiting techniques for the discontinuous Galerkin method on unstructured meshes
(University of Waterloo, 2022-08-18)Many complex phenomena like shock-shock interactions, shock-vortex interactions, stratified flows, etc., are governed by nonlinear hyperbolic conservation laws. Higher order numerical schemes like the discontinuous Galerkin ... -
Linearized Stability of Partial Differential Equations with Application to Stabilization of the Kuramoto--Sivashinsky Equation
(Society for Industrial and Applied Mathematics, 2018-01-05)Linearization is a useful tool for analyzing the stability of nonlinear differential equations. Unfortunately, the proof of the validity of this approach for ordinary differential equations does not generalize to all ... -
Lithium-Ion battery SOC estimation
(University of Waterloo, 2017-01-23)Lithium-ion batteries are frequently used in Hybrid electric vehicles (HEVs), which are taking the place of gas-engine vehicles. An important but not measurable quantity in HEVs is the amount of charge remaining in the ... -
Local measurements in Relativistic Quantum Information: localization and signaling
(University of Waterloo, 2023-12-12)In this thesis, we study some foundational aspects of detector models in quantum field theory (QFT) related to signaling and localization, and we analyze certain frictions with relativistic causality. We characterize the ... -
Localising Information in Bandlimited Quantum Field Theory
(University of Waterloo, 2015-09-24)A deeply-held belief in fundamental physics is that interactions must happen locally. Despite the great success of local models, there are many indications that locality must be abandoned in a theory of quantum gravity. For ... -
Long-time behaviour of a coupled PDE model of high intensity focused ultrasound heating of biological tissue
(University of Waterloo, 2021-11-11)High Intensity Focused Ultrasound (HIFU) has emerged as a novel therapeutic modality, for the treatment of various cancers, that is gaining significant traction in clinical oncology. It is a cancer therapy that avoids many ...