PhD Theses - Applied Mathematics

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PhD Theses 2025

Author	Title
Yazdan Babazadeh Maghsoodlo	Deep Learning and Dynamical Systems Approaches to Critical Transitions in Socioâ€“Climate and Complex Systems
Ruikun Zhou	Learning-Based Stability Certification and System Identification of Nonlinear Dynamical Systems
Zitao He	Heterogeneity and homophily in coupled behavior-disease dynamics: from model structure to early warnings
Avneet Kaur	State estimation using machine learning
Mahdi Yavarian	Modeling the Frequency Response of the Graphene/Electrolyte Interface in Electrochemical Systems
Brayden Hull	Nonlinear Fields in Gravitation: Investigations in Black Hole and Cosmological Spacetimes
Adam Teixido-Bonfill	Harvesting entanglement from quantum fields: from theory to proposed superconducting implementations
Melissa Stadt	Mathematical modeling of whole-body electrolyte homeostasis
Maliha Ahmed	Multi-scale Modelling of Neurosteroid-mediated Seizure Trajectories in Childhood Absence Epilepsy
Kwan Tsaan Lai	Kinetic Energy Spectra, Backscatter, and Subgrid Parameterization Analysis in Radiative-Convective Equilibrium
Dongchang Li	Quickest Change Detection in Nonlinear Hidden Markov Models Using a Generalized CUSUM Procedure
Yusuf Aydogdu	Reduced-Order Modeling and Data Assimilation of the El Niño–Southern Oscillation
Jose Polo Gomez	Measurements of quantum fields with particle detectors
Amirhossein Dehghanizadeh	Cosmic Frontiers: From the Origins to Gravitational Wave Astronomy
Tales Rick Perche	The Information Locally Stored in Quantum Fields: From Entanglement to Gravity
Athira Satheesh Kumar	Examining Social and Climate Feedbacks: Linking Climate Opinions and Climate System in Social Networks
Mohammad Aali	Learning-Based Safety-Critical Control Under Uncertainty with Applications to Mobile Robots
Mehrshad Sadria	Deep Learning Models of Cellular Decision-Making Using Single-Cell Genomic Data

PhD Theses 2024

Author	Title
Sepehr Ghadami	Designing and simulating a micro-robot for transporting filamentous cargos in Newtonian and viscoelastic fluids
Milad Moshayedi	Mathematical modeling and computer simulation of interactions of charged particles with 2D materials
Hank Chen	Hopf 2-Algebras: Homotopy Higher Symmetries in Physics
Stephanie Abo	Multiscale Modelling of Biological Rhythms and Systems
Ala' Alalabi	Controller and Observer Designs for Partial Differential-Algebraic Equations
Liang Chen	Collective Dynamics of Large-Scale Spiking Neural Networks by Mean-Field Theory
Alexey Smirnov	Discrete total variation in multiple spatial dimensions and its applications
Mengyao Zhang	On Convergence Analysis of Stochastic and Distributed Gradient-Based Algorithms
Yuan Wang	Space-time Hybridizable Discontinuous Galerkin Method for the Advection-Diffusion Problem
Chuanzheng Wang	Safety-Critical Control for Dynamical Systems under Uncertainties

PhD Theses 2023

Author	Title
Donovan Allum	Simulations of Radiatively Driven Convection and Spatially Heterogeneous Solar Radiation Intensity in Ice-Covered Lakes
Maxwell Fitzsimmons	Properties of difference inclusions with computable reachable set
Maria-Eftychia Papageorgiou	Local measurements in Relativistic Quantum Information: localization and signaling
Esha Saha	Expanding the Scope of Random Feature Models: Theory and Applications
Zhanlue Liang	Formation Control of Multi-agent Systems via Impulsive Strategy
Dorsa Mohammadrezaei	Integrating Experimental and Computational Approaches to Optimize 3D Bioprinting of Cancer Cells
Aditya Jain	Improved Diagnostics & Performance for Quantum Error Correction
Cameron Meaney	Applications of Deep Learning to Differential Equation Models in Oncology
Panagiotis Tsimiklis	Higher Gauge Theory and Discrete Geometry
Julian Smith-Roberge	Motion from Growth, Order, and Incompressibility
Vahid Nourian	Modeling and simulation of uni- and multi-flagellar bacterial locomotion in a viscous fluid

PhD Theses 2022

Author	Title
James Petrie	Decentralized contact tracing protocols and a risk analysis approach to pandemic control
Yiming Meng	Bifurcation and Robust Control of Instabilities in the Presence of Uncertainties
Mana Donganont	Consensus Problems in Hybrid Multi-Agent Systems
Russell Milne	A spatially explicit modelling approach for predicting and managing the effects of coral reef stressors
Alison Cheeseman	A Critical Examination of Two Specific Approaches Used to Characterize Medical Images: i) Projection-based Descriptors for Image Retrieval and ii) Estimating Fractal Dimensions of Discrete Sets
Qiaoyin Pan	q-deformed LQG in three dimensional space-time
Krishna Dutt	Limiting techniques for the discontinuous Galerkin method on unstructured meshes
Andrew Grace	Numerical simulations of convection and gravity currents near the temperature of maximum density
Keegan Kirk	Numerical analysis of space-time hybridized discontinuous Galerkin methods for incompressible flows
Brydon Eastman	Machine Learning Techniques and Stochastic Modeling in Mathematical Oncology
Benjamin Lovitz	Tensors: Entanglement, Geometry, and Combinatorics

PhD Theses 2019

Author	Title
Yangang Chen	Numerical Methods for Hamilton-Jacobi-Bellman Equations with Applications
Kamran Akbari	Relativistic Theory of the Interaction of Two-Dimensional Materials with Moving Charged Particles
Lindsey Daniels	The Interactions of Graphene with Ionic Solutions and Their Effects on the Differential Capacitance for Sensing Applications
Kevin E.M. Church	Invariant manifold theory for impulsive functional differential equations with applications
Chengzhu Xu	Numerical Simulations of Internal Solitary and Solitary-Like Waves: Wave Interactions and Instabilities

PhD Theses 2018

Author	Title
Julian Rennert	Quasi-Hopf Symmetry in Loop Quantum Gravity with Cosmological constant and Spinfoams with timelike surfaces
Andrew Giuliani	A parallel, adaptive discontinuous Galerkin method for hyperbolic problems on unstructured meshes
Ian Hincks	Exploring Practical Methodologies for the Characterization and Control of Small Quantum Systems
Daniel Puzzuoli	Entanglement in single-shot quantum channel discrimination
David Deepwell	High resolution simulations of mode-2 internal waves: transport, shoaling, and the influence of rotation
Tahmina Akhter	Stochastic Effects and Fractal Kinetics in the Pharmacokinetics of Drug Transport

PhD Theses 2017

Author	Title
Cong Wu	Stability and Control of Caputo Fractional Order Systems
Monjur Morshed	Efficient Finite-difference Methods for Sensitivity Analysis of Stiff Stochastic Discrete Models of Biochemical Systems
Alexander James Maxwell Howse	Nonlinear Preconditioning Methods for Optimization and Parallel-In-Time Methods for 1D Scalar Hyperbolic Partial Differential Equations
Zhen Wang	Clustering behaviour in networks with time delayed all-to-all coupling
Kexue Zhang	Impulsive Control of Dynamical Networks
Mikhail Panine	On Perturbative Methods in Spectral Geometry
Keegan Keplinger	Persistent oscillations in the Aplysia bag cell network
Subasha Wickramarachchi	The hydrodynamics of two-dimensional oscillating flows over ripples: the effect of asymmetries in ripple shape and currents
Jared Penney	Direct Numerical Simulation of Salt Fingering Gravity Currents and Double-Diffusive Rayleigh-Taylor Instabilities
Sepideh Afshar	Lithium-Ion battery SOC estimation
Ali Mahdipour Shirayeh	Evolutionary Dynamics of Cancer: Spatial and Heterogeneous Effects

PhD Theses 2016

Author	Title
Giuseppe Sellaroli	Non-compact groups, tensor operators and applications to quantum gravity
Robert H. Jonsson	Decoupling of Information Propagation from Energy Propagation
John Lang	Mathematical Modelling of Social Factors in Decision Making Processes at the Individual and Population Levels
John Yawney	Stability of Coastal Jets: Linear Stability Calculations and Nonlinear Simulations
Kristopher Rowe	Simulation of Vortex Interactions With a Solid Wall Using Adaptive Mesh Refinement
Manda Winlaw	Algorithms and Models for Tensors and Networks with Applications in Data Science
Anton Baglaenko	The Effects of Confinement on Kelvin-Helmholtz Billows

PhD Theses 2015

Author	Title
Taghreed Sugati	On Stability and Stabilization of Hybrid Systems
Wilten Nicola	Bifurcation Analysis of Large Networks of Neurons
Herbert Tang	The Effects of Extrinsic and Intrinsic Noise on a Tumour and a Proposed Metastasis Model
Noel Chalmers	Superconvergence, Superaccuracy, and Stability of the Discontinuous Galerkin Finite Element Method
Puneet Sharma	Modeling Interactions of Graphene with Electrolyte in the Field-Effect Transistor Configuration
Daniel Otero	Function-valued Mappings and SSIM-based Optimization in Imaging
Sina Khani	Large eddy simulations and subgrid scale motions in stratified turbulence
Ilona Anna Kowalik-Urbaniak	The quest for "diagnostically lossless" medical image compression using objective image quality measures

PhD Theses 2014

Author	Title
Michael Dunphy	Focusing and Vertical Mode Scattering of the First Mode Internal Tide via Mesoscale Eddy Interactions
Peter Stechlinski	Qualitative Theory of Switched Integro-differential Equations with Applications
Colin Phipps	Mathematical models for angiogenic, metabolic and apoptotic processes in tumours
Andree Susanto	High-Order Finite-Volume Schemes for Magnetohydrodynamics
Derek Steinmoeller	High-Order Numerical Methods in Lake Modelling
Venkata Manem	Mathematical Modeling of Secondary Malignancies and Associated Treatment Strategies
Alex Shum	Optimal Direction-Dependent Path Planning for Autonomous Vehicles

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PhD Theses 2013

Author	Title
József Vass	On the Geometry of IFS Fractals and its Applications
Andrijana Burazin	Application of Mixture Theory to solid tumors and normal pressure hydrocephalus
Nancy Soontiens	Stratified Flow Over Topography: Steady Nonlinear Waves, Boundary Layer Instabilities, and Crater Topography
Amenda Chow	Control of Hysteresis in the Landau-Lifshitz Equation
Rasha Al Jamal	Bounded Control of the Kuramoto-Sivashinsky equation
Wentao Liu	Three Dimensional Hydrodynamic Modelling of Lake Erie: Kelvin Wave Propagation and Potential Effects of Climate Change on Thermal Structure and Dissolved Oxygen
Minghua Lin	Angles, Majorization, Wielandt Inequality and Applications
Killian Miller	Algebraic Multigrid for Markov Chains and Tensor Decomposition

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PhD Theses 2012

Author	Title
Rahul Rahul	Kinetic Modeling of Pyruvate Recycling Pathways in Pancreatic β-Cells
Ruibin Qin	The discontinuous Galerkin method on Cartesian grids with embedded geometries: spectrum analysis and implementation for Euler equations
Dominique Brunet	A Study of the Structural Similarity Image Quality Measure with Applications to Image Processing
Yasunori Aoki	Study of Singular Capillary Surfaces and Development of the Cluster Newton Method
Easwar Magesan	Characterizing Noise in Quantum Systems
Christopher Ferrie	Some Theory and Applications of Probability in Quantum Mechanics
Dhanaraja Kasinathan	H-∞ optimal actuator location
Wai Man NG	Energy Shaping for Systems with Two Degrees of Underactuation
Matthew Johnston	Topics in Chemical Reaction Network Theory

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PhD Theses 2011

Author	Title
Raluca Jessop	Stability and Hopf Bifurcation Analysis of Hopfield Neural Networks with a General Distribution of Delays
Yufang Hao	Generalizing sampling theory for time-varying Nyquist rates using self-adjoint extensions of symmetric operators with deficiency indices (1,1) in Hilbert spaces
Mohamad Alwan	Qualitative Properties of Stochastic Hybrid Systems and Applications
Yanwei Wang	Efficient Stockwell Transform with Applications to Image Processing
Christopher Subich	Simulation of the Navier-Stokes Equations in Three Dimensions with a Spectral Collocation Method
Timothy Rees	Internal Wave Generation and Near-Resonant Interactions: Theory and Applications
Volodymyr Gerasik	Energy transport in saturated porous media

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PhD Theses 2010

Author	Title
Jun Liu	Qualitative Studies of Nonlinear Hybrid Systems
Kathleen Wilkie	Cerebrospinal Fluid Pulsations and Aging Effects in Mathematical Models of Hydrocephalus
Sean Speziale	A Poroelastic Model of Transcapillary Flow
Nataliya Portman	The Modelling of Biological Growth: a Pattern Theoretic Approach

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PhD Theses 2009

Author	Title
Rudy Gunawan	Bayesian Inference Methods Applied to Cancer Research
Gibin George Powathil	Modeling of Brain Tumors: Effects of Microenvironment and Associated Therapeutic Strategies
Matthew Calder	Dynamical Systems Methods Applied to the Michaelis-Menten and Lindemann Mechanisms

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PhD Theses 2008

Author	Title
Gregory Mayer	Resolution Enhancement in Magnetic Resonance Imaging by Frequency Extrapolation
Cedric Beny	Information flow at the quantum-classical boundary
Lijun Wang	Internet Congestion Control: Modeling and Stability Analysis
Kahrizsangi Ebrahimi	Inverse Problems and Self-similarity in Imaging
Robert Martin	Bandlimited functions, curved manifolds, and self-adjoint extensions of symmetric operators

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PhD Theses 2007

Author	Title
Shannon Kennedy	Hedging Contingent Claims in Markets with Jumps
Alexander Korobov	Spectral analysis of internal waves generated by tide-topography interaction
Qing Wang	Stability and Boundedness of Impulsive Systems with Time Delay
Duncan Mowbray	Hydrodynamic Modelling of the Electronic Response of Carbon Nanotubes
Donald Campbell	The Sigma-Delta Modulator as a Chaotic Nonlinear Dynamical System

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