Applied Mathematics Commons^™

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 …

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, …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

Fuzzy-Ahp Based Decision Support System For The Selection Of Optimal Maintenance Strategy For Meter Gauge Railway Infrastructure: A Review, Hamisi J. Maulid

Tanzania Journal of Engineering and Technology (TJET)

There are many uncertainties and complexities associated with maintaining Meter Gauge Railway (MGR) infrastructure, which calls for a methodical approach to decision-making. The development and application of a fuzzy-AHP-based decision support system (DSS) to select the optimal maintenance strategy for the MGR are presented in this study. The review covers research from 2013 to 2023 and focusses on the use of Multi-Criteria Decision Making (MCDM) and Fuzzy Analytic Hierarchy Process (Fuzzy-AHP) techniques in railway infrastructure maintenance. To manage the inherent uncertainties and subjective judgements involved in maintenance decision-making, the Fuzzy-AHP methodology combines fuzzy logic with the Analytic Hierarchy Process (AHP). …

Review On Gas-To-Liquids Conversion Technology: Lessons From Case Studies And Potential Strategies For Implementation In Tanzania, Joseph H. Kihedu

Tanzania Journal of Engineering and Technology (TJET)

This review paper explores the transformative potential of Gas-to- Liquids (GTL) technology for harnessing Tanzania's vast natural gas resources. With significant discoveries of natural gas reserves totalling up to 57 Tcf in fields such as Songosongo, Mnazi Bay, Block 1, 2, 3 and 4. Tanzania is positioned to leverage GTL technology to convert these resources into high-value liquid fuels like gasoline, diesel and naphtha. Review of GTL process, its products and applications has been done. By analysing successful GTL projects globally and drawing lessons applicable to Tanzania, this paper provides strategic recommendations for policymakers and stakeholders to foster GTL development. …

Assessment Of Maintenance Performance Level Of Selected Hydropower Plants In Tanzania, Mahamudu H. Mtebwa

Tanzania Journal of Engineering and Technology (TJET)

Despite significant progress in increasing electricity access to over 78%, electricity reliability in Tanzania remains a concern, with frequent power outages reported. Maintenance issues in hydropower plants have been identified as a critical factor contributing to this problem. However, the specific maintenance performance levels have not been fully assessed. This study conducts a comprehensive evaluation of the maintenance performance of four key hydropower plants: Kidatu (204 MW), Kihansi (180 MW), Mtera (80 MW), and New Pangani Falls (68 MW). Data collected from staff surveys and maintenance records between 2018 and 2022 were used in the study. Although staff demonstrated a …

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 …

Assessment Of Digital Solutions For Conformity Assessment Of Legally Controlled Measuring Instruments In Tanzania, Faraja Nyoni

Tanzania Journal of Engineering and Technology (TJET)

The advent of state-of-the-art digital technologies since 2011 has led to the digital transformation of legal metrology practices to ensure the trustworthiness of software-controlled measuring instruments globally. Despite the digital transformation in legal metrological practices, the conformity assessment of legally controlled measuring instruments is manually done (i.e., paper-based) in Tanzania. The paper-based conformity assessment of legally controlled measuring instruments is prone to error and lacks efficiency and effectiveness. This study aimed to assess digital solutions for improving conformity assessment through a comprehensive survey conducted across various regions in Tanzania, targeting a stratified sample of 51 respondents from organizations involved in …

The Evolution Of Global Gold And Copper Trade Networks, Oleksandr Hulianskyi

Northeast Journal of Complex Systems (NEJCS)

Gold and copper have emerged as two of the most vital commodities in global trade. Despite serving distinct purposes, their international trade networks reveal interconnected patterns, critical to understanding the dynamics of global economics. This paper studies these attributes and their evolution during the last 36 years for both metals and finds correlations between them. The first part of the research is focused on the sustainability of networks through efficiency and robustness indexes; the second part is dedicated to interconnectedness – the Louvain and Bayesian SBM algorithms, partition, and modularity instruments are used. Community detection algorithms provide valuable insights into …

Exploring The Potential Of Large Language Models (Llms) To Simulate Social Group Dynamics: A Case Study Using The Board Game "Secret Hitler", Kaj Hansteen Izora, Christof Teuscher

Northeast Journal of Complex Systems (NEJCS)

This study explores the capacity of large language model-powered agents to simulate human-like behavior in multi-agent social systems. Using Secret Hitler — a hidden-role board game centered on trust, deception, and strategic communication — we evaluate how LLM agents navigate dynamic group interactions. Our findings show that agents exhibit human-like behaviors, including strategic temporal adaptation, contextual reasoning, and complex social cognition such as theory of mind and implicit coordination. Notably, 85% of agent decisions factored in at least two other players’ mental states, highlighting their capacity for multi-agent mental state inference. However, they struggled with key aspects of human gameplay, …

Orchestrating Complexity: The Art Of Virtual Leadership In System Modelling, Vijay Kumar Sonawane, Bipllab Roy, Purnendu Bikash Acharjee, Indu Pv

Northeast Journal of Complex Systems (NEJCS)

This paper explores the dynamics of virtual leadership within global remote work environments, focusing on the application of complex system modelling to understand and enhance leadership efficacy. The application of computational modelling has been a regular feature in economics, science and technology fields, however its application in virtual leadership with linkage to sport leadership appears to be a novel concept. Adopting a multidisciplinary approach, this paper incorporates Game Theory as a conceptual framework to make the leadership model more relevant and applicable that can offer simpler understanding of complex play of leadership drivers. The model incorporates five key leadership dimensional …

Leveraging Usage Of Ai In Education: Knowledge, Attitude And Behavioral Analysis On Students, Bipllab Roy, Purnendu Bikash Acharjee, Rohit Kumar Sharma, Ruptaheen Kramsapi, Shruti P

Northeast Journal of Complex Systems (NEJCS)

The paper explores the possible advantages and drawbacks of artificial intelligence (AI) on sustainability, with an emphasis on using AI to positively achieve SDGs. The study finds a significant vacuum in the literature on the association between knowledge, attitudes, and behaviors towards the use of AI tools and techniques in education and demographic characteristics (sex, age, education level, area of study, and city of origin). The purpose of this research is to close this knowledge gap and advance our understanding of how these demographic factors affect the integration of AI in educational environments. The study specifically aims to comprehend how …