Applied Mathematics
This is the collection for the University of Waterloo's Department of Applied Mathematics .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
Recent deposits
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Data-Driven Methods for System Identification and Lyapunov Stability
(University of Waterloo, 2023-01-27)This thesis focuses on data-driven methods applied to system identification and stability analysis of dynamical systems. In the first major contribution of the theorem we propose a learning framework to simultaneously ... -
Road Surface Estimation Using Machine Learning
(University of Waterloo, 2023-01-19)Vehicle motion control systems are present on commercial vehicles to improve safety and driving comfort. Many of these control systems could be further improved given accurate online information about the road condition ... -
Modeling and simulation of uni- and multi-flagellar bacterial locomotion in a viscous fluid
(University of Waterloo, 2023-01-16)Flagellated bacteria categorized as microorganisms, play vital roles in human life such that their beneficial and detrimental effects on different aspects of the ecosystem are indisputable. Flagellated bacteria propel ... -
From Astrophysics of Galaxies to Binary Black Hole Mergers: Theoretical Modelling of the Gravitational-Wave Bias Parameter
(University of Waterloo, 2023-01-04)In the past few decades, the field of cosmology has become a fascinating field of study in physics. The computational advances and precision observational measurements such as Cosmic Microwave Background (CMB) measurements ... -
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 ... -
Sensitivity of the Thermal Structure and Circulation Patterns of a Simple Idealized Lake and Lake Erie to External Driving Forces
(University of Waterloo, 2022-12-22)Lake Erie has been a great source of economic growth and drinking water for both Canada and the United States. All lakes in temperate regions that stratify during summer are prone to hypoxia as they will experience some ... -
On the evaluation of quantum instruments with a consideration to measurements in trapped ion systems
(University of Waterloo, 2022-12-20)Trapped ion chains have shown promise in their application as quantum simulators. However, the close proximity of ions in the trap leads to operations such as state detection causing loss of coherence of other ions due to ... -
Almost-Sure Stability of a Noisy Autoparametric Vibration Absorber
(University of Waterloo, 2022-12-13)This thesis investigates the almost-sure stability of the single mode solution of a two degree-of-freedom, noisy, nonlinear autoparametric system. While only the first mode is forced in such a system, the nonlinear coupling ... -
Modelling Subglacial Hydrology under Future Climate Scenarios in Wilkes Subglacial Basin, Antarctica
(University of Waterloo, 2022-10-21)The Greenland and Antarctic ice sheets have differing climates, which makes surface melt a significant hydrological source in Greenland but not currently in Antarctica. Due to a changing climate and warming air temperatures, ... -
Bifurcation and Robust Control of Instabilities in the Presence of Uncertainties
(University of Waterloo, 2022-10-06)In real-world applications, nominal mathematical models that are used to describe the state behaviors of dynamical systems are usually less robust to deal with environmental disruptions. Uncertainties, such as imprecision ... -
Consensus Problems in Hybrid Multi-Agent Systems
(University of Waterloo, 2022-09-28)A multi-agent system (MAS) is a dynamic system that consists of a group of interacting agents distributed over a network. In the past decades, the study of distributed coordination of multi-agent systems has been widely ... -
Examination of Parametric Subharmonic Instability of K₁ Internal Tides Generated by Tidal Flow over a Ridge
(University of Waterloo, 2022-09-26)Internal gravity waves are thought to be a predominant source of mixing in the Earth's oceans. Here, we explore the interplay between two phenomena experienced by internal gravity waves - parametric subharmonic instability ... -
Theoretical Description of the Forces on a Point Charge Moving Parallel to a Supported Two-dimensional Material
(University of Waterloo, 2022-09-22)A charged particle, moving at a certain distance and parallel to a target, experiences a stopping force that slows it down and an image force that deflects it towards the target's surface. In this work, we aimed to describe ... -
A spatially explicit modelling approach for predicting and managing the effects of coral reef stressors
(University of Waterloo, 2022-09-09)Coral reefs represent simultaneously one of the most beloved and one of the most endangered ecosystems in the world. Millions of people visit coral reefs every year for tourism purposes, and millions of people living in ... -
Examining the consistency between subglacial hydrology and basal friction inversion modeling for Slessor Glacier, East Antarctica.
(University of Waterloo, 2022-08-31)In light of rising global surface temperatures and sea-level rise, it is more important now than ever to understand what role the cryosphere will play in the Earth's evolution. The Antarctic ice sheet contains enough ice ... -
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 ... -
Boundary-Bound Reactions: Pattern Formation with and without Hydrodynamics
(University of Waterloo, 2022-08-23)Pattern formation through chemical morphogenesis has received a significant amount of attention since Alan Turing's original analysis in a Chemical Basis for Morphogenesis. In that article, Turing showed the surprising ... -
High-Resolution Analysis of Snow Albedo Interactions in the Arctic
(University of Waterloo, 2022-08-23)The Snow Albedo Feedback (SAF) is an important contributor to Arctic warming, however models disagree significantly on the strength of this effect. Previous work has investigated the influence of vegetation on surface ... -
q-deformed LQG in three dimensional space-time
(University of Waterloo, 2022-08-23)Loop quantum gravity (LQG) is a canonical, background-independent and non-perturbative approach to quantum gravity. This thesis is devoted to studying three-dimensional (3D) quantum gravity with a non-vanishing cosmological ... -
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 ...
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