Applied Mathematics Commons^™

Uncertainty Quantification, Propagation & Conjunction Assessment In Orbital Mechanics Using Generalized Polynomial Chaos Expansion & 2-Dimensional Conjunction Plane Analysis Techniques, Monalisa Karim

Mechanical and Aerospace Engineering Theses

Uncertainties, that are inherent to dynamic models, can be associated with state initial conditions, force modelling errors, navigation and actuation errors. In system modelling stochastic differential equations are used to represent dynamic phenomena with uncertainties, for which the solutions are probability density functions of quantities of interest characterizing the realization of the stochastic processes. In Polynomial Chaos Expansion (PCE) propagation, these solutions are represented as weighted sums of multivariate spectral polynomials that are functions of the input random variables. Generalized polynomial chaos expansion (gPC) is an extension to the original homogenous PCE which projects the random solution onto a basis …

A 1d Symmetric Interior Penalty Discontinuous Galerkin Solver In Rust, William Aey

Williams Honors College, Honors Research Projects

This honors project will build a 1D Symmetric Interior Discontinuous Galerkin (SIPDG) solver in Rust for Stum-Liouville type problems such as the Poisson equation, with Robin, Dirichlet, and Neumann boundary conditions. The work will cover the full pipeline: starting from the strong form of the PDE, deriving the DG weak form, implementing element and interface operators, and assembling or apply the discrete operator. Rust's safety and concurrency (e.g, via Rayon) will be used to explore serial and parallel performance. A test-driven development approach will be used to maintain a strong suite of tests. The project will result in a documented …

Dataless Neural Networks For Boolean Satisfiability And Network Optimization, Andrew Evan Gautier

Graduate Theses, Dissertations, and Problem Reports (ETD)

Combinatorial optimization problems (COPs) require searching over a finite solution space subject to constraints, with the goal of satisfying an objective function. They arise in operations research, scheduling, resource allocation, circuit design, and many other fields. Many problems in combinatorial optimization (including satisfiability and network design) are NP-hard. Traditionally, researchers have built approximate solvers that return near- optimal solutions efficiently by developing increasingly sophisticated heuristics and meta- heuristics. Deep learning has provided new opportunities for improving combinatorial solvers by leveraging neural guidance to prune the search space. Traditional neural networks have distinct drawbacks in this context: separate training and …

A Reconstruction Method For The Anisotropic Electrical Conductivity In A Hybrid Planar Inverse Problem, Athanasios Dimitriadis

Graduate Studies Theses and Dissertations 2026

Some single-physics medical imaging methods fail to reliably discriminate benign from malignant biological tissue. In partial response, a new class of inverse problems employ multi-physics phenomena, coupling methods of high resolution with methods of high contrast. In this thesis we are concerned with one such problem in which an anisotropic electrical conductivity is to be recovered from some internal knowledge of the current density field generated by maintaining a fixed boundary voltage. This internal data is obtained by the method of Current Density Impedance Imaging (CDII), which combines Maxwell's equations with Magnetic Resonance Imaging (MRI) measurements. The anisotropy class is …

Revolution In The Age Of Social Media: A Mathematical Model For Information, Dissent, And Stability, Killian Muollo

Graduate Studies Theses and Dissertations 2026

Revolutions, defined by Skocpol as rapid transformations in class, state, and/or social structures, are important world events that can cause civil wars, spark international trends, and result in transitions toward democratic and autocratic regimes alike. They are characterized largely by the mechanism of mass mobilization, which is increasingly facilitated by online networks and digital communication. In this dissertation, we investigate such means and outcomes of revolutions as dynamical systems. We construct three models describing separate but complementary aspects of revolution, beginning at the smallest unit of analysis and then moving outward in scope. First, we construct a graph-based model to …

Microgravity-Induced Alterations In Left Atrial Hemodynamics And Thrombogenic Risk: Insights From Healthy And Atrial Fibrillation Models, Grace M. Hoeppner

Dissertations, Master's Theses and Master's Reports

Background: Microgravity exposure alters cardiovascular loading, yet its impact on left atrial flow dynamics and thrombotic risk remains poorly understood. This study investigates how spaceflight-relevant microgravity-induced changes in cardiac outflow affect left atrial hemodynamics in healthy individuals and patients with atrial fibrillation.

Methods: Patient-specific left atrial models were generated for three healthy individuals and three AF patients. Computational fluid dynamics (CFD) simulations were performed using each patient’s baseline mitral outflow waveform and two modified waveforms representing short- and long-duration post-flight cardiac loading changes derived from echocardiographic observations. Hemodynamic metrics included left atrial velocity, time averaged wall shear stress, oscillatory shear …

A Parallel Interval Modeling Framework For Nonlinear Systems: Application To A Modified Duffing Oscillator, Roman Voliansky, Nina Volianska

Northeast Journal of Complex Systems (NEJCS)

The paper presents a mathematical framework for converting nonlinear dynamical systems into parallel forms. This framework replaces the exact system motion equations with interval equations, enabling the representation of nonlinear functions over piecewise linear domains. Such representation enables the description of system motions using linear-like differential equations, which can be analyzed and manipulated using well-known control methods. One such method is eigenvalue analysis, a powerful tool in classical control theory since many techniques rely on the system’s characteristic polynomial and its eigenvalues. We apply this method to define interval system eigenvalues and track their variation during system operation. These eigenvalues …

Stability Analysis Of Thermohaline Convection With A Time-Varying Shear Flow Using The Lyapunov Method, Kalin Kochnev

Honors Scholar Theses

This work applies the Lyapunov method to identify instabilities and compute the growth rate of a linear time-varying system. The linear system studied describes cold fresh water on top of hot salty water with a periodically time-varying background shear flow. A time-dependent weighting matrix is employed to construct a Lyapunov function candidate. The resulting linear matrix inequalities are discretized in time using the forward Euler method. As the number of temporal discretization points increases, the growth rate predicted by the Lyapunov method or Floquet theory, used for comparison, will converge to the same value obtained from numerical simulations. Furthermore, the …

Global-Local Method For Poroelasticity Problems With Localized Pressure Effects, Hemantha Kunwar

Math Department Colloquium Series

In many poroelasticity applications, pressure effects are confined to a small region, making it inefficient and possibly unnecessary to solve the full system across the entire domain. Instead, we propose to solve the poroelasticity problem locally, where pressure effects are significant, and use a simpler linear elasticity model elsewhere. This creates a coupled elasticity–poroelasticity problem with transmission conditions. To solve this coupled problem, we propose a new non-intrusive global–local algorithm that iteratively solves the elasticity problem in the entire (global) domain and the poroelasticity problem only in a local domain, ensuring proper transmission conditions across the interface. This approach, which …

Reverse (Bio)Engineering: A Machine Learning Approach To Optimize Baseball Pitcher Health And Performance, Robert C. Moore

All Dissertations

Ball tracking systems are becoming ubiquitous in sport, creating an unprecedented opportunity for big data applications to optimize human health and performance. These applications are especially common in baseball, a sport known for analyzing ball flight data to quantify performance. Analysts routinely use ball flight data to identify the attributes of top performing pitchers, finding that the best pitchers throw with optimal combinations of release speed and spin to precise locations. However, for certain pitchers, the throwing motion required to produce optimal ball flight places exceedingly high biomechanical load on the elbow, and consequently injury rates continue to rise. This …

Universal Systems Simulation Via Constraint Hypergraphs With Applications To Digital Twins, John Morris

All Dissertations

The characterization of systems encompasses a variety of modeling frameworks designed to capture specific behaviors and components of various system domains. Whatever the framework, the core elements of a system representation are the information of the system and a description of how that information is related. The relations in deterministic systems are functions, which, when composed to form executable processes, can be used to simulate system data. A declarative modeling framework is one that encodes mechanisms for preparing these simulations within the model structure, allowing an external agent to form the execution processes required for a given context. To date, …

On The Scalability Of Anisotropic Mesh Adaptation On Distributed And Shared Memory Architectures For Numerical Approximations, Kevin Mark Garner Jr.

Computer Science Theses & Dissertations

Mesh generation is a critical component in numerical approximations of Partial Differential Equations (PDEs). One such example includes Computational Fluid Dynamics (CFD), as CFD simulations in turn are crucial for applications in many industries, such as personalized healthcare and the design of aerospace vehicles. Generating high quality meshes for large-scale CFD problems presents a significant bottleneck in the CFD workflow. This dissertation proposes “fast,” parallel 3D mesh generation methodologies that are designed to leverage the concurrency offered by emerging High-Performance Computing (HPC) architectures. First, a distributed memory method is presented that integrates a sequential state-of-the-art isotropic, advancing front local reconnection-based …

Ai-Driven Optimization Of Wind Energy Distribution In Texas Using Multi-Agent Reinforcement Learning, Waleed Amer, Owolabi Oluwadamilola, Bassey Ogbonnaya

SMU Data Science Review

Abstract. The integration of large-scale wind power into modern electrical grids presents persistent challenges due to variability, curtailment, and compliance with operational constraints. This study proposes a multi-agent reinforcement learning (MARL) framework for optimizing wind energy distribution within the Texas power grid. The system employs three specialized agents—managing wind curtailment, storage utilization, and load adjustments—to collaboratively balance supply and demand under dynamic grid conditions. Using historical operational data from the Electric Reliability Council of Texas (ERCOT), the framework was trained and evaluated on a range of scenarios encompassing both typical and extreme operating conditions. Results demonstrate substantial performance improvements compared …

Towards Robust Autonomous Systems: Handling Multi-Modal Uncertainties In Gps-Denied Environments, Vivya Kalidindi

Doctoral Dissertations

This dissertation focuses on designing a robust and uncertainty-aware framework for autonomous systems operating in GPS-denied environments, such as indoor infrastructures, underground tunnels, and lunar surfaces. The proposed framework addresses the challenges posed by multi-modal uncertainties, including sensor noise, distributional shifts under adverse conditions, and conflicting decision-making preferences. These challenges compromise the reliability and adaptability of autonomous platforms. To overcome these challenges, the proposed framework adopts a layered architecture that integrates advanced methodologies across the sensing, perception, and decision-making layers. At the sensing layer, an Edge-Kalman Filter combined with a density ratio-based update mechanism is employed to reduce aleatoric uncertainty …

Modeling Synaptic Dysfunction As Neural Contagion: A Graph-Based Sedr Framework For Simulating Signal Spread, Michelle Marfo, Dr. Padmanabhan Seshaiyer, Alonso Ogueda-Oliva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Hybrid Data Assimilation Approach For Parameter Estimation In Dynamical Systems, Xuejian Li

Math Department Colloquium Series

In this talk, we present a hybrid data assimilation (DA) method that integrates continuous data assimilation (CDA) with particle filtering to estimate parameters in dynamical systems. Parameter estimation in such systems is particularly challenging because it involves both determining the parameters and estimating the often high-dimensional physical state. To address this difficulty, we decouple the estimation of states and parameters by employing CDA for state estimation and particle filtering for parameter estimation, with information exchanged alternately between the two. This hybrid framework leverages the strengths of CDA in handling high-dimensional state estimation and the efficiency of particle filters in estimating …

Cnn-Based Hybrid Model For Detecting Blight Diseases In Potato Crops With Advanced Image Processing Techniques, Farian S. Ishengoma

Tanzania Journal of Engineering and Technology (TJET)

Potato production plays a vital role in global agriculture as a major food source for large populations. However, potato crops are highly susceptible to diseases, particularly Early Blight and Late Blight, which result in substantial yield losses. Timely detection and effective control of these diseases are essential for maintaining stable crop output. This study explores the integration of Convolutional Neural Networks (CNNs) and advanced image processing techniques to differentiate between diseased and healthy potato plants accurately. Two datasets comprising original and enhanced images were used to train four CNN models: InceptionV3, Xception, Densenet201, and Resnet152V2. The original images underwent background …

Optimal Location And Sizing Of Facts Devices To Improve Voltage Profiles On A 132 Kv Mwanza-Musoma-Nyamongo Transmission Line, Peter Makolo

Tanzania Journal of Engineering and Technology (TJET)

Recently, utility companies have desired to supply quality, stable and reliable power to customers, and ensure they meet the demand. Flexible AC Transmission Systems (FACTS) dynamic compensator devices such as Static Synchronous Compensator (STATCOM), Static VAr Compensator (SVC) and Unified Power Flow Controller (UPFC) are an impeccable choice, however, cost is one of the limiting factors following these technologies. In addition, using FACTS devices in the system requires a detailed steady state, dynamic and optimisation analysis to effectively meet the purpose and ensure reduced cost. This paper proposes using an optimised FACTS device to improve voltage profile, power transfer, system …

Meshless Discrete Velocity Boltzmann Model For Porous Media Flow, Amandine Maidenberg

Doctoral Dissertations and Master's Theses

This dissertation explores the combination of two sophisticated techniques for addressing computational fluid dynamics: the discrete velocity Boltzmann equation (DVBE) and the localized collocation meshless model with upwinding (U-LCMM). The DVBE is a high-level model that describes the foundations of transport phenomena by addressing the microscale motions of particles themselves and the effect of their aggregate behaviors on continuum principles. This equation integrates multiple scales of phenomena; while it can be used for fluid flow at Navier-Stokes scales, it can also resolve fine features that can only be described at the molecular level. This type of model is necessary for …

Stabilized Weak-Gradient Discontinuous Finite Elements With Optimal Error Estimates For Second-Order Elliptic Pdes, Aymen Laadhari

Mathematical Modelling and Numerical Simulation with Applications

This work introduces an accurate finite element approach employing a new stabilized discrete weak gradient, designed for second-order elliptic problems on arbitrary conforming meshes. We formulate the approach within a discontinuous Galerkin framework and derive a consistent and coercive bilinear form. Appropriate error analysis on a model problem confirms optimal convergence. Building on the core analysis, we extend the method to more challenging settings, including time-dependent heterogeneous scenarios and a biophysically realistic optimal-control model of photobleaching in the budding yeast cell. We further illustrate the versatility of the weak-gradient construction by applying it to an unsteady level-set equation relevant to …

Two Analytic Issues Arising From Models In Probability And Materials Science, Giang Vu Thanh Nguyen

Mathematics & Statistics Theses & Dissertations

This dissertation explores two distinct topics centered on mathematical models in probability theory and materials science. The first part investigates a series of functions derived from an adaptive algorithm designed to address the score-based secretary problem, a classic challenge in probability theory. This problem involves making immediate decisions to select the best candidate from a sequence of interviews. The algorithm aims to maximize the probability of selecting the optimal candidate based on observed scores. We prove two fundamental analytic properties of this sequence of functions as a theoretic support of the algorithm: first, the functions in the sequence each possess …

A Strict Physicality-Preserving Scheme For A 2d Q-Tensor Flow With A Singular Potential, Md Mashud Parvez

Mathematics & Statistics Theses & Dissertations

Nematic liquid crystals are a state of matter that exhibit properties between those of conventional liquids and solid crystals. Their unique ability to align molecules in specific directions makes them essential in various applications, including display technologies and advanced materials. To model their complex behavior, mathematical frameworks such as the Q-tensor model are used to describe the orientation and degree of molecular order. In this work, we introduce a numerical scheme for a two-dimensional (2D) dynamic Q-tensor model, which is formulated as an L²-gradient flow driven by the liquid crystal free energy and incorporates a singular potential to …

Advancing Real-World Implementation Of The Well Optimized Linear Finder (Wolf) High-Speed Atmospheric Turbulence Compensation Method, Timothy Evan Coon

Theses and Dissertations

This dissertation advances the real-world implementation of the Well Optimized Linear Finder (WOLF) method for high-speed Atmospheric Turbulence Compensation (ATC). Atmospheric turbulence introduces phase aberrations into optical wavefronts and degrades image quality in terrestrial imaging systems. Traditional phase diversity methods are computationally intensive and poorly suited to real-time operation. The WOLF method addresses these limitations through a novel, point-wise formulation of the optical transfer function (OTF) as a structured autocorrelation of the generalized pupil function (GPF). This formulation enables the estimation of phase aberrations at individual spatial coordinates with distributed computational complexity.

The research begins by developing a MATLAB-based simulation …

Mass Effects On Energy Transfer Paths In Nonlinear Vibrating Systems, Manal Mustafa

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

This dissertation examines the role of mass in nonlinear systems, uncovering its role in enabling passive energy redistribution and robust vibration control in both idealized and real-world structures. Focusing on a strongly nonlinear two-degree-of-freedom system, it investigates how changes in mass ratio influence the dynamics of energy transfer, nonlinear normal modes (NNMs), and dissipation behavior.

A number of significant contributions are introduced in this work beginning with the introduction of the frequency-energy-peaks (FE-pks) plot, a novel tool that visualizes how energy flows through the system, revealing transient resonance orbits, internal resonance effects, and effectively capturing the different nonlinear phenomena with …

Theoretical And Experimental Investigation Of Liquid-Liquid Phase Separation: Characterizing Elastin-Like-Polypeptides, Adam D. Quintana

Chemical and Biological Engineering ETDs

This dissertation develops and validates a semi-empirical Flory–Huggins-based interaction model, combined with Cahn–Hilliard simulations, for predicting multi-component liquid–liquid phase separation (LLPS) in elastin-like polypeptide (ELP) systems. Equilibrium droplet compositions, measured using a PDMS-based microfluidic device, enabled direct parameterization of interaction coefficients. The model was applied to generate phase diagrams and assess composition dependence in ternary mixtures. Cahn–Hilliard simulations were conducted to explore potential phase morphologies under different interfacial conditions. Multi-component Lattice Boltzmann simulations were implemented to model droplet morphology evolution under varying interfacial and diffusive parameters, reproducing experimentally relevant morphologies. A three-phase wetting study revealed conditions for selective wetting and …

Modifications To The Spiral Array: A Computational Approach To Music Analysis, Rose Bittle

DePaul Discoveries

The Spiral Array is a geometric model of musical tonality and exists as a tool in computer-aided music analysis. The model was first published in 2000 by Elaine Chew, PhD, in her thesis, Towards a Mathematical Model of Tonality. This project aimed to restructure the Spiral Array, limiting user ambiguity and optimizing the application of musical key finding. The existing model defines pitch, chord, and key location to form a series of spirals dependent on a set of flexible weights. In our research we were able to identify potential issues with the pitch definitions themselves and experiment with methods …

Fuzzy Logic-Based Decision Support System For Adoption Of Industry 4.0 Predictive Maintenance By Manufacturing Industries, Fred E. Peter

Tanzania Journal of Engineering and Technology (TJET)

In the context of Industry 4.0, predictive maintenance enhances operational efficiency by optimizing processes, minimizing downtime, and improving cost-effectiveness. However, implementing predictive maintenance requires a systematic approach due to its complexity. This study collected expert input from 15 food and beverage manufacturing industries located in Dar es Salaam, Tanzania, using a purposive sampling technique. Six representatives were selected from each industry, and their opinions were analyzed using MATLAB 7.6 through a fuzzy logic inference system. The analysis focused on key factors influencing Industry 4.0 technology adoption for predictive maintenance, including adoption intention (strategic decision, equipment data, perceived benefit) and perceived …

The Role Of Internal Factors On Vehicular Mobility, Aziz Mdimi

Tanzania Journal of Engineering and Technology (TJET)

Vehicle mobility internal factors are influenced by the performance state of the road surface quality, governor, engine, gear train, differential unit and mobility unit. Studies on vehicular mobility models exist for off-road external factors but absent on on-road internal factors. The on-road internal factors model describes the vehicular mobility performance as a function of internal factors. In the current undertaking, results are generated by the determination of mobility performance characteristics with the application of 2nd Order Ordinary Differential Equations and using Laplace operator with MATLAB Software simulation. The effect of road surface against the time taken varies accordingly. At a …

Towards Effective Academia-Industry Collaborations: The Case Of Higher Learning Institutions In Tanzania, Fatuma S. Ikuja

Tanzania Journal of Engineering and Technology (TJET)

Industries are the main consumers of products from higher learning institutions (HLIs); graduates for employment and research outputs for socio-economic development. Research outputs from HLIs are commercialized as services or products facilitated by academia-industry collaborations. The collaborations are expected to address mismatch between labour market needs and HLIs’ products, which has resulted in graduates’ employability challenges. Despite their importance, effective academia-industry collaborations remain challenging. This study explores the effectiveness of Academia-Industry collaborations established by HLIs in implementing the Higher Education Economic Transformation (HEET) project (2021-2026) in Tanzania. One of the project objectives is to build functional linkages between industry and …

Towards Future Sustainable Infrastructure: The Role Of Technical Audit In Tanzania’S Public Works, George C. Haule

Tanzania Journal of Engineering and Technology (TJET)

This study aimed to investigate the vital role and impact of technical audits in promoting sustainable infrastructure development in Tanzania. The role and effects of technical audits in long-term infrastructure development were studied using a mixed-methods approach with both quantitative and qualitative parts. Data were collected through analysis of technical audit documentation, a semi-structured questionnaire, and stakeholder interviews. The study revealed the various dimensions of infrastructure investment projects, including initiation and planning, design, procurement of contractors and consultants, contract management, environment, health, and safety. The technical audit findings reported weaknesses or non-performance issues in infrastructure planning at the national level …