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Browsing Applied Mathematics by Title
Now showing items 236-255 of 502
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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 ... -
M-current induced Bogdanov–Takens bifurcation and switching of neuron excitability class
(Springer, 2021-02-15)In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations in the parameter space consisting of the applied current Iapp, the maximal ... -
Machine Learning Techniques and Stochastic Modeling in Mathematical Oncology
(University of Waterloo, 2022-07-18)The cancer stem cell hypothesis claims that tumor growth and progression are driven by a (typically) small niche of the total cancer cell population called cancer stem cells (CSCs). These CSCs can go through symmetric ... -
Math and the Fountain of Youth
(University of Waterloo, 2020-12-10)Ageing is associated with impairments in a number of regulatory processes, including in energy dysregulation that affects multiple metabolic pathways and in the circadian rhythms. In the management of metabolic stress ... -
Mathematical approaches to the study of cellular heterogeneity, treatment design, and immune response in cancer
(University of Waterloo, 2020-01-09)One of the complicating factors in treating cancer patients is the different levels of heterogeneity involved. In this thesis, we use a combination of mathematical methods (in silico experiments) and experimental data (in ... -
Mathematical Aspects of Scalar-Tensor Field Theories
(University of Waterloo, 2016-09-27)This thesis is based on a study of Lagrange scalar densities which are, in general, concomitants of the metric tensor gij (and its first and second derivatives) together with a scalar field ∅ (and its first derivative). ... -
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 ...