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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Higher Gauge Theory and Discrete Geometry
(University of Waterloo, 2023-06-05)In four dimensions, gravity can be seen as a constrained topological model. This provides a natural way to construct quantum gravity models, since topological models are relatively straightforward to quantize. Difficulty ... -
Predictability of Stratified Turbulence
(University of Waterloo, 2023-05-19)In the study of geophysical fluid dynamics, predictability of dynamics at different scales still stands in the foreground of interest as one of the primary challenges. Following Lorenz's pioneering framework, several results ... -
Calcium Transport and Regulation in Male and Female Rat Kidney
(University of Waterloo, 2023-05-16)Calcium is an essential mineral that plays a critical role in many biological processes, such as muscle contraction, nerve function, and bone health. However, maintaining the right balance of calcium in the body is crucial ... -
Turnpike Property for Generalized Linear-Quadratic Optimal Control Problem
(University of Waterloo, 2023-04-28)The turnpike phenomenon describes the long time behavior of optimally controlled systems whose optimal trajectories over a sufficiently large time horizon stay for most of the time close to a prescribed trajectory of the ... -
Microcolony Dynamics: Motion from Growth, Order, and Incompressibility
(University of Waterloo, 2023-04-27)Rod-shaped bacteria such as E. coli reproduce by expanding along their long axis and splitting into pairs of daughter cells. If conditions are favourable for growth, they will continue in this way, doubling repeatedly until ... -
Mathematical Modelling of the Intrarenal Renin Angiotensin System in Hypertension
(University of Waterloo, 2023-04-24)Hypertension is the leading cause of cardiovascular disease and premature death world-wide. It is a highly multi-factorial disease associated with multiple risk factors and patho-physiological changes, including impaired ... -
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 ...
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