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

Consensus Problems in Hybrid MultiAgent Systems
(University of Waterloo, 20220928)A multiagent 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 multiagent systems has been widely ... 
Examination of Parametric Subharmonic Instability of K₁ Internal Tides Generated by Tidal Flow over a Ridge
(University of Waterloo, 20220926)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 Twodimensional Material
(University of Waterloo, 20220922)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, 20220909)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, 20220831)In light of rising global surface temperatures and sealevel 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) Projectionbased Descriptors for Image Retrieval and ii) Estimating Fractal Dimensions of Discrete Sets
(University of Waterloo, 20220831)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 ... 
BoundaryBound Reactions: Pattern Formation with and without Hydrodynamics
(University of Waterloo, 20220823)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 ... 
HighResolution Analysis of Snow Albedo Interactions in the Arctic
(University of Waterloo, 20220823)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 ... 
qdeformed LQG in three dimensional spacetime
(University of Waterloo, 20220823)Loop quantum gravity (LQG) is a canonical, backgroundindependent and nonperturbative approach to quantum gravity. This thesis is devoted to studying threedimensional (3D) quantum gravity with a nonvanishing cosmological ... 
Limiting techniques for the discontinuous Galerkin method on unstructured meshes
(University of Waterloo, 20220818)Many complex phenomena like shockshock interactions, shockvortex interactions, stratified flows, etc., are governed by nonlinear hyperbolic conservation laws. Higher order numerical schemes like the discontinuous Galerkin ... 
Numerical analysis of spacetime hybridized discontinuous Galerkin methods for incompressible flows
(University of Waterloo, 20220809)Many industrial problems require the solution of the incompressible NavierStokes equations on moving and deforming domains. Notable examples include the simulation of rotating wind turbines in strong air flow, wave impact ... 
Numerical simulations of convection and gravity currents near the temperature of maximum density
(University of Waterloo, 20220809)Recently, the dynamics of flows in cold freshwater (temperatures around the temperature of maximum density, 3.98 oC) has garnered much interest in the environmental fluid dynamics community. From a dynamical perspective, ... 
Jets, Vortices and Turbulence in QuasiGeostrophic Magnetohydrodynamics
(University of Waterloo, 20220728)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 fplane. We explore the effects of a strong uniform ... 
Machine Learning Techniques and Stochastic Modeling in Mathematical Oncology
(University of Waterloo, 20220718)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 ... 
Threedimensional simulations of sound propagation in a trumpet with accurate mouthpiece shank geometry
(arXiv, 20161101)The length and bore geometry of musical instruments directly influences the quality of sound that can be produced. In brass instruments, nonlinear effects from finiteamplitude wave propagation can lead to wave distortion ... 
Galerkin Finite Element Based Modeling of One Dimensional Packed Bed Reactor for Underground Coal Gasification (UCG) Process
(IEEE, 20201211)Mathematical models of a complex physicochemical underground coal gasification process involve multidimensional nonlinear partial differential equations (PDEs). Therefore, researchers always seek a suitable numerical ... 
On the TVD property of second order methods for 2D scalar conservation laws
(arXiv, 20211005)The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of onedimensional scalar conservation laws. However, it proved to be challenging ... 
Bidirectional TopK Sparsification for Distributed Learning
(University of Waterloo, 20220527)Training large neural networks requires a large amount of time. To speed up the process, distributed training is often used. One of the largest bottlenecks in distributed training is communicating gradients across different ... 
Analysis of a pressurerobust hybridized discontinuous Galerkin method for the stationary NavierStokes equations
(Springer, 20190830)We present wellposedness and an a priori error analysis of the hybridized discontinuous Galerkin method for the stationary form of the NavierStokes problem proposed in (J Sci Comput, 76(3):1484{ 1501, 2018). This scheme ... 
Mathematical Modeling of Kidney Function During Pregnancy
(University of Waterloo, 20220516)During pregnancy major adaptations must occur in the maternal body to be able to support the rapidly developing fetus and placenta. Adaptations occur in almost all tissues and organs. These changes are dynamic, complex, ...