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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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Reactive Tracers in Turbulence Models
(University of Waterloo, 2024-07-25)This thesis characterizes the nature of inaccuracies in the description of two tracers, one passive and one reactive (with a particular choice of model) within Reynolds Averaged Navier Stokes simulations (RANS) and Large ... -
Exponential Stability of Maxwell’s Equations
(University of Waterloo, 2024-07-25)The control of electromagnetic systems, which is governed by Maxwell's equations, is of interest for various reasons such as controlling plasma in a nuclear fusion reactor or magnetically trapping antiparticles for ... -
Hopf 2-Algebras: Homotopy Higher Symmetries in Physics
(University of Waterloo, 2024-06-26)The theory of Hopf algebras and quantum groups have led to very rich and interesting developments in both mathematics and physics. In particular, they are known to play crucial roles in the interplay between 3d topological ... -
On Enabling Layer-Parallelism for Graph Neural Networks using IMEX Integration
(University of Waterloo, 2024-06-20)Graph Neural Networks (GNNs) are a type of neural networks designed to perform machine learning tasks with graph data. Recently, there have been several works to train differential equation-inspired GNN architectures, ... -
Stability Analysis and Formally Guaranteed Tracking Control of Quadrotors
(University of Waterloo, 2024-06-19)Reach-avoid tasks are among the most common challenges in autonomous aerial vehicle (UAV) applications. Despite the significant progress made in the research of aerial vehicle control during recent decades, the task of ... -
Controller and Observer Designs for Partial Differential-Algebraic Equations
(University of Waterloo, 2024-06-19)Partial differential-algebraic equations (PDAEs) arise in numerous situations, including the coupling between differential-algebraic equations (DAEs) and partial differential equations (PDEs). They also emerge from the ... -
Ice/hydrology feedback in the Siple Coast, Antarctica, from two-way coupled modeling
(University of Waterloo, 2024-06-18)Subglacial hydrological processes have long been understood to play a critical role in ice dynamics (Budd et al., 1979). Consequently, the recent emergence of complex two-dimensional subglacial hydrology models with both ... -
Multiscale Modelling of Biological Rhythms and Systems
(University of Waterloo, 2024-06-17)Living organisms possess the remarkable ability to both respond to rhythms and generate them. In some instances, unintended rhythms arise, leading to undesirable or even hazardous consequences, such as synchronized neuronal ... -
Collective Dynamics of Large-Scale Spiking Neural Networks by Mean-Field Theory
(University of Waterloo, 2024-05-31)The brain contains a large number of neurons, each of which typically has thousands of synaptic connections. Its functionality, whether function or dysfunction, depends on the emergent collective dynamics arising from the ... -
A geometric investigation of non-regular separation applied to the bi-Helmholtz equation & its connection to symmetry operators
(University of Waterloo, 2024-05-23)The theory of non-regular separation is examined in its geometric form and applied to the bi-Helmholtz equation in the flat coordinate systems in 2-dimensions. It is shown that the bi-Helmholtz equation does not admit ... -
Space-time Hybridizable Discontinuous Galerkin Method for the Advection-Diffusion Problem
(University of Waterloo, 2024-05-22)In this thesis, we analyze a space-time hybridizable discontinuous Galerkin (HDG) method for the time-dependent advection-dominated advection-diffusion problem. It is well-known that solutions to these problems may admit ... -
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 ... -
On Convergence Analysis of Stochastic and Distributed Gradient-Based Algorithms
(University of Waterloo, 2024-05-08)Optimization is a fundamental mathematical discipline focused on finding the best solution from a set of feasible choices. It is vital in various applications, including engineering, economics, data science, and beyond. ... -
Safety-Critical Control for Dynamical Systems under Uncertainties
(University of Waterloo, 2024-02-15)Control barrier functions (CBFs) and higher-order control barrier functions (HOCBFs) have shown great success in addressing control problems with safety guarantees. These methods usually find the next safe control input ... -
Spatial and Temporal Discounting in a Social-Climate Model
(University of Waterloo, 2024-01-25)This thesis analyzes how individuals' devaluation of distant impacts of climate change affects mitigation behaviours and projected climate conditions. To approach this question, spatial and temporal discounting is applied ... -
Entropy-Stable Positivity-Preserving Schemes for Multiphase Flows
(University of Waterloo, 2024-01-22)High-intensity focused ultrasound is a promising non-invasive medical technology that has been successfully used to ablate tumors, as well as in the treatment of other conditions. Researchers believe high-intensity focused ... -
Optimal trajectory calculation using neural networks
(University of Waterloo, 2024-01-08)Optimal control methods for linear systems have reached a substantial level of maturity, both in terms of conceptual understanding and scalable computational implementation. For non-linear systems, an open-loop feedback ... -
Simulations of Radiatively Driven Convection and Spatially Heterogeneous Solar Radiation Intensity in Ice-Covered Lakes
(University of Waterloo, 2023-12-22)At the end of winter as sunlight and increasing air temperatures melt the snow layer above the ice, allowing significant radiation from the sun to enter the water column. In the cold water regime (T < 4 °C, where 4 °C is ... -
Properties of difference inclusions with computable reachable set
(University of Waterloo, 2023-12-13)Dynamical systems have important applications in science and engineering. For example, if a dynamical system describes the motion of a drone, it is important to know if the drone can reach a desired location; the dual ... -
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 ...