## 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