Recent Master's Theses - Applied Mathematics

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Master's Theses 2024

Omer Ege Kara On Enabling Layer-Parallelism for Graph Neural Networks using IMEX Integration
Haocheng Chang Stability Analysis and Formally Guaranteed Tracking Control of Quadrotors
Koi McArthur Ice/hydrology feedback in the Siple Coast, Antarctica, from two-way coupled modeling
Mackenzie Cameron Spatial and Temporal Discounting in a Social-Climate Model
Ben Simpson Entropy-Stable Positivity-Preserving Schemes for Multiphase Flows

Sounak Majumder

Optimal trajectory calculation using neural networks

Master's Theses 2023

Michael Willette

Modelling the Subglacial Hydrology of Trinity-Wykeham Glaciers of the Northern Canadian Arctic

Adam Winick Theory and Mitigation of Crosstalk on Quantum Information Processors
Akihiro Takigawa

A comparison of the Kalman filter and recurrent neural networks for state estimation of dynamical systems

Kaiwen Jiang Mathematical Modeling of the Vaporization of Encapsulated Perfluorocarbon Nanodroplets using Chirp Ultrasound
 Amelia Kunze

An investigation of the use of gradients in imaging, including best approximation and the Structural Similarity image quality measure

Shervin Hakimi Calcium Transport and Regulation in Male and Female Rat Kidney
Martin F. Diaz Robles

Predictability of Stratified Turbulence

Zhuqing Li

Turnpike Property for Generalized Linear-Quadratic Optimal Control Problem

Delaney Smith  Mathematical Modelling of the Intrarenal Renin Angiotensin System in Hypertension
Thanin Quartz Data-Driven Methods for System Identification and Lyapunov Stability
Brian Mao Road Surface Estimation Using Machine Learning
Dorsa Sadat Hosseini Khajouei

From Astrophysics of Galaxies to Binary Black Hole Mergers: Theoretical Modelling of the Gravitational-Wave Bias Parameter

Master's Theses 2022

Funmilayo Adeku Sensitivity of the Thermal Structure and Circulation Patterns of a Simple Idealized Lake and Lake Erie to External Driving Forces
Darian McLaren On the evaluation of quantum instruments with a consideration to measurements in trapped ion systems
Oluyemi Momoiyioluwa Almost-Sure Stability of a Noisy Autoparametric Vibration Absorber

Kevin Siu

Modelling Subglacial Hydrology under Future Climate Scenarios in Wilkes Subglacial Basin, Antarctica
Andrew Bernakevitch

Examination of Parametric Subharmonic Instability of K₁ Internal Tides Generated by Tidal Flow over a Ridge

Maria Rosa Preciado Rivas

Theoretical Description of the Forces on a Point Charge Moving Parallel to a Supported Two-dimensional Material

Dylan Ruth Examining the consistency between subglacial hydrology and basal friction inversion modeling for Slessor Glacier, East Antarctica
Aiden Huffman Boundary-Bound Reactions: Pattern Formation with and without Hydrodynamics
Daniel Hogg High-Resolution Analysis of Snow Albedo Interactions in the Arctic
Jonathan Tessier

Jets, Vortices and Turbulence in Quasi-Geostrophic Magnetohydrodynamics

Melissa Maria Stadt

Mathematical Modeling of Kidney Function During Pregnancy

Duy Nguyen

Some Mathematical Perspectives of Graph Neural Networks

Nicholas Joseph Emile Richardson A Sparse Random Feature Model for Signal Decomposition

Nicolas Castro-Folker   

Three-dimensional Simulations of an Internal Solitary Wave Shoaling Over a Shallow Slope

Aaron Baier-Reinio    Numerical analysis of divergence-free discontinuous Galerkin methods for incompressible flow problems

Master's Theses 2019

Cameron Meaney          

Mathematical Modelling of Cancer Treatments Involving Radiation Therapy and Hypoxia-Activated Prodrugs

Jennie Newman

Model for the RE-TC thalamic circuit with application to childhood absence epilepsy
Jesse Legaspi Prandtl number dependence of stratified turbulence
Kate Clements Black Hole to White Hole Quantum Tunnelling
Maliha Ahmed Model for a cortical circuit associated with childhood absence epilepsy
Rishiraj Chakraborty Particle Clustering and Sub-clustering as a Proxy for Mixing in Geophysical Flows
Stanislav Zonov Kalman Filter Based Sensor Placement For Burgers Equation
Petar Simidzija Correlation and Communication via a Quantum Field
Fabian Germ Estimation for Linear and Semi-linear Infinite-dimensional Systems

Master's Theses 2018

Jonathan Horrocks              Sparse Identification of Epidemiological Models from Empirical Data
Luc Larocque     Kinodynamic Planning with μ-Calculus Specifications
Ding Jia Quantum Indefinite Spacetime: Part II
Sarah Hyatt  Influence of the Atlantic Multidecadal Variability on the climate response to external forcing
Andrew Grace Direct Numerical Simulations of the Degeneration and Shear Instability of Large and Small Amplitude Basin Scale Internal Waves at Varied Aspect Ratios
Adam Morgan Finite Element Exterior Calculus with Applications to the Numerical Solution of the Green–Naghdi Equations
Heming Wang A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis

Khalida Parveen

Explicit Runge-Kutta time-stepping with the discontinuous Galerkin method

Master's Theses 2017

Robert Gooding-Townsend

The forest transition and ecological thresholds: resilience, recovery, and predictions

Hyung Jin Kim

The Early Universe: New Aspects of Cuscuton Theory, Modified Dispersion Relations and Pulsar Constraints on Vacuum Noise

Christian Ogbonna

Non-linear Interactions between Internal Wave Beams: Beyond the Traditional Approximation

Paul Tiede

The Relation between Polygonal Gravity and 3D Loop Quantum Gravity

Anthony Caterini

A Novel Mathematical Framework for the Analysis of Neural Networks

Matthew Ambacher

Normal Mode Wave-Vortex Decompositions of Mesoscale Simulations

Shawn Corvec

A modelling investigation into the impacts of the convective parameterization on the tropical circulation

Lorena Cid-Montiel

Existence and uniqueness of attracting slow manifolds: An application of the Ważewski principle

An Zhou

Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations

Guillaume Verdon-Akzam

Probing Quantum Fields: Measurements and Quantum Energy Teleportation                     

Master's Theses 2016

Erik Maki

Iterated Function Systems with Place-Dependent Probabilities and the Inverse Problem of Measure Approximation Using Moments

Athanasios (Demetri) Pananos

Early Warning Signals of Vaccine Scares.

Joanna Boneng

Infectious Disease Modeling with Interpersonal Contact Patterns as a Heterogeneous Network

Justin Shaw

A Model for Shear Response in Swimming Plankton

Brian Fernandes 

Modeling Photoluminescence Decay Dynamics in Nanocrystals

David Layden

Indirect Quantum Control: An Implementation-Independent Scheme

Hanzhe Chen

Floating Bodies with Surface Tension

Aaron Coutino

Halocline mixing due to heavy rainfall in the cenote's of the Yucatan Peninsula

Michael Hynes

A Taylor polynomial expansion line search for large-scale optimization

Cesar Ramirez Ibanez

Stability of Nonlinear Functional Differential Equations by the Contraction Mapping Principle

Minxin Zhang

Infinite-dimensional Kalman Filtering and Sensor Placement Problem

Sandhya Harnanan                          

Internal Wave Interaction with Broad Topography in the Presence of a Near-Bottom Stratification

Alexander Ashbourne

Efficient Runge-Kutta Based Local Time-Stepping Methods

Master's Theses 2015

Tian Qiao

Design of Tubular Network Systems Using Circle Packing and Discrete Optimization

Sumit Sijher

Topological Quantum Computation and Protected Gates

Jason Pye

Localising Information in Bandlimited Quantum Field Theory

Tawsif Khan

Optimal Sensor Location for the Estimation of a Linear Dispersive Wave Equation

Shaun Sawyer Gain-Scheduled Control of a Quadcopter UAV

Wenzhe Jiang 

Construction of Optimal Tubular Networks in Arbitrary Regions in R^3

Marie Barnhill

Extensions of Randomized Benchmarking

Seyed Ali Madani Tonekaboni

Quantitative Approaches to the Cancer Stem Cell Hypothesis

Naijing Kang

Green’s Function for Poisson Equation in Layered Nano-Structures including Graphene

Chengzhu Xu Numerical Simulations of Shoaling Internal Solitary Waves of Elevation
Brandon May                                              A Hybrid Cellular Automata Model for the Role of Reactive Oxygen Species in Novel Tumour Treatments Strategies

James Sandham     

Spectral Energy Balance in Convective Boundary Layers

Master's Theses 2014

Anson Maitland A First Taste of Quantum Gravity Effects: Deforming Phase Spaces with the Heisenberg Double
Oleg Kabernik Quantum Reference Frames and The Poincaré Symmetry
Abdulhamed Alsisi Quasi-Static Approximation for Numerical Computation of Plasmon Eigenfrequencies in Nanoparticles
Eric Bembenek Realizing Surface Driven Flows in the Primitive Equations
Jason Boisselle (QI) Port-based teleportation of continuous quantum variables
Keenan Lyon Analysis of Plasmons Sustained on the Surface of Graphene
Robert Leslie Irwin The Instability of Mesoscale Jets in Idealized Two-Layer Models
Junyu Lai Implementations of iterative algorithms in Hadoop and Spark
Arman Tavakoli H2-Optimal Sensor Location
John Ladan An Analysis of Stockwell Transforms, with Applications to Image Processing
Yangxin He Modelling Internal Solitary Waves and the Alternative Ostrovsky Equation
Daniel Puzzuoli (QI) Honest Approximations to Realistic Fault Models and Their Applications to Efficient Simulation of Quantum Error Correction
Krishan Rajaratnam                                          Orthogonal Separation of The Hamilton-Jacobi Equation on Spaces of Constant Curvature

Master's Theses 2013

Luke Bovard

Short-wave vortex instabilities in stratified flow

Mikhail Panine Explorations of Infinitesimal Inverse Spectral Geometry
Remziye Karabekmez Modeling of Cancer Signaling Pathways
Rastko Anicic Effects of the Dielectric Environment on the Electrical Properties of Graphene
Aidan Chatwin-Davies A Covariant Natural Ultraviolet Cutoff in Inflationary Cosmology
Victor Veitch Negative Quasi-Probability in the Context of Quantum Computation
Shyamila Wickramage Mathematical Modelling and Numerical Simulation of Marine Ecosystems With Applications to Ice Algae
Jason Olsthoorn The Impact of Internal Solitary Waves on the Nutrient Circulation System
Martin Fuhry An Implementation of the Discontinuous Galerkin Method on Graphics Processing Units
Janelle Resch Nonlinear Wave Propagation in Brass Instruments
Eric Webster (QI) On the Relation between Quantum Discord and Purified Entanglement

Master's Theses 2012

Boglarka Soos Multi-scale Models of Tumor Growth and Invasion
Jonathan Murley The two-space homogenization method
Jared Penney A Computational Study of Pressure Driven Flow in Waste Rock Piles
Zhaoxin Wan Flocking for Multi-Agent Dynamical Systems
Dale Connor The Discontinuous Galerkin Method Applied to Problems in Electromagnetism
Zhao Jin Application of repetitive control to the lateral motion in a roll-to-roll web system
Nazgol Shahbandi Interaction of Brain Cancer Stem Cells and the Tumour Microenvironment: A Computational Study

Master's Theses 2011

Anton Baglaenko Simulating lake dynamics: the effects of bathymetry and bottom drag
Christopher Morley Pricing CPPI Capital Guarantees: A Lagrangian Framework

Eduardo Dos Santos Lobo    Brandao  

On Infinitesimal Inverse Spectral Geometry

Drew Lloyd A Mathematical Model of the Bag-Cell Neuron in Aplysia Californica
Sonia Markes An Examination of Quantum Foundations
William Ko High-Resolution Numerical Simulations of Wind-Driven Gyres
Lisa Nagy Epidemic Models with Pulse Vaccination and Time Delay
Devin Glew Self-Similarity of Images and Non-local Image Processing
Tyler Holden Time-Optimal Control of Quantum Systems: Numerical Techniques and Singular Trajectories
Todd Murray Kemp Floating Bodies in the Absence of Gravity
Kelly Anne Ogden Flow Down a Wavy Inclined Plane

Master's Theses 2010

Joshua Fletcher Motion Planning and Observer Synthesis for a Two-Span Web Roller Machine
Benjamin Turnbull Stability of Impulsive Switched Systems in Two Measures
Mathieu Cliche Information propagation and entanglement generation between two Unruh-DeWitt detectors
Mahmoudreza Ghaznavi Nonlinear screening of external charge by doped graphene
Nitin Upadhyaya                                   Brownian Dynamics Simulation of Dusty Plasma: Comparison with Generalized Hydrodynamics
Antonia Sanchez Dynamic Magnetic Resonance Elastography
Adley Au A Multilevel Method for Image Segmentation

Master's Theses 2009

Colin Phipps Combination of Chemotherapy and Antiangiogenic Therapies: A Mathematical Modelling Approach
Herbert Tang Bayesian Analysis of Intratumoural Oxygen Data
Ryan Morris Topics in Quantum Foundations: Ontological Models, and Distinguishability as a Resource
Michael Dumphy The Influence of Mesoscale Eddies on the Internal Tide
Robert Huneault Time-Optimal Control of Closed Quantum Systems
Colin Turner Mathematical Modelling of Cancer Stem Cells
Chad Wells                                                                  Comparison of Approximation Schemes in Stochastic Simulation Methods for Stiff Chemical Systems
Scott Rostrup Solving Hyperbolic PDEs using Accelerator Architectures
Edward Dupont The Effect of Time-Varying Boundary Conditions on the Generation of Sum and Difference Frequency Tones in a Coaxial Loudspeaker
Katie Ferguson A Mathematical Model of CA1 Hippocampal Neurons with Astrocytic Input
Peter Stechlinski A Study of Infectious Disease Models with Switching
Derek Steinmoeller Flow Separation on the β-plane
Alen Shun PID Control of Systems with Hysteresis
Subasha Wickramarachichi Numerical Simulation of Surface Waves using Meshfree Methods
Wentao Liu Poincare Waves and Kelvin Waves in a Circular Lake

Master's Theses 2008

Edward Platt WKB Analysis of Tunnel Coupling in a Simple Model of a Double Quantum Dot
Ranmal Perera Unsteady Free Convection from Elliptic Tubes at Large Grashof Numbers
Ilya Kobelevskiy                                    Bifurcation analysis of a system of Morris-Lecar neurons with time delayed gap junctional coupling
Christopher Scott Ferrie Contrasting classical and quantum theory in the context of quasi-probability
Cameron Christou Optimal Dither and Noise Shaping in Image Processing
Easwar Magesan Gaining Information About a Quantum Channel Via Twirling
William Donnelly Entanglement Entropy in Quantum Gravity
Angus Prain Vacuum Energy in Expanding Spacetime and Superoscillation - Induced Resonance
Jeff Timko Bohmian Trajectories of the Two-Electron Helium Atom

Master's Theses 2007

Elham Monifi Root-Locus Theory for Infinite-Dimensional Systems
Yasunori Aoki Analysis of Asymptotic Solutions for Cusp Problems in Capillarity
James Gordon  Annular Capillary Surfaces: Properties and Approximation Techniques
Youna Hu                                                 The Effects of the Earth's Rotation on Internal Wave Near-resonant Triads and Weakly Nonlinear Models
Lei Tang Efficiency-based hp-refinement for finite element methods
Paul Ullrich Exact and Perturbed Friedmann-Lemaitre Cosmologies
Yijia Li   Determining relaxation times for porous media: Theory, measurement, and the inverse problem
Scott Sitar Entire Solutions to Dirichlet Type Problems
Anthony Chak Tong Chan        Distorted Wave Born Approximation For Inelastic Atomic Collision
Tyler Wilson Non-linear Effects on Stopping of Fast Moving Molecular Ions Through Solids
Roger Chor Chun Chau Controller Gain Optimization for Position Control of an SMA Wire
Eduardo Barrenechea A Query-Based Approach for the Analysis of Aspect-Oriented Systems