Applied Mathematics Commons^™

Numerical Simulation Via Homotopy Perturbation Approach Of A Dissipative Squeezed Carreau Fluid Flow Due To A Sensor Surface, Sara Abdelsalam, W. Abbas, A.M. Megahed, H. M.H. Sadek, M.S. Emam

Basic Science Engineering

This study rigorously examines the interplay between viscous dissipation, magnetic effects, and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro cantilever channel, aiming to deepen our understanding of heat transport processes in complex fluid dynamics scenarios. The primary objective is to elucidate how physical operational parameters influence both the velocity of fluid flow and its temperature distribution, utilizing a comprehensive numerical approach. Employing a combination of mathematical modeling techniques, including similarity transformation, this investigation transforms complex partial differential equations into more manageable ordinary ones, subsequently solving them using …

Quantitative Preventive Approaches To Diabetes: Mathematical Modeling And Analysis, Rushi P. Bhatt

Theses, Dissertations and Culminating Projects

The rising prevalence of diabetes presents a pressing global health concern, necessitating effective control strategies. This study aims to construct a mathematical model to analyze the influence of diverse factors on blood sugar levels, with a focus on identifying optimal methods for maintaining healthy glucose levels. Employing ordinary differential equations (ODE), the model investigates variables including leptin resistance, fat mass, glucose, insulin resistance, beta cell mass, daily physical activity, and dietary intake. Utilizing parameter estimates from existing literature, the model’s framework is established, and simulation results elucidate the intricate interplay between lifestyle choices and blood glucose dynamics. Furthermore, the model …

The Anatomy Of A Reconstruction: From Fourier Space To Image Recovery In Computed Tomography, Charlotte P. Maurer

Honors Theses

This thesis develops the mathematical foundations of computed tomography (CT) reconstruction through the lens of harmonic analysis. Beginning with the Schwartz class, we introduce the Fourier transform and its role in expressing the Radon transform and its inversion via a fractional Laplacian. After constructing the Radon transform in general dimension R^d, we specialize to the cases d = 2 and d = 3, demonstrating explicit inversion formulas and the associated instability in lower dimensions. For its computational advantages, we study filtered back-projection using classical low-pass filters (Ram-Lak, Shepp–Logan, Cosine, Gaussian) and formulate a discrete reconstruction algorithm grounded in …

Wave Reflections In A Biophysically Detailed Model Of Cardiac Tissue, Grace Moberg

Honors Theses

Regular heart rhythms are governed by the coordinated spread of action potentials through cardiac tissue. The interaction of an action potential with a tissue heterogeneity may lead to a reflection, where both a retrograde and an anterograde wave propagate off of the initial impulse. Reflections have been experimentally linked to cardiac arrhythmias, but their mechanisms of generation are not well-understood. Mathematically, reflections in phenomenological models of cardiac tissue have been linked to an unstable periodic orbit. These models typically sacrifice detail about the variety of ionic currents and processes involved in action potential propagation in favor of mathematical simplicity. Biophysically …

Estimating Pedestrian Crossing Times At Scramble Crossings Via Machine Learning And Agent-Based Modeling, Sho Takami

CURE Proceedings

Scramble crosswalks differ from conventional crosswalks in their ability for pedestrians to cross diagonally. This research compares the average crossing times and investigates the walking behaviors that pedestrians adopt to produce the speediest times in the two crosswalk configurations. Identification of the most efficient set of walking behaviors is done through an agent-based model, whereas producing polynomials relating crossing times to the most prominent walking behaviors is done through regression algorithms in machine learning. With the combination of these two approaches, it is revealed that pedestrians must adopt a relaxed walking style to make each crosswalk configuration efficient. Additionally, between …

Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita

Branch Mathematics and Statistics Faculty and Staff Publications

The study of uncertainty has been a significant area of research, with concepts such as fuzzy sets [87], fuzzy graphs [51], and neutrosophic sets [58] receiving extensive attention. In Neutrosophic Logic, indeterminacy often arises from real-world complexities. This paper explores the concept of locality as a key factor in determining indeterminacy, building upon the framework introduced by F. Smarandache in [73]. Locality refers to processes constrained within a specific region, where an object or system is directly influenced by its immediate surroundings. In contrast, nonlocality involves effects that transcend spatial or temporal boundaries, where changes in one location have direct …

Suntan (And Other Solar Trigonometric Functions): Solutions For Fermi Questions: February 2025, John Adam

Mathematics & Statistics Faculty Publications

The article discusses the intensity of sunlight on the side of the author's face as they walk to and from their office, focusing on the solar zenith angle θ. It presents a formula for solar irradiance and explores how the intensity changes based on the angle and elevation. The solutions to the questions posed in the article provide insights into the maximum irradiance levels at different angles and elevations.

Forecasting Equity Betas Using Option-Implied Moments, Ivan Kolesnikov

CMC Senior Theses

Traditional beta estimates are constructed from historical stock‑and‑market returns and therefore adjust only as fast as realized data accrue. This thesis investigates whether the forward‑looking information embedded in equity‑option prices can enhance beta forecasts. Using near‑end‑of‑day quotes for 236 S&P 500 firms between 2007 and 2024, I extract risk‑neutral variance and skewness, construct five alternative beta estimators (historical, option‑implied, and three hybrids), and evaluate them against realized betas over six‑, twelve‑, and twenty‑four‑month windows. Rolling‑OLS beta remains the most accurate benchmark at short horizons, yet option‑implied moments add economically and statistically significant value when systematic exposure is expected to change …

Mathematical Modeling Of Lead Climbing Falls, Rosemary Christmas Evans

EWU Masters Thesis Collection

This thesis presents a force-based mathematical model for simulating dynamic falls in lead sport climbing, with an emphasis on physical realism and empirical validation. The system is modeled as a mass–spring–damper, incorporating gravity, nonlinear rope stiffness, internal damping, and Capstan-style friction at protection points. The goal is to predict peak forces and rope elongation while capturing the complex dynamics of real climbing ropes. Several novel features are introduced. Activation switches ensure forces only engage when the rope is tensioned, preventing premature response. A velocity-sensitive stiffness transition function allows the rope to stiffen smoothly with increasing fall speed, reflecting rate-dependent rope …

Centralized Deep Reinforcement Learning For Homogeneous Multi-Component Maintenance Optimization, Joseph W. Wittrock

Theses and Dissertations

This thesis explores an application of reinforcement learning (RL) in maintenance optimization. Recent advances in hardware-accelerated computation and deep learning have made RL a powerful tool for solving optimization problems which are too complex for traditional methods. Maintenance optimization involves improving the efficiency and effectiveness of maintenance activities through data-driven approaches, ultimately reducing costs and increasing asset availability. Making informed maintenance decisions is crucial to long-term sustainability.

A desirable maintenance policy maximizes a utility signal while minimizing the cost of maintenance. Techniques in sequential decision making such as dynamic programming (DP) and RL have found success in optimizing these maintenance …

Regularized Methods For Tensor Recovery And Processing, Katherine J. Henneberger

Theses and Dissertations--Mathematics

The rapid growth of high-dimensional data has exposed the limitations of traditional vector and matrix-based methods for data analysis. These methods often struggle with computational inefficiencies, loss of critical cross-dimensional correlations, and challenges inherent in high-dimensional data. Tensors—multidimensional arrays—offer a robust framework for modeling and analyzing complex data. Tensor methods have proven valuable in tasks such as dimensionality reduction, feature extraction, and data compression, underpinning advancements in machine learning, computer vision, signal processing, and remote sensing.

This thesis focuses on two challenges in tensor analysis: tensor recovery and tensor processing. Tensor recovery addresses the reconstruction of incomplete or corrupted tensors. …

Novel Generative And Language Model Architectures With Applications, Edison Mucllari

Theses and Dissertations--Mathematics

This dissertation investigates novel architectures to address fundamental challenges in machine learning, particularly focusing on transformer models, recurrent neural networks, GAN and continual learning and their applications in natural language processing and computer vision. We propose the Neumann-Cayley Gated Recurrent Unit (NC-GRU), which leverages a Neumann series-based Scaled Cayley transformation to maintain orthogonal weight matrices, effectively mitigating exploding gradients problems while improving long-term memory retention across prediction tasks. We demonstrate the practical applications of NC-GRU by implementing our proposed architecture into an autoencoder to derive neural molecular fingerprints. Building upon these advancements, we turn our attention to the transformer architecture, …

Mathematical Contributions To The Study Of Chemotaxis And Cell Signaling, Hajr Zam

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation presents results from two mathematical projects concerned with the biology of cells. Chapter 1 provides biological background and places the two mathematical problems in the context of cell signaling. The larger project, with Prof. H. Hattori on a chemotaxis model is presented in Chapters 3 and 4. Work with Prof. \'{A}. Hal\'{a}sz on a chemical reaction network system with linear multimers and two types of labels is presented in Chapter 2. The chemotaxis system describes the one-dimensional dynamics of a species of cells with two chemical species, a chemo-attractant and chemo-repellent. The goal is to analyze the behavior …

Eulerian Smoke Simulation With Multiple Fields, Diyang Zhang

Dartmouth College Master’s Theses

Fluid simulation is a cornerstone of computer graphics, enabling the realistic depiction of dynamic phenomena such as smoke, fire, and other gaseous behaviours. This thesis focuses on advancing Eulerian smoke simulation techniques, with a particular emphasis on grid-based simulations that capture intricate vortical structures and fine visual details.

We propose several detail-preserving frameworks that incorporate various scalar and vector fields within the simulation pipeline, including velocity, impulse, and Lamb vectors, along with their decompositions and transformed representations. By mathematically analyzing the properties of impulse, we derive its scalar fields decomposition (ImpSFD), which introduces an alternative numerical interpretation, and Vortex-Particles in …

Horizontal Infiltration Of Water Through Porous Snow As A Gravity Current, Anthony Cheng

Dartmouth College Master’s Theses

On the surface of the Greenland ice sheet or around the margins of the Antarctic ice shelf, water infiltrates porous ice. It is important to understand this infiltration process since water populating the pore space of ice directly impacts the density, porosity, and wetness of ice. These properties influence the mechanics and tensile strength of ice, as greater amounts of infiltration result in faster or more widespread deformation events, which may lead to adverse climatic effects such as sea level rise and ocean current disruption. While studies have considered the thermodynamics and fluid mechanics of water vertically percolating through snow …

Integrating Sentiment Analysis In Predictive Models: A Comparative Study On Game Popularity On Steam, Khaleefa Alhemeiri

CMC Senior Theses

Over the past decades, the gaming industry has managed to evolve into a multi-billion-dollar enterprise. Gaming platforms such as Steam foster unprecedented amounts of engagement among players worldwide daily. In this thesis, we investigate the effect of incorporating sentiment-driven metrics, specifically YouTube view counts and positive reviews, into predictive models for game popularity. In addition, by comparing our linear regression sentiment-based approach to the Bayesian hierarchical folded normal model used by De Luisa et al. (2021), we can understand the many differences, strengths, and limitations of each methodology. In our thesis, we focus on three games. Each is of varying …

A Mathematical Modeling Approach To Investigate The Impacts Of Post-Infection Mortality And Partial Immunity On Disease Endemicity, Brendan M. Shrader

Honors Undergraduate Theses

A number of infectious diseases cause post-infection conditions or complications, such as COVID- 19, Q fever, and Polio. These conditions result in recovered individuals having a higher mortality rate than susceptibles, and this can impact disease dynamics. An existing mass-action model in the literature that incorporated post-infection mortality was shown to have limit cycles, or persistent oscillations, in the infected population. To better understand what causes these limit cycles, we develop and analyze a new epidemiological model with standard incidence. We show standard results, including the existence, uniqueness, and stability of the disease-free and endemic equilibria, and we rule out …

Harnessing Electroosmotic Hybrid Nanofluid Dynamics In Curved Arteries: Insights Into Biomedical Flow Enhancement, M. A. El Kot, A. M. Alsharif, Y. Abd Elmaboud, Sara Abdelsalam

Basic Science Engineering

No abstract provided.

A Finite Difference Analysis Of Electroosmotic Flow Of A Two-Layer Jeffrey Fluid In A Vertical Porous Nanochannel, Y. Abdelmaboud, M. A. Elkot, Sara Abdelsalam

Basic Science Engineering

In this paper, we discuss the unsteady two-layer electroosmotic flow (EOF) of the Jeffrey fluid in a vertical porous nanochannel, taking into account the effect of the heat transfer and alternating current (AC) electric fields. In this model, the two layers have different densities and viscosities. The finite difference method is used to solve the governing equations of electrical potential, velocity, and temperature. The results show that the Debye-Hückel parameter is significant in managing electroosmotic flow (EOF) because it affects the electrical double layer (EDL) compression and velocity gradients on the wall. The higher the radiation parameter, the lower the …

Scalable Parallel-In-Time Integration For Equations Of Motion, Nathan W. Chapman

All Master's Theses

Physical simulations always need to balance accuracy and run-time. This work implements the Parareal Algorithm using graphics processing units across a distributed system to accurately simulate time-dependent physics while attempting to minimize runtime. Data-transfer latency is identified as the primary bottleneck, for which mitigation methods are provided. Benchmarks comparing single-GPU and distributed implementations on a spectrum of coarse and fine discretizations are analyzed.