Past PhD Dissertations
2023
- Nicholas Barendregt
Adaptive Decision-Making in Dynamic Environments Using Sequential Bayesian Inference - Abe Ellison
Gyroscopic Polynomials - Shay Gilpin
A New Perspective on Covariance Propagation for Data Assimilation Applications - Evan Gorman
On the Three-dimensional, Quadratic Differomorphism: Anti-integrability, Attractors, and Chaos - Amanda Hampton
On the Three-dimensional, Quadratic Differomorphism: Anti-integrability, Attractors, and Chaos - Yifeng Mao
Two-phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics - Ruyu Tan
Methods for Change Points Detection and Model Selection in State-Space Models - Kris Tucker
Analyzing Properties of Driven-Dissipative Quantum Systems from the Mean Field to Machine Learning
2022
- Subekshya Bidari
Models of Foraging Decisions in Social Animal Groups - Richard Clancy
Mathematical Formulations with Uncertain Data in Optimization and Inverse Problems - Ellen Ellefsen
Nonlocal Models with Applications in Ecology - Daniel Ferguson
Inference of Multiple Diffusion Coefficients from Single Particle Trajectories - Mingyu Hu
Micromagnetic modeling and waves in magnetic materials - Nicholas Landry
Contagion on Complex Systems: Structure and Dynamics - Allen Alvarez Loya
High-Order Methods for Wave Phenomena - Daniel Messenger
Weak-form Sparse Identification of Differential Equations from Noisy Measurements - Liam Madden
First-order Methods for Online and Stochastic Optimization, and Approximate Compiling - Graham Kesler O'Connor
Source Localization on Infection Networks - Samuel Ryskamp
Line Soliton Interactions and Dispersive Magnetoelastic Waves - Lyndsey Wong
Mathematical Models of Wealth Distribution Through An Amenities-Based Theory - Kiera van der Sande
Contributions to Computational Techniques and Machine Learning for Applied Science
2021
- Sabina Altus
Analysis of Multi-Structured Population Models - Lewis Baker
Inference of Multiple Diffusion Coefficients from Single Particle Trajectories - Alec Dunton
Matrix Methods for Low-Rank Compression in Large-Scale Applications - Fortino Garcia
Numerical Methods for Wave Phenomena - David Gunderman
High-order Spatial Discretization and Numerical Integration Schemes for Curved Geometries - Erik Johnson
Measuring image resolution in super-resolution microscopy and Bayesian estimation of population size and overlap and vaccine effectiveness - Osman Asif Malik
Topics in Matrix and Tensor Computations - Nathaniel Mathews
Computational Modeling for 3D Data Reconstruction of Solar Coronal Magnetic Fields - Caleb Miller
Monte Carlo Methods with Space Domain Applications - Joy Mueller
Perfectly Simulated and Exact Analytic Solutions for Chemical Reaction Networks and a Level Set Inspired Image Segmentation Algorithm - Zofia Stanley
Applications of Mathematics to Climate Modeling: Analysis and Development of Ocean Parameterizations and Multivariate Localization Functions - Jeremy Thompson
Local Fourier Analysis of Domain Decomposition and Multigrid Methods for High-Order Matrix-Free Finite Elements - Lucia Minah Yang
Numerical Analysis of Mixed Precision Algorithms and Time-steppers for Wave Turbulence, and Generative Modeling for Analogs in Data Assimilation
2020
- Dylan Abrahamsen
Space-time Evolution with Radial Basis Functions and Hermite-based Finite Difference Methods - Joshua Aurand
Optimal Control of Epstein-Zin Utility on Random Time Horizons - Harry Dudley
Dynamical System Analysis and Data-Driven Model Selection for Differential-Algebraic Equation Models of Microbial Electrolysis - Zhishen Huang
Randomization in Statistical Machine Learning - Mitchell Krock
Some Models for Large Spatial Data - Antony Pearson
On Hidden Structures in Contaminated Symbolic Data - Peter Shaffery
Understanding the Variance Reduction Effect and Bayesian Structural Time Series for Behind-the-Meter Disaggregation - Wenqi Zhang
Statistical Approaches to Assess High Frequency Variability of Solar Irradiance - Jacqui Wentz
Spatial-temporal Effects of Diffusion in Complex Biochemical Networks - Ashton Wiens
Using Gaussian Processes for Registration and Nonstationarity Emulation - Hao Xu
Qualitative Analysis of Some Elliptic Differential Equations
2019
- Tracy Babb
Accelerated Time-Stepping of Parabolic and Hyperbolic PDEs via Fast Direct Solvers for Elliptic Problems - Anna Broido
Describing the Tails of Degree Distributions in Real-World Networks - Jessica Gronski
Non-Convex Optimization and Applications to Bilinear Programming and Super-Resolution Imaging - Nathan Heavner
Building Rank-Revealing Factorizations with Randomization - Eric Kightley
Sparsified Gaussian Mixture Models - Michelle Maiden
Dispersive Hydrodynamics in Viscous Fluid Conduits
2018
- Joseph Benzaken
Propogation and Control of Geometric Variation in Engineering Structural Design and Analysis - Hillary Fairbanks
Low-Rank, Multi-Fidelity Methods for Uncertainty Quantification of High-Dimensional Systems - James Folberth
Fast and Reliable Methods in Numerical Linear Algebra, Signal Processing and Image Processing - Delyan Kalchev
Dual Least-Squares Finite Element Methods ofr Hyperbolic Problems - Zachary Mullen
Joint Temporal Modeling of Wind Speeds and Directions via the Projected Normal - John Nardini
Partial Differential Equation Models of Collective Migration During Wound Healing - Meredith Plumley
Investigations of Asymptotic Models for Convection-Driven Flows in Astrophysical and Geophysical Fluids - Benjamin Southworth
Seeking Space Aliens and the Strong Approximation Property: A (Disjoint) Study in Dust Plumes on Planetary Satellites and Nonsymmetric Algebraic Multigrid - Jay Stotsky
Computational and Mathematical Studies of Biomechanics of Biofilms - Peter Wills
Studies in the Analysis of Stochastic Processes - Xinshuo Yang
Reduction of Multivariate Mixtures and Its Applications
2017
- Jeffery Allen
What’s Cooler Than Being Cool? Ice Sheet Models Using a Fluidity-Based FOSLS Approach to Nonlinear-Stokes Flow - Alyson Fox
Algebraic Multigrid (AMG) for Graph Laplacian Linear Systems: Extensions of AMG for Signed, Undirected and Unsigned, Directed Graph - Inomzhon Mirzaev
Analytical and Numerical Investigation of Long-term Behavior of Microbial Flocculation Equations - Rebecca Mitchell
Designing a Finite-Time Mixer: Optimizing Stirring for Two-dimensional Maps - Wayne Mitchell
Low-communication, Parallel Multigrid Algorithms of Elliptic Partial Differential Equations - Ben O'Neill
Multigrid Reduction in Time for Parabolic Problems - Ignas Satkauskas
Numerical Calculus of Probability Density Functions
2016
- Dale Jennings
Advances in MCMC Methods with Applications to Particle Filtering, DSMC and Bayesian Networks - Benjamin Sturdevant
Fully Kinetic Ion Models for Magnetized Plasma Simulations - Ze Chang
Qualitative Analysis of Some Nonlinear PDE Systems - Anthony Wong
The Impact of Stable Water Isotopic Information on Parameter Calibration in a Land Surface Model - Ashar Ali
ULF Waves and Diffusive Radial Transport of Charged Particles - Lei Bao
Efficient Time-Integration Schemes for the Discontinuous Galerkin Non-Hydrostatic Atmospheric Models - David Nieves
Investigations of Reduced Equations for Rotating, Stratified and Non-hydrostatic Flows - Bradley Martin
Application of RBF-FD to Wave and Heat Transport Problems in Domains with Interfaces
2015
- David J. Appelhans
Trading Computation for Communication: A Low Communication Algorithm for the Parallel Solution of PDEs Using Range Decomposition, Nested Iteration, and Adaptive Mesh Refinement - Michael Brutz
Mathematical Modelling and Analysis of Several Diffusive Processes - Sijia Hao
Numerical Methods for Solving Linear Elliptic PDEs: Direct Solvers and High Order Accurate Discretizations - Christopher A. Leibs
First-Order Systems Least-Squares Finite Element Methods and Nested Iteration for Electromagnetic Two-Fluid Kinetic-Based Plasma Models - Nathan D. Monnig
From Nonlinear Embedding to Graph Distances: A Spectral Perspective - Henry P. Romero
Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach
2014
- Yuanting Chen
Bayesian Semi-parametric Modeling of Time-to-Event Data - Jose Humberto Garcia
Beta-Plane Approximation Of wind Driven Ocean Circulation Using A First Order System Least-Squares Formulation - Dustin Keck
Aggregation Dynamics: Numerical Approximations, Inverse Problems and Generalized Sensitivity - Amrik Sen
A Tale Of Waves And Eddies In A Sea Of Rotating Turbulence - Sekson Sirisubtawee
Stability and Bifurcations of a Piecewise-Smooth Elasto-Plastic Inverted Pendulum Model: Towards an Understanding of Dynamics of Buildings under Earthquake-type Forcing
2013
- Douglas Eugene Baldwin
Dispersive Shock Wave Interactions And Two-Dimensional Oceanwave Soliton Interactions - Adam Merritt Fox
Destruction Of Invariant Tori In Volume-Preserving Maps - Ryan Dean Lewis
Nonlinear Approximations In Filter Design And Wave Propagation - Brock Mosovsky
Finite-Time Transport In Aperiodic Dynamical Systems - Jonah A. Reeger
A Computational Study Of The Fourth Painlevé Equation And A Discussion Of Adams Predictor-Corrector Methods - Per Sebastian Skardal
Periodic Behavior In Cardiac Tissue: Dynamics Of Spatially Discordant Calcium Alternans - Dane Robert Taylor
Spectral Theory For The Robustness And Dynamical Properties Of Complex Networks - John Villavert
The Analysis Of Some Nonlinear Partial Differential Equations
2012
Zachary Alexander
A Topology-based Approach for Nonlinear Time Series with Applications in Computer Performance Analysis
David Biagioni
Numerical Construction of Green's Functions in High-dimensional Elliptic Problems with Variable Coefficients and Analysis of Renewable Energy Data via Sparse and Separable Approximations
Nathan Halko
Randomized Methods for Computing Low-rank Approximations of Matrices
Jason Hammond
Analysis and Simulation of Partial Differential Equations in Mathematical Biology: Applications to Bacterial Biofilms and Fisher's Equation
Jerrad Hampton
Dissimilarity and Optimal Sampling in Urn Ensembles
Daniel Kaslovsky
Geometric Sparsity in High Dimension
Daniel Larremore
Critical Dynamics in Complex Excitable Networks
Douglas Lipinski
Efficient Ridge Tracking Algorithms for Computing Lagrangian Coherent Structures in Fluid Dynamics Applications
Kuo Liu
Hybrid First-Order System Least-Squares Finite Element Methods with the Application to Stokes and Navier-Stokes Equations
Matthew Reynolds
Nonlinear Approximations in Tomography, Quadrature Construction, and Multivariate Reductions
Yuqi Wu
Parallel Scalable Domain Decomposition Method for Simulating Blood Flows in Three-dimensional Compliant Arteries
2011
Erin Byrne
The Post-fragmentation Probability for Bacterial Aggregates
Adrianna Gillman
Fast Direct Solvers for Elliptic Partial Differential Equations
Ian Grooms
Asymptotic and Numerical Methods for Rapidly Rotating Buoyant Flow
Sean Nixon
Development and Applications of Soliton Perturbation Theory
Kristine Snyder
Tuning and Control in Human Locomotion
Kye Taylor
Modeling and Analysis of the Low-dimensional Geometry of Signal and Image Patch-sets
2010
Jinyu Li
An Improved Short-DNA Elasticity Theory and a Model of the Dynamics of Biological Signaling Networks
Min Ho Park
Relaxation-corrected Bootstrap Algebraic Multigrid (rBAMG)
Lei Tang
Parallel Efficiency-based Adaptive Local Refinement
Patrick Young
Numerical Techniques for the Solution of Partial Differential and Integral Equations on Irregular Domains with Applications to Problems in Electrowetting
2009
James Adler
Nested Iteration and First Order Systems Least Squares on Incompressible Resistive Magnetohydrodynamics
Andrew Barker
Parallel Monolithic Fluid-structure Interaction Algorithms with Application to Blood Flow Simulation
Benjamin Jamroz
Reduced Modeling of the Magnetorotational Instability
Christian Ketelsen
Least-squares Finite Element Methods for Quantum Electrodynamics
Michael Levy
A High-order Element-based Galerkin Method for the Global Shallow Water Equations
Si Liu
Parallel Fully Coupled Domain Decomposition Algorithm for Some Inverse Problems
Gregory Norgard
Shock regularization of conservation laws through use of spatial averaging in nonlinear terms
2008
Nathan Aragon
Flip Estimators, Cross-Entropy, and Half-Stationary Bounding Processes for Monte Carlo Simulations
Seth Claudepierre
Solar Wind Driving of Magnetospheric Ultra-Low Frequency Pulsations
Terry Haut
Nonlocal Formulations of Ideal Fluids and Applications
Christopher Kurcz
Fast Convolutions with Helmoholtz Green's Functions and Radially Symmetric Band-Limited Kernels
Joshua Nolting
Efficiency-Based Local Adaptive Refinement for FOSLS Finite Elements
Cecile Piret
Analytical and Numerical Advances in Radial Basis Functions
Geoffrey Sanders
Extensions to Adaptive Smooth Aggregation (alphaSA) Multigrid: Eigensolver Initialization and nonsymmetric Problems
Michael Watson
A Study of Rotationally Constrained Convection in Tall Aspect Ratio Annular Geometries
2007
Chao Jin
Parallel Domain Decomposition Methods for Stochastic Partial Differential Equations and Analysis of Nonlinear Integral Equations
Jisun Lim
The Qualitative Study of a Chemical Reaction Diffusion System and Some Integral Equations
Wenjin Mao
Demension Jumping and Auxiliary Variable Techniques for Markov Chain Monte Carlo Algorithms
Jonathan Pietarila-Graham
Regularizations as Subgrid Models for Turbulent Flows
Thaned Rojsiraphisal
A Study of the Variablility in the North Indian Ocean
Brendan Sheehan
Multigrid Methods for Isotropic Neutron Transport
Jian Wang
Recovering Bayesian Networks with Applications to Gene Regulatory Networks
Julia Zuev
Recent Advances in Numerical Partial Differential Equations
2006
- Cory Ahrens
The Asymptotic Analysis of Communications and Wave Collapse Problems in Nonlinear Optics - Hong Liu
Rare Events, Heavy Tails, and Simulation - Mark Hoefer
Dispersive Shock Waves in Bose-Einstein Condensates and Nonlinear Nano-oscillators in Ferromagnetic Thin Films
2005
Marcio Carvalho
Applying Perfect Simulation to solve Stochastic Difference Equations that arise from certain Time Series Models
Paki Suwannajan
Evaluating the Performance of Latent Semantic Indexing
Srinath Vadlamani
An Algorithmic Unification of Particle-In-Cell and Continuum Methods and a Wave-Particle Description for the Electron Temperature Gradient (ETG) Instability Saturation
2004
Neil Martinsen-Burrell
Merger and Alignment of Three-dimensional Quasigeostrophic Vortices
Feng-Nan Hwang
Some Parallel Linear and Nonlinear Schwarz Methods with Applications in Computational Fluid Dynamics
Eunjung Lee
FOSLL* for Eddy Current Problems with Three-dimensional Edge Singularities
Scott MacLachlan
Improving Robustness in Multiscale Methods
Richard McNamara
Applications of Spanning Trees to Continuous-Time Markov Processes, with Emphasis on Loss Systems
Paul Mullowney
Lagrangian Particle Transport/Mixing in Blinking-Roll Systems
Mark Petersen
A Study of Geophysical and Astrophysical Turbulence using Reduced Equations
Oliver Roehrle
Multilevel First-Order System Least Squares for Quasilinear Elliptic Partial Differential Equations
Matthew Tearle
Optimal Perturbation Analysis of Stratified Shear Flows
Eric Thaler
An evaluation of the operational use of numerical solutions to the quasigeostrophic diagnostic equations by weather forecasters
Chad Westphal
First-Order System Least Squares for Geometrically-Nonlinear Elasticity in Nonsmooth Domains
2003
Allison Baker
Improving the performance of the linear solver restarted GMRES
Adriana Gómez-Hoyos (Dept. of Mathematics)
Conservative Maps: Reversibility, Invariants and Approximation
Luke Olson
Multilevel Least-Squares Finite Element Methods for Hyperbolic Partial Differential Equations
Cristina Perez
Simulating the Interaction Between Intraseasonal and Interannual Variability in the Tropical Pacific with a Coupled System of Nonlinear Ordinary Differential Equations
Kristian Sandberg
Forward and inverse wave propagation using bandlimited functions and a fast reconstruction algorithm for electron microscopy
Ulrike Schneider
Advances and Applications in Perfect Sampling
Grady Wright
Radical Basis function Interpolation: Numerical and Analytical Developments
2002
- Eric S. Wright
Modeling and Analysis of Aqueous Chemical Reactions in a Diffusive Environment
2001
Travis Austin
Advances on a Scaled Least-Squares Method for the 3-D Linear Boltzman Equation
Brian Bloechle
On the Taylor Dispersion of Reactive Solutes in a Parallel-Plate Fracture-Matrix System
John Carter
Stability and Existence of Traveling Wave Solutions of the Two-Dimensional Nonlinear Schrödinger Equation and its Higher-Order Generalizations
Tim Chartier
Element-Based Algebraic Multigrid (AMGe) and Spectral AMGe
Andrea Codd
Elasticity-Fluid Coupled Systems and Elliptic Grid Generation (EGG) based on First-Order System Least Squares (FOSLS)
Rudy Horne
Collision induced timing jitter and four-wave mixing in wavelength division multiplexing soliton systems
Hugh MacMillan
First-Order System Least Squares and Electrical Impedance Tomography
Bobby Phillip
Asynchronous Fast Adaptive Composite Grid Methods for Elliptic Problems on Adaptively-Refined Curvilinear Grids
2000
- Vlatcheslave Akmaev
Phylogenic Approach to Molecular Structure Prediction - Michelle Ghrist
High-order finite difference methods for wave equations - Ken Jarman
Stochastic immiscible flow with moment equations - Vanessa Robins
Computational Topology at Multiple Resolutions - David Trubatch
Topics in Solitons and Inverse Scattering: I. Discretization of the vector nonlinear Schrodinger equation, and II. A new class of 'reflectionless' potentials of the nonstationary Schrodinger equation and solutions of the Kadomtsev and Petviashvili I equation
1999
- Markus Berndt
Adaptive refinement and the Treatment of Discontinuous Coefficients for Multilevel First-Order System Least Square (FOSLS) - David Sterling
Anti-integrable continuation and the destruction of chaos
1998
- Lora Billings
Dynamical Systems Methods Applied to Polynomial Factorization Families: a Study of Chaotic Attractors - Bernard Deconinck
The initial-value problem for multiphase solutions of the Kadomtsev-Petviahvili equation - Laurie Heyer
The probabilistic behavior of sequence analysis scores with application to structural alignment of RNA - Peter Staab
Three-dimensional acoustic-rotational flows in solid-fuel rocket motors
1997
- Nicholas Coult
A Multiresolution Strategy for Homogenization of Partial Differential Equations
1996
- Robert Cramer
A Multiresolution Approach to Fast Summation and Regularization of Singular Operators - Barry Lee
First-Order Systems least Squares for Electromagnetics - Alejandro Spina
Confined States in Large Aspect Ratio Thermohaline Convection
1995
- Erik Bollt
Controlling Chaos, Targeting and Transport - James Keiser
I. Wavelet Based approach to Numerical Solution of Nonlinear Partial Differential Equations, and II. Nonlinear Waves I Fully Discrete Dynamical Systems - David Sholl
Lattice Gas Models of Surface Chemistry
1994
- Scott Herod
Computer Assisted Determination of Lie Point Symmetries with Application to Fluid Dynamics - Arthur Mizzi|
Spectral Representation of the Vertical Coordinate in Three-Dimensional Atmospherical Models on Tropical B- and f- Planes - Linda Sundbye
Global Existence of Solutions for the Shallow water Equations
1991
- James Brannick
Compatible Relaxation and Optimal Interpolation - Martha Nesbitt Limber
The Dynamics of Shooting Methods for Solving Sturm-Liouville Problems