Ph.D. Dissertations

Dissertation Title
Advising Professor(s)


Yuying Liu Neural Networks for Nonlinear Dynamical Systems Nathan Kutz & Steven Brunton
Jianghong Shi Representations of Biological and Artificial Neural Networks Eric Shea-Brown


Bobby Baraldi A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized Optimization Aleksandr Aravkin
Yu-Chen Cheng Asymptotic Behaviors and Perturbation Analysis of Stochastic Dynamics and Applications to Complex Systems Hong Qian
Kenan Li Crouzeix’s Conjecture and Beyond for Special Classes of Matrices Anne Greenbaum
Benjamin Liu Invasions with Fat-Tailed and Long-Distance Dispersal Mark Kot
Kelsey Maass Optimization Formulations and Algorithms for Cancer Therapy Aleksandr Aravkin
Megan Morrison From worms to wars, modeling and controlling networked dynamical systems Nathan Kutz
Diya Sashidhar Data-Driven Methods for Time Series Forecasting, Classification, and Uncertainty Quantification Nathan Kutz
Lowell Thompson Affine structures and stochastic thermodynamics on the space of measures Hong Qian
Xin Yang On the Riemann-Hilbert approach to the numerical solution of boundary-value problems for evolution partial differential equations Bernard Deconinck & Thomas Trogdon
Yang Zhou Stochastic Control Methods for Dynamic Futures Portfolios Tim Leung


Matthew Farrell Revealing structure in trained neural networks through dimensionality based methods Eric Shea-Brown
Andreas L. Freund Wavelet-spectral analysis and large-eddy simulation using neural networks of droplet-laden decaying isotropic turbulence Antonio Ferrante
Yuan Gao Generalized Matrix-fractional Functions and Their Applications James Burke
Kelsey Marcinko Mathematical Analysis of Host–Parasitoid Dynamics Mark Kot
Sean Santos Time Step Sensitivity and Process Coupling in Climate Models Chris Bretherton/Peter Caldwell
Brian de Silva Data-driven discovery and model reduction of complex systems Nathan Kutz/Steven Brunton
Jeremy Upsal Stability of solutions of integrable partial differential equations Bernard Deconinck
Xin Yang On the Riemann-Hilbert approach to the numerical solution of boundary-value problems for evolution partial differential equations Bernard Deconinck/Tom Trogdon
Jize Zhang Nonconvex Optimization Methods with Applications to Portfolio Selection and Hybrid Systems Aleksandr Aravkin
Yang Zhou Stochastic control methods for dynamic futures portfolios Tim Leung


Weston D. Barger A Partial Differential Equation Approach to Three Problems in Finance: Barrier Option Pricing, Optimal Asset Liquidation and Insider Trading Matthew Lorig
Kathleen P. Champion From data to dynamics: discovering governing equations from data Nathan Kutz
Samuel H. Rudy Computational methods for system identification and data-driven forecasting Nathan Kutz/Steven Brunton
Peng Zheng Algorithm design for nonconvex and nonsmooth problems and its applications Aleksandr Aravkin


Tommaso Buvoli Polynomial-Based Methods for Time Integration Randall LeVeque
Krithika Manohar Data-Driven Sensor Placement Methods Nathan Kutz/Steven Brunton
Jacob Price Multiscale Techniques for Nonlinear Dynamical Systems: Applications and Theory Panos Stinis 
Yue Wang Some Problems in Stochastic Dynamics and Statistical Analysis of Single-Cell Biology of Cancer Hong Qian
Felix Xiaofeng Ye Stochastic Dynamics: Markov Chains, Random Transformations and Applications Hong Qian


Kameron Decker Harris This Brain is a Mess: Inference, Random Graphs, and Biophysics to Disentangle Neuronal Networks Eric Shea-Brown
Benjamin Lansdell On neural encoding: its estimation, application, and development Adrienne Fairhall
Yian Ma Irreversibility in Stochastic Dynamic Models and Efficient Bayesian Inference
Hong Qian
Susan C. Massey Multi-scale modeling of paracrine PDGF-driven glioma growth and invasion Kristin Swanson
Scott Moe High order shock capturing methods with compact stencils for use with adaptive mesh refinement and mapped grids Randall LeVeque
Donsub Rim Uncertainty quantification problems in tsunami modeling and reduced order models for hyperbolic partial differential equations Randall LeVeque
Daniel Shapero Data assimilation problems in glaciology Randall LeVeque/Ian Joughin
Timothy B. Oleskiw  On computing shape: a study of the neural processes concerning naturalistic boundary conformation within the ventral visual pathway Eric Shea-Brown 
Niket Thakkar Energy and Charge Transfer in Open Plasmonic Systems David Masiello
Benjamin Segal The stability and instabilities of stationary solutions to the nonlinear Schroedinger and sine-Gordon equation Bernard Deconinck


Xing Fu Integrating Data-Driven Methods in Nonlinear Dynamical Systems: Control, Sparsity, and Machine Learning Nathan Kutz
Jakob Kotas Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing Archis Ghate
Bethany Lusch Machine learning and data decompositions for complex networked dynamical systems Nathan Kutz
Syuzanna Sargsyan Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters Nathan Kutz
Mauricio del Razo Sarmina Stochastic Modeling of Reversible Biochemical Reaction-Diffusion Systems and High-Resolution Shock-Capturing Methods for Fluid Interfaces Randall LeVeque/Hong Qian


Natasha A. Cayco Gajic Coordinated Neural Activity: Mechanistic Origins and Impact on Stimulus Coding Eric Shea-Brown
Kathleen M. Curtius Multiscale Modeling of Esophageal Adenocarcinoma Georg Luebeck
Mikala C. Johnson Self-Optimizing Metamaterial Antennas Nathan Kutz
Pedro D. Maia Mathematical Modeling of Focal Axonal Swellings Arising in Traumatic Brain Injuries and Neurodegenerative Diseases Nathan Kutz
Natalie E. Sheils Interface Problems Using the Unified Transform Method Bernard Deconinck 
Olga Trichtchenko On the Instability of Water Waves with Surface Tension Bernard Deconinck 


Meng-Huo Chen Analysis of an Aggregation-based Algebraic Multigrid Method and its Parallelization Anne Greenbaum 
Yu Hu Collective Activity in Neural Networks: the Mathematical Structure of Connection Graphs and Population Codes Eric Shea-Brown 
Jihwan Kim Finite Volume Method for Tsunamis Generated by Submarine Landslides Randall LeVeque
Guillaume Lajoie On Driven Neural Assemblies: Synchrony, Chaos and Entropy Eric Shea-Brown


Jacob R. Grosek Robust Real-Time Image Processing Through Dynamic Mode Decomposition Nathan Kutz 
Christopher R. Jones Single-column and mixed-layer model analysis of subtropical stratocumulus response mechanisms relevant to climate change Christopher Bretherton
Grady I. Lemoine Numerical Modeling of Poroelastic-Fluid Systems Using High-Resolution Finite Volume Methods Randall LeVeque
Russell C. Rockne Patient-Specific Mathematical Radiation Oncology Kristin Swanson
Thomas D. Trogdon Riemann-Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions Bernard Deconinck 
Mingyuan Zhong Value function approximation methods for Linearly-solvable Markov Decision Process Emo Todorov
Ying Zhou Geographic Range Shifts under Climate Warming Mark Kot


Nicholas Cain Probabilistic, Statistical, and Dynamical Models of Neural Decision Making Eric Shea-Brown 
Joshua Jacobs Vortex Dynamics of Geostrophically Adjusted Density Perturbations in Stratified, Incompressible Fluids Randall LeVeque/Pascale Lelong
Laura Matarajt Arbetman Optimal Vaccine Allocation for Pandemic Influenza Mark Kot/Ira Longini
Vishal Vasan Some Boundary-Value Problems for Water Waves  Bernard Deconinck
Matthew Williams Exploiting Low Dimensionality in Nonlinear Optics and Other Physical Systems  Nathan Kutz
Yun Zhang ETG-ETL Portfolio Optimization James Burke 
Jiansong Zhou Climate Response to Solar Variation: Cyclic and Secular Ka Kit Tung


Lisa Bishop  The Origin of Noise-Induced Phenomena: A Mathematical Analysis of Mesoscopic Chemical and Biochemical Dynamics Hong Qian
Jonathan Claridge Numerical methods and studies of parabolic problems, operator splitting, and adaptive mesh refinement Randall LeVeque
Joshua Goldwyn Mathematical modeling of cochlear implants -- from single neurons to psychoacoustics Eric Shea-Brown
Edwin Ding Modeling High-Energy Temporal and Spatial Mode-Locking Nathan Kutz
Woo Hyun Kim On the Behavior of the Entropy Production Rate of a Diffusion Process in Nonequilibrium Steady State Hong Qian
Eleftherios Kirkinis Renormalization Group Methods in Applied Mathematics Robert O'Malley
Christine Lind Mathematical Models for Molecular Motors Hong Qian
Kyle Mandli Finite Volume Methods for the Multilayer Shallow Water Equations with Applications to Storm Surges Randall LeVeque
Peizhe Shi The Coupled Process and its Applications in Cellular Molecular Biology Hong Qian


Kirsten Fagnan High-resolution Finite Volume Methods for Extracorporeal Shock Wave Therapy Randall LeVeque
Minsun Kim A mathematical framework for spatiotemporal optimality in radiotherapy Archis Ghate
Eric MacHorro A study of several numerical methods for the Boltzmann transport problems   Anne Greenbaum
Junya Uchida Mixed-Layer Models and Large-Eddy Simulations of Stratocumulus-Topped Marine Boundary Layers: Their Nonlinear Dynamics and Sensitivity to Cloud Droplet Concentration Chris Bretherton 


Christopher Curtis  Exact and approximate methods for computing the spectral stability of traveling-wave solutions Bernard Deconinck
Dean Gull Steady State Analysis of Chemical Reaction Systems Hong Qian
Larry Jean Stochastic multi-scale modeling of carcinogenesis Georg Luebeck
David Ketcheson High Order Strong Stability Preserving Time Integrators and Numerical Wave Propagation Methods for Hyperbolic PDEs Randall LeVeque
Michael Nivala Nonlinear Stability in Integrable Hamiltonian Systems Bernard Deconinck
Katie Oliveras Stability of periodic surface gravity water waves Bernard Deconinck 
Yiyi Shi Theory of Random Networks and Their Applications Hong Qian
Melissa Vellela Mesoscopic dynamics of biochemical kinetic equations Hong Qian


Brandon Bale Modeling the stability and dynamics of mode-locked fiber lasers Nathan Kutz
Miguel Gomez Optimization-based Analysis of Rigid Mechanical Systems with Unilateral Contact and Kinetic Friction." Anne Greenbaum
Gunog Seo The dynamics of simple predator-prey models with Holling functional responses Mark Kot
Jason Slemons Toward the solution of the eigenproblem: Nonsymmetric tridiagonal matrices Loyce Adams


Jihyoun Jeon Mathematical modeling of pre-malignant lesions in multistage carcinogenesis Suresh Moolgavkar
Matthew Patterson  Algebro-geometric algorithms for integrable systems Bernard Deconinck
Santosh Srivastava Bayesian Minimum Expected Risk Estimation of Distributions for Statistical Learning Maya Gupta


David George Finite volume methods and adaptive refinement for tsunami propagation and inundation Randall LeVeque 
Eleftherios Gkioulekas A theoretical study of the cascades of 3D, 2D, and QG turbulence Ka Kit Tung
Rafael Meza Some Extensions and Applications of Multistage Carcinogenesis Models Suresh Moolgavkar
Damon Toth Analysis of Age-Structured Chemostat Models Mark Kot


Edward Farnum Stability and Dynamics of Solitary Waves in Nonlinear Optical Materials Nathan Kutz
William Heuett New Methods for Modeling Large-Scale Biochemical Networks Hong Qian
Rie Komuro Multi-Objective Evolutionary Algorithms for Ecological Process Models E. David Ford 
Marica Pelanti Wave Propagation Algorithms for Multicomponent Compressible Flows with Applications to Volcanic Jets Randall LeVeque
Matthew Peters Moist convection and the large scale tropical circulation Christopher Bretherton
David Williams Solving singular perturbation problems: An amplitude equation approach Robert O'Malley 


Sarah Hewitt Dynamics and Stability of Periodic Spatial Patterns in the Optical Parametric Oscillator Nathan Kutz
Viktoria Hsu Ion Transport through Biological Cell Membranes: From Electro-Diffusion to Hodgkin-Huxley via a Quasi Steady-State Approach Hong Qian
Jan Medlock Integro-differential-Equation Models in Ecology and Epidemiology Mark Kot
Timothy Reluga Some results on temporal and spatial heterogeneity in theoretical ecology Mark Kot


Kathleen Coughlin Stratospheric and Tropospheric Signals Extracted Using the Empirical Mode Decomposition Method Ka Kit Tung
Rebecca Crabb A Dynamic Game for Managing a Conservative Pollutant in an Estuary Thomas Leschine
Steven Kusiak The Scattering Support and the Inverse Scattering Problem at Fixed Frequency John Sylvester


Derek Bale Wave Propagation Algorithms On Curved Manifolds With Applications to Relativistic Hydrodynamics Randall LeVeque
Eric Dolven Seaquake Waves - Standing Wave Dynamics with Faraday Excitation and Radiative Loss Harry Yeh 
Long Lee Immersed Interface Methods for Incompressible Flow with Moving Interfaces Randall LeVeque
Blessing Mudavanhu A New Ronormalization Method for the Asymptotic Solution of Multiple Scale Singular Perturbation Problems Robert O'Malley
James Rossmanith A Wave Propagation Method with Constrained Transport for Ideal and Shallow Water Magnetohydrodynamics Randall LeVeque


Tiernan Fogarty Finite Volume Methods for Acoustics and Elasto-plasticity with Damage in a Heterogeneous Medium Randall LeVeque
Karl Knaub On the Asymptotic Behavior of Internal Layer Solutions of Advection-Diffusion-Reaction Equations Robert O'Malley
David Luke Analysis of Optical Wavefront Reconstruction and Deconvolution in Adaptive Optics James Burke


Arnold Kim Optical Pulse Propagation, Diffusion and Depolarization in Discrete Random Media Akira Ishimaru
Mark Martin The Influence of Seasonal and Climatic Environmental Changes on Plankton in the Marine Mixed Layer Mark Kot
Benjamin Moskowitz An Analysis of Frictional Feedback in the Madden-Julian Oscillation Christopher Bretherton
Dominik Obrist On the stability of the swept leading-edge boundary layer Peter Schmid
Darryl Yong Solving boundary-value problems for systems of hyperbolic conservation laws with rapidly varying coefficients Jirair Kevorkian


Donna Calhoun A Cartesian Grid Method for Solving the Streamfunction Vorticity Equations in Irregular Geometries Randall LeVeque
Kristin Swanson  Mathematical Modeling of the Growth and Control of Tumors James Murray


Trachette Jackson Mathematical Models in Two-Step Cancer Chemotherapy James Murray
Patrick Nelson  Mathematical Models of HIV Pathogenesis and Immunology James Murray 
Eric Stollnitz  Reproducing Color Images with Custom Inks David Salesin
Christopher Thompson  A Linear, Stochastic, Dynamical Model of El Nino/Southern Oscillation Ka Kit Tung


David Salinger A Splitting Algorithm for Multistage Stochastic Programming with Application to Hydropower Scheduling Terry Rockafellar


Daphne Manoussaki Modelling formation of vascular networks in vitro James Murray
Wendell Orlando Nonlinear Baroclinic Adjustment and Wavenumber Selection as a Mechanism for Atmospheric Heat Transport Ka Kit Tung 
Louis Stern An Explicitly Conservative Method for Time-Accurate Solution of Hyperbolic Partial Differential Equations on Embedded Chimera Grids Randall LeVeque
Rebecca Tyson Pattern formation by E. coli - mathematical and numerical investigation of a biological phenomenon James Murray
Zhiyun Yang A Cartesian Grid Method For Elliptic Boundary Value Problems in Irregular Regions Loyce Adams
Cynthia Young The two-frequency mutual conherence function of a Gaussian beam pulse in weak turbulence Akira Ishimaru
Chaoming Zhang Immersed interface methods for hyperbolic systems of partial differential equations with discontinuous coefficients Randall LeVeque


Julian Cook Mathematical Models for Dermal Wound Healing: Wound Contraction and Scar Formation James Murray
Ming Fang On the Axisymmetric Circulation of the Atmosphere Ka Kit Tung
Paul Kulesa A Model Mechanism for the Initiation and Spatial Patterning of Teeth Primordia in the Alligator James Murray
Thomas Milac The Linear Elastostatics of Spherical Shells Frederic Wan
Hugh Rand Mesoscale Dynamics of the Marine Atmospheric Boundary Layer Christopher Bretherton
Lei Wang Asymptotic Analysis of a Class of Three-Degree-Of-Freedom Hamiltonian Systems Near Stable Equilibria Jirair Kevorkian
Katrin White Territoriality and Survival in Wolf-Deer Interactions James Murray


Margaret Brown Geophysical inverse methods applied to the deduction of the emissions of atmospheric source gases Ka Kit Tung
George Chen Forward-Backward splitting techniques: Theory and Applications Terry Rockafellar
Chonghua Gu Shear Center of Plates with Variable Thickness Frederic Wan 
Jacques Laforgue  Using Exponential Asymptotics to Study the Metastability and Supersensitivity of Shock and Transition Layers Robert O'Malley
Zhilin Li  The Immersed Interface Method - A Numerical Approach for Partial Differential Equations with Interfaces Randall LeVeque
Kristyn Maschhoff Methods for Solving Large Symmetric Eigenvalue Problems Associated with Configuration Interaction Electronic Structure Calculations Loyce Adams
William Mell An Investigation of Closure Models for Nonpremixed Turbulent Reacting Flow George Kosaly 
Mike Neubert The Nonlinear Dynamics of Predator-Prey Growth and Dispersal Mark Kot
David Stevens An Adaptive Multilevel Method for Boundary Layer Meteorology Chris Bretherton
Mei Zhu Mechanisms for Biological Pattern Formation: Nonlinear Effects James Murray


Charles Mannix An Investigation of Numerical Methods Applicable to a Certain Class of Singular Integral Equations Ka Kit Tung
Keh-Ming Shyue Front Tracking Methods based on Wave Propagation Randall LeVeque


Yeng Bun Evolution of Three-Dimensional Disturbances in a Mixing Layer William Criminale
Kevin Gates Divide and Conquer Methods for the Symmetric Tridiagonal Eigenvalue Problem Loyce Adams
Jeffrey Greenough A Weakly Nonlinear Theory of Confined Supersonic Instability Modes James Riley
Steven Siems A Numerical Investigation of Cloud-Top Entrainment Instability and Related Experiements Chris Bretherton
Ciyou Zhu Methods for Large-Scale Extended Linear-Quadratic Programming Terry Rockafellar


Scott Coble Automatic Control of Extracorporeal Blood Oxygenation Juris Vagners
Mark Pernarowski The Mathematical Analysis of Bursting Electrical Activity in Pancreatic Beta Cells Jirair Kevorkian
Ruoxin Zhang Problems of Hierarchical Optimization: Nonsmoothness and Analysis of Solutions Terry Rockafellar


Richard Beyer A Computational Model of the Cochlea using the Immersed Boundary Method Randall LeVeque 
David Bosley Transient and Sustained Resonance in Very Slowly Varying Oscillatory Hamiltonian systems with Application to Free-Election Lasers Jirair Kevorkian
Marie Lelong Weakly-nonlinear Internal Wave/Vortical Mode Interactions in Stably-Stratified Flows  James Riley
Joseph Manke A Tensor Product B-spline Method for Numerical Grid Generation Loyce Adams
Maria Ong Hierarchical Basis Preconditioners for Second-Order Elliptic Problems in Three Dimensions Loyce Adams
Radhakrishnan Srinivasan Asymptotic Solutions of Weakly Nonlinear, Dispersive Wave Propagation Problems by Fourier Analysis Jirair Kevorkian
Kraig Winters Intensification and Instability of Internal Gravity Waves at Caustics and Critical Levels James Riley


Philip Harrison A New Algorithm for Parsing Generalized Phrase Structure Grammar Juris Vagners
Angel Muleshkov Analytical and Numerical Determination of Steady Seepage Towards Vertical Cuts Chris Bretherton
Jun Yu Passage Through the Critical Froude Number for Shallow Water Waves over a Variable Bottom Jirair Kevorkian


Pierre Mourad A Nonlinear Wave-Wave Interaction Theory for the Generation of Multiscale Large Eddies in a Neutral Atmospheric Boundary Layer  
Donald Owen A Numerical Streamline Approach to Steady Internal Flows Carl Pearson 


Jeffrey Cordova Numerical Streamline Methods for Solving Steady Flow Problems (Methods, Compressible, Free Surface, Finite Difference.)  
Jie Sun On Monotropic Piecewise Quadratic Programming (Network, Algorithm, Convex Programming, Decomposition Method.)