Recent Master's Theses - Applied Mathematics

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Master's Theses 2024

Author	Title
Zhongyu Xie	Continuous-Galerkin Summation-by-Parts Discretization of the Khokhlov-Zabolotskaya-Kuznetsov Equation with Application to High-Intensity-Focused Ultrasound
Alexandra Maierean	Blackbox Optimization for Free-space Quantum Key Distribution
Panagiotis Vlachos	Degenerate Parabolic Diffusion Equations: Theory and Applications in Climatology
Sonja Cotra	Systems biology models for cancer immunotherapy
Nat Kendal-Freedman	Analyzing Bacterial Conjugation with Graphical Models: A Model Comparison Approach
Sierra Legare	Reactive Tracers in Turbulence Models
Joeseph Poulin	Exponential Stability of Maxwell's Equations
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

Author	Title
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

Author	Title
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 Kâ‚ 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

Author	Title
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

Author	Title
Jonathan Horrocks	Sparse Identification of Epidemiological Models from Empirical Data
Luc Larocque	Kinodynamic Planning with Î¼-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 Greenâ€“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

Author	Title
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

Author	Title
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

Author	Title
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

Author	Title
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

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Master's Theses 2013

Author	Title
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

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Master's Theses 2012

Author	Title
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

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Master's Theses 2011

Author	Title
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

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Master's Theses 2010

Author	Title
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

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Master's Theses 2009

Author	Title
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

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Master's Theses 2008

Author	Title
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

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Master's Theses 2007

Author	Title
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

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