Applied Mathematics Commons^™

Applications Of Physics-Informed Graph Neural Networks In Wind Farm Layout Optimization, Emma R. Martin

Theses and Dissertations

Rapid advancements in data-driven deep learning models have led to their increased usage in recent years. Highly-effective models for conducting complex decision-making tasks have been developed. Given their success, data-driven deep learning models are being developed and improved in a variety of areas, one of which is renewable energy. In this thesis, we discuss the development of data-driven, deep learning models for optimizing wind farm layouts for maximum power output. We include a background for wind energy, the physics of fluid flow and power production, and two types of neural networks: graph neural networks and physics-informed neural networks. Additionally, we …

Analysis And Detection Of Cyber Attacks In Multi Vehicle Systems Using Macroscopic Models, Abhishek Kashyap

Mechanical and Aerospace Engineering Dissertations - Archive

The study of potential cyber-attacks in different domains is an active area of research. Given that systems are becoming more and more interconnected, cyber physical systems that operate infrastructure and/or plants can make these assets more vulnerable and open to different attack vectors. The primary focus of this research is the modeling, analysis and detection of cyber-attacks on platoons of autonomous cars and swarms of UAVs. In this work, we consider scenarios wherein an attacker may hack into a subset of vehicles in a multi-vehicle system and make subtle modifications in their parameters. Due to the interconnected nature of the …

A New Mechanistic Model Of Brain Metabolism With Optimal Parametrization, Alice Lubbe

Mathematics Dissertations - Archive

Models of glucose metabolism in the brain often focus on chemical exchanges and reactions that occur as part of the tricarboxylic acid cycle (TCA cycle). Experiments involving nuclear magnetic resonance (NMR) spectroscopy to detect and measure carbon-labeled isotopomers of metabolites such as glutamate in vivo inform kinetic, mechanistic models used to study metabolic pathways. In the present work, a new model with two compartments, astrocytic and neuronal, is developed using known biochemical processes and fit to experimental data coming from fully labeled glucose infusions. A gradient descent method is introduced and employed to obtain optimal flux parameter values involved in …

Uniform Regularity Estimates For The Stokes System In Perforated Domains, Jamison R. Wallace

Theses and Dissertations--Mathematics

We consider the Stokes equations in an unbounded domain $\omega_{\epsilon,\eta}$ perforated by small obstacles, where $\epsilon$ represents the minimal distance between obstacles and $\eta$ is the ratio between the obstacle size and $\epsilon$. We are able to obtain uniform $W^{1,q}$ estimates for solutions to the Stokes equations in such domains with bounding constants depending explicitly on $\epsilon$ and $\eta$.

Advancements In Elliptic Mesh Redistribution And Automated Overset Grid Generation For Computational Fluid Dynamics, Chase Ashby

Theses and Dissertations--Mathematics

Automated and robust structured curvilinear overset grid generation remains a significant challenge for the application of computational fluid dynamics. This thesis intro- duces a specialized anisotropic Mach cone aligned adaptation algorithm for low-boom simulations and an automated procedure for generating structured curvilinear overset grids for immersed boundary simulations. Results demonstrate that anisotropic mesh adaptation can reduce computational resource usage by over 50% while maintaining sonic boom prediction accuracy across the entire sonic boom domain compared to user-constructed Mach cone aligned grids. The proposed immersed overset grid gen- eration procedure eliminates the need for complex surface generation algorithms, producing grids suitable …

Investigation Of Space Charge Effects On Co2 Electrocatalytic Reduction On Gd-Doped Ceria Via Scanning Kelvin Probe And Model-Based Bayesian Analysis, Alejandro Mejia

Graduate Theses, Dissertations, and Problem Reports (ETD)

In studying novel energy conversion and storage systems, such as high-temperature electrolysis, numerous underlying fundamental physical processes remain unclear or inadequately understood. Among these, the modeling and comprehension of surface reaction mechanisms, coupled with the intricate effects of space‑charge interfaces, remains an unclear and challenging area of research.

The work of this dissertation involves the development of a 2D finite element analysis model, leveraging the robust MOOSE framework from INL. This model, featuring inhomogeneous defect thermodynamics for near-surface chemistry, formulated through Poisson‑Cahn variational theory, has been exploited for studying the electrocatalytic reduction of CO₂ on gadolinia doped ceria. The …

A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd

Mathematics Dissertations - Archive

In this dissertation, we first present a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune responses. A stochastic process that captures the system's inherent randomness determines the dynamics of colon cancer. The stochastic framework is based on the Fokker-Planck equation, which represents the evolution of the probability density function corresponding to the stochastic process. We formulate an optimization problem that takes individual patient data with randomness present and solves it to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, we perform a sensitivity analysis of the optimal parameter set to identify the …

Batch Culture Models Of The Murine Gut Microbiome & The Impact Of Simple Dormancy On Dormancy-Capable Microorganisms Models, Ana C. Mendez

Mathematics Dissertations - Archive

The proposed mathematical biology research utilizes mathematical models to gain insight into biological systems. These systems of ordinary differential equations model diverse topics, ranging from gut microbiomes to harmful algal blooms. A complete stability analysis, supporting phase plane portraits, bifurcation diagrams, and numerical simulations will accompany the models presented. In Chapter 2, the murine gut microbiome is modeled to match laboratory experiments in the literature. In these experiments, mice eat plasmid-carrying “donor” bacteria and naturally carry plasmid-free “resident” bacteria in their gut. The models aim to capture the behavior of plasmids, donor bacteria, and resident bacteria. Chapter 3 explores dormancy …

The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, Atallah El-Shenawy, Mohamed El-Gamel, Muhammad E. Anany

Mansoura Engineering Journal

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the …

Echolocation On Manifolds, Kerong Wang

Honors Theses

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.

In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …

The Precedence-Constrained Quadratic Knapsack Problem, Changkun Guan

Honors Theses

This thesis investigates the previously unstudied Precedence-Constrained Quadratic Knapsack Problem (PC-QKP), an NP-hard nonlinear combinatorial optimization problem. The PC-QKP is a variation of the traditional Knapsack Problem (KP) that introduces several additional complexities. By developing custom exact and approximate solution methods, and testing these on a wide range of carefully structured PC-QKP problem instances, we seek to identify and understand patterns that make some cases easier or harder to solve than others. The findings aim to help develop better strategies for solving this and similar problems in the future.

Adaptive Neh With Constrained Nearest Neighbor Subtours For The Electric Vehicle Routing Problem With Time Windows, Andrew Struthers

All Master's Theses

The development of electric vehicles is currently considered one of the most innovative areas in manufacturing. Largely driven by the desire to reduce greenhouse emissions, electric vehicles are seen as a viable alternative to internal combustion engine cars. Starting from consumer cars, a dedicated effort is being made to translate this into commercial vehicles for freight and delivery. This research introduces a novel adaptive Nawaz, Enscore, Ham (NEH) algorithm with constrained nearest neighbor subtour (NEH-NN). This algorithm is tested on the standard benchmark problems in literature and used as a seed solution for the Genetic Algorithm (GA). The performance and …

Beyond Cryptic Equations: Reimagining Concepts In Physics Through Metaheuristics And Fantasy Stories Using Neutrosophic Venn Diagram, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Physics, the grand narrative of the universe, bas long been viewed as realm of cold, hard equations. But what if we looked beyond the formulas and considered a more imaginative origin for some of its concepts? This article explores the intriguing possibility that physics, and even cosmology, might share a surprising kinship with metaheuristics and fantastical fiction.

Ermakov Equations Can Be Derived From Zel’Dovich Pancake, And They Are Cold And Nonlocal Through Using Neutrosophic Venn Diagram, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As we argue in a previous article, the labyrinthine worlds of Jorge Luis Borges are more than captivating narratives; they are portals to a deeper understanding of existence. By weaving elements of science-fiction fantasy with philosophical and ethical inquiries, Borges's short stories bridge the seemingly disparate realms of physics and the humanities, offering fertile ground for contemporary physics research. The present-day universe consists of galaxies, galaxy clusters, one-dimensional filaments and two-dimensional sheets or pancakes, all of which combine to form the cosmic web. The so called ”Zeldovich pancakes”, are very difficult to observe, because their overdensity is only slightly greater …

New Trends In Neutrosophic Theories And Applications, Volume Iii, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

The field of neutrosophic set theory and its applications has been rapidly expanding, particularly since the introduction of the journal "Neutrosophic Sets and Systems." New theories, techniques, and algorithms are being developed at a very high rate. One of the most notable trends in neutrosophic theory is its hybridization with other set theories such as rough set theory, bipolar set theory, soft set theory, hesitant fuzzy set theory, and more. Various hybrid structures like rough neutrosophic sets, neutrosophic soft set, single valued neutrosophic hesitant fuzzy sets, among others, have been proposed in a short period. Neutrosophic sets have proven to …

Combined Plithogenic Hypersoft Sets In Decision Making On Supplier Selection With Different Mcdm Approaches., Sikkanan Sudha, Ravi Priya, Nivetha Martin, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Decision making methods integrated with Plithogenic sets are highly feasible and resilient in designing optimal solutions. This research work identifies the research gaps of limited applications of combined plithogenic hypersoft sets (CPHSS) and hence proposes a supplier selection decision problem with an integrated approach combining CPHSS with MCDM methods. A generalized form of Plithogenic accuracy function is used in determining the plithogenic accuracy matrix to which the prominent ranking methods of TOPSIS, ELECTRE, VIKOR and MAIRCA are applied. The proposed hybrid decision approach is illustrated using supplier selection decision problem as a case study. The ranking results are compared with …

Logical Pluralism And Neutrosophy: Reflections On The Nature Of Truth, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The article explores the shift from classical binary logic (true and false) to a more complex landscape of logical frameworks. It introduces logical pluralism, which suggests that no single, universally accepted system of logic exists. The paper connects this idea to neutrosophy, a framework that extends fuzzy logic by incorporating a third value: indeterminacy. This triadic approach, where every proposition has a degree of truth (T), falsity (F), and indeterminacy (I), is particularly useful for managing incomplete or contradictory information. The author argues that different logical systems, like different tools, are suited for different problems, and that the …

Associated A Nexus With A Treesoft Sets And Vice Versa, Akbar Rezae, Karim Ghadimi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We recall the definitions of a nexus and a TreeSoft Set, and investigate the relation between them. We associated a nexus with a TreeSoft Set induced by a tree graph and vice versa.

An Innovative Approach On Yao’S Three-Way Decision Model Using Intuitionistic Fuzzy Sets For Medical Diagnosis, Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Florentin Smarandache, Hamza Ghazanfar Toor, Faiza Asif

Branch Mathematics and Statistics Faculty and Staff Publications

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a …