Applied Mathematics Commons^™

Thermo-Entropic Analysis Of Unsteady Mhd Nanofluid Couette Flow: A Classical Spectral Approach With An Exploratory Quantum Linear-Solver Application, Serai Israel Mosala, Oluwole Daniel Makinde, Azwinndini Muronga

Mathematical Modelling and Numerical Simulation with Applications

This study presents a thermo-entropic analysis of unsteady MHD nanofluid Couette flow, combining a classical bivariate spectral quasilinearisation (BI-SQLM) and Crank--Nicolson solution with an exploratory application of quantum linear solvers. An incompressible, electrically conducting nanofluid flows between parallel plates under partial slip and convective heat exchange; the discretised linear systems are additionally solved via the Harrow--Hassidim--Lloyd (HHL) algorithm and the Variational Quantum Linear Solver (VQLS). Results are presented for Pure Water, Cu-Water, and Al₂O₃-Water across seven parameter variations. The Hartmann number dominates velocity suppression and entropy amplification, while velocity slip reduces upper-wall entropy generation more than …

Effects Of Co-Rotating Cylinders And Boundary Conditions On Heat And Mass Transfer In A Trapezoidal Enclosure, Olalekan Adebayo Olayemi, Olalekan Tajudeen Popoola, Leke Thaddeus Oladimeji, Isaac Kayode Adegun, Taofiq Omoniyi Amoloye, Oluwatayo Babatope Ojo, Benjamin Ohida Daniel, Michael Olabode Ibiwoye

Mathematical Modelling and Numerical Simulation with Applications

This study investigates the effects of rotational speed $(\Omega)$, Richardson number $\left(Ri\right)$, and Lewis number $\left(Le\right)$ on heat and mass transfer (HMT) around two co-rotating cylinders symmetrically situated in a trapezoidal enclosure. In the double-diffusive mechanism, the bottom wall of the trapezium is at a high temperature $\left(T_h\right)$ and concentration $\left(C_h\right)$, while the top wall is at a low temperature $\left(T_c\right)$ and concentration $\left(C_c\right)$. The side walls are perfectly insulated with zero mass flux, while the buoyancy ratio $\left(Br\right)$ is fixed at 1.0.  Two thermal-mass boundary scenarios are considered. Scenario 1: Cylinders are thermally insulated with zero mass flux, and …

Using Graphic Novels In The Teaching And Learning Of Mathematics And Physics, Jason Ho, David Klanderman, Sarah Klanderman, James Turner

University Faculty Publications and Creative Works

Are you looking for innovative teaching strategies for geometry or other mathematics and physics courses? In this article, we o!er a discussion of several graphic novels and their potential for successful teaching and learning at the high school and university levels. We describe how engaging stories, combined with mathematical and scientific meaning found in both text and image, can help to excite students, enrich learning, and explain mathematical concepts. We report on recent data collected from multiple mathematics and physics classes that extend prior research on the use of graphic novels to teach English Language Arts (Boerman-Cornell and Kim, 2020) …

The Inverse Elasto-Acoustic Problem, Patrick Grice

Dissertations

A stable and numerically efficient boundary integral method formulation of the elasto-acoustic problem is presented, based on Fourier analysis. The method generalizes well to multiple scattering. The Frechet derivative of the elasto-acoustic problem with respect to shape perturbations is derived, and geometric flow theory is used to design stable numerical methods for the simulation of moving boundaries. The shape derivative is used to define a regularized Gauss-Newton algorithm for shape fitting of elasto-acoustic scatterers.

Evaluating A Dual-Beacon Hartmann Turbulence Profiling Technique Using Wave Optics Simulations, Benjamin C. Wilson, Matthew Kalensky, Santasri Bose-Pillai, Jack E. Mccrae

Faculty Publications

Resolving how optical turbulence varies along a propagation path remains a key challenge for designers of free-space optical propagation systems. Instruments such as scintillometers and differential image motion monitors are commonly used, but only provide path-integrated turbulence estimates. Point sensors provide localized estimates of turbulence strength and can be used to generate path-resolved profiles when an array of point sensors are distributed along the optical path. However, this approach can be costly and complex to deploy in certain environments. Alternatively, a single point sensor can be mounted on a mobile platform that collects data while traversing the optical path, although …

Electronic Structure Discretization And Compression Using Diagonal Basis Sets, Casey Lee Dowdle

Dartmouth College Ph.D Dissertations

Numerically solving the electronic structure problem is a fundamentally difficult problem due to the exponential growth in the dimension of the Hilbert space as the system size increases. In order to solve problems at a chemically relevant accuracy, both the choice of basis set and numerical method are important factors that are intrinsically connected.

In this thesis, we study the discretization and resulting compression of electronic Hamiltonians using diagonal basis sets. A diagonal basis set approximately diagonalizes the matrix and tensor representations of the one- and two-body potentials. This can reduce storage, simplify matrix-vector products, and lower the complexity of …

Numerical Modeling Of Thermo-Poroelasticity Using Finite Element Method, Maya Mckean

Discovery Day - Daytona Beach

We propose a numerical method for solving and modeling thermo-poroelasticity problems using a finite element formulation. Thermo-poroelasticity models describe the coupled interaction between mechanical deformation, fluid flow, and heat transfer in specific materials or environments over time. These models demonstrate the evolution of displacement, pressure, and temperature; we compute these fields in this work using backward Euler time discretization and Enriched Galerkin finite element spatial discretization. For these computations we used FreeFEM, a partial differential equation solver that uses the finite element method, which produced our numerical results. We then compared these values with the expected analytical solution. This was …

The Motion Of A Falling Object Under Linear Drag And How Differential Equations Can Be Used To Find It, Lukas Estrella

Discovery Day - Daytona Beach

This project, "The Motion of a Falling Object Under Linear Drag and How Differential Equations Can Be Used To Find It," investigates the motion of a falling object subject to air resistance through a combination of mathematical modeling and fundamental physical principles. The analysis is grounded in Newton’s second law, which yields a differential equation describing the forces acting on the object. Assuming a linear drag model, in which the resistive force is proportional to velocity, the governing equation reduces to a first-order ordinary differential equation for velocity. This equation is solved using the integrating factor method, yielding an explicit …

Motion With Air Resistance, Gauge Mccain, Jacob Bealefeld, Francesca Wise

Discovery Day - Daytona Beach

The motion of objects moving through air is influenced not only by gravity but also by air resistance, which affects the speed and acceleration of the object over time. This project examines the motion of a falling object by modeling it with an ordinary differential equation that accounts for both gravitational force and a resistive drag force proportional to velocity. Using Newton’s Second Law, a first-order differential equation is derived to describe how the velocity of the object changes as it falls. The solution of this equation demonstrates how the velocity increases initially and gradually approaches a constant value known …

On A Classification Of Goy/Sabra-Type Shell Models Of Turbulence, Austin Ho

Theses and Dissertations

Since their inception in the 1970s, shell models have proved to be a fruitful testbed for studying theories of turbulence. This thesis considers variations of two classical shell models: the Gledzer–Ohkitani–Yamada (GOY) model and the Sabra model. Up to conjugacy classes, we classify all possible GOY-type and Sabra-type models. We numerically approximate the scaling exponents for the newly identified models and develop their mathematical well-posedness.

Modelling Of Dust Devil Flow Dynamics: Effects Of The Sharpness Parameter On Velocity And Pressure, Deepanshu Kumar, Hossein Jafari

Mathematical Modelling and Numerical Simulation with Applications

This work discusses the development of a straightforward model of dust devils, demonstrating a method for estimating wind speed and pressure. The current model incorporates momentum equations and the mass conservation equation for steady, axisymmetric, inviscid, and incompressible flow. In this model, the radial velocity is first considered, which is restricted in both the radial and axial directions. The sharpness parameter is also incorporated into the radial velocity formulation, as described by Vatistas model. Using the radial velocity as a foundation, we derive the azimuthal and axial velocities. The study further evaluates the pressure. Notably, for large values of the …

Numerical Method For Strongly Variable-Density Flows At Low Mach Number: Flame-Sheet Regularisation And A Mass-Flux Immersed Boundary Method, Matheus P. Severino, Fernando F. Fachini, Elmer M. Gennaro, Daniel Rodríguez, Leandro F. Souza

Mathematical Modelling and Numerical Simulation with Applications

A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the disparity between the flow and acoustic speed. Therefore, low-Mach-number flows impose mathematical and computational challenges in their description. Standard numerical methods for compressible flows, which are typically designed for problems with a single dominant spatial and temporal scale, require alternative approaches, such as preconditioning techniques or solvers tailored for low-Mach-number equations. The present work introduces a simplified fluid dynamics model for flows …

(R2149) Heat, Hall, And Ion Slip Effects On Chemically Reacting Mhd Casson Flow Through Moving Surface, Gaurav Kumar, Vinod Kumar

Applications and Applied Mathematics: An International Journal (AAM)

The present investigation aims to analyze the combined effects of heat generation/absorption, Hall current, and ion slip on the flow of chemically reacting MHD Casson fluid over a moving vertical surface, considering ramped wall temperature and mass diffusion. The flow medium has been made porous. The analytical solution of the model's partial differential equations is derived using the Laplace transform technique aided by the Heaviside step function. The expressions for the Sherwood Number, Nusselt Number, and shear stress on the plate have been derived. The results obtained are found to be in outstanding agreement. The outcomes achieved are displayed through …

The Method Of Periodic Averaging Applied To Reduced Coupled Mode Theory Models For Fiber Laser Amplifiers, Rebecca Nicole Bryant

Dissertations and Theses

Fiber laser amplifier (FLA) models are often implemented without rigorous mathematical justification or thorough numerical validation. Without a proper theoretical basis for assumptions and approximations, or a technical analysis of model performance, there is significant uncertainty about the limitations of any given reduced model and its suitability for an application. This research aims to address the lack of comprehensive assessment of FLA models by directly comparing distinct models and recommending a mathematical alternative to replace heuristic model-reduction techniques. The work in this dissertation is divided into two projects: a comparative study that uses existing FLA models to assess the validity …

Generating Live Heatmaps Of Edr Data Through A Spatiotemporal Weighting, Joel T. Williams, C. Sean Bohun, Alberto Fornaci, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

This paper introduces a novel method for generating live heatmaps of eddy dissipation rate (EDR) data through a spatiotemporal weighting designed to enhance turbulence visualization in aviation. As more flight data become available, approaches relying solely on in-flight EDR measurements have the potential to accurately nowcast and visualize turbulence with low computational cost. The proposed method significantly improves the turbulence visualization capabilities of common commercial aircraft. This is particularly valuable for pilot decision-making and trip planning, enhancing flight safety and operational efficiency. This approach also incorporates an innovative uncertainty threshold, which refrains from predicting when there are insufficient data, thereby …

An Analytical Framework For Quantifying Urban And Community Resilience To Natural Hazards From Cell-Phone Gps-Location And Traffic-Flow Data, Georgios Chatzikyriakidis

Civil and Environmental Engineering Theses and Dissertations

Urban areas are increasingly exposed to natural hazards while accommodating a growing share of the global population, yet a consistent science-based framework for quantifying urban and community resilience remains lacking. This dissertation develops a physics-based analytical framework grounded in statistical mechanics and the quantitative theory of Brownian motion. A city is conceptualized as a complex medium in which citizens move analogously to Brownian particles within a viscoelastic environment, influenced by socioeconomic interactions and infrastructure functionality.

A central premise is that urban resilience, interpreted as engineering resilience (an outcome), can be quantified through a single metric: the mean-square displacement MSD=⟨r²(t)⟩, of …

Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard

LSU Doctoral Dissertations

Numerical algorithms for computing the electronic structure of incommensurate 2D-materials using ab initio models are critical for predicting material properties and guiding experiments. For bilayers, momentum space and continuum models have been introduced to approximate observables of ab initio tight-binding models using a momentum description, despite the lack of periodicity in the tight-binding model required for Bloch theory. A similar structure has been introduced for double-incommensurate trilayers using a continuum model, where the three lattices are mutually incommensurate. However, this description leads to a four-dimensional lattice space, and numerical convergence of the density of states has been observed to be …

Intermediate-Scale Outflow Dynamics Of Eta Carinae, Edmund J. Garcia, Matthew C. Fleenor

Departmental Honors & Graduate Capstone Projects

η Carinae (η Car) is a binary system, with the larger star being an extremely massive, luminous blue variable (LBV) beyond the Eddington Limit. Surrounding the η Car system, numerous multi-wavelength imaging campaigns reveal axisymmetric structures with the expanding bipolar Homunculus Nebula (¡1 pc). In combination with the episodic eruptive history of the η Car system, our initial intermediate-scale imaging revealed further axisym- metric structures (1-5 pc). To gain a more expansive view of how the small scale structure connects to panoramic imaging of the η Car region, we constructed a deep, optical, narrowband mosaic of 189 images utilizing the …

Physics-Informed Neural Network Solution Of The 2d Helmholtz Equation With A Gaussian Source, Theodoros Panagiotakopoulos, Chris Velissaris, Aristotelis Nikolaos Rapsomanikis

Faculty Scholarship and Creative Works

We present a physics-informed neural network (PINN) framework for solving the complex-valued two-dimensional Helmholtz equation with a localized Gaussian source and spatially varying permittivity. Starting from Maxwell’s equations, the frequency-domain scalar Helmholtz formulation under transverse electric (TE) polarization is derived and enforced directly within the neural network loss function. The model employs a sinusoidal representation network (SIREN) architecture to capture the oscillatory nature of wave solutions and incorporates the Sommerfeld radiation condition to impose open boundary conditions. Training is performed using a hybrid collocation strategy combined with a two-stage optimization procedure consisting of Adam followed by L-BFGS. Numerical experiments in …

Analysis Of The Effects Of Magnetic Field, Heat Transfer, And Thermal Radiation On Blood Flow Through Bifurcated Artery To Enhance Tumor Treatments, Abdullahi Isah, Dauda Gulibur Yakubu, Ali Musa

Tanzania Journal of Science

The work presents the effects of some pertinent parameters on blood flow through bifurcated artery to enhance tumor treatments. Combining appropriately the basic equations, together with the fractionalized Maxwell fluid model allow us to determine the velocity, temperature and concentration of blood flow through bifurcated artery. The study adopted the Atangana-Baleanu fractional time derivative on fluid model to describe the non-Newtonian behavior of blood flow. The numerical simulations were performed using the combined Laplace transform and the method of undetermined coefficients and the results obtained with the aid of Mathcad software were simulated and presented graphically. From the graphical results, …

Information Theory Analysis Of The Solar Wind Magnetic Structures For Space Weather Prediction, Katherine Holland

Doctoral Dissertations and Master's Theses

Forecasting space weather at Earth is highly complicated, because of the limited measurements of the dynamic processes in the Sun that span multiple temporal, spatial, and energy-scales. The solar wind is a highly structured, multi-scale, evolving plasma and consists of coronal mass ejections (CMEs), stream interaction regions (SIRs), expanding flux tubes (Borovsky, 2008), and interplanetary magnetic field (IMF) discontinuities and fluctuations. The aim of this research is to improve our understanding of the evolution and dissipation of different scale-size solar wind magnetic structures as they move from the Sun-Earth Lagrange point 1 (L1) to Earth's bow shock and, ultimately, to …

Bifurcation Exploration Of Ion Acoustic Solitons Formation Of A Nonlinear Beta Fractional Kadomtsev-Petviashvili Burger Model In Plasma State, Mst. Razia Pervin, Alrazi Abdeljabbar, Fahad Sameer Alshammari, Mst. Shekha Khatun, Harun Or-Roshid

Mathematical Modelling and Numerical Simulation with Applications

This research presents an extensive investigation of Ion acoustic soliton dynamics governed by a Beta-fractional Kadomtsev-Petviashvili-Burgurs (KPB) model. By engaging the planar dynamical system scheme in aggregation with the extended $(\phi, \psi)$ expansion, Kudryashov expansion, and the NMKM analytic schemes, we create a broad class of exact nonlinear pattern wave solutions. The local stability edifice of the fractional plasma model is explored through bifurcation theory, enabling the far-reaching classification of all admissible phase diagrams. Conforming Ion acoustic wave structures allied with every detour alignment are systematically assembled. Owing to the fractional and dissipative appearances of the model, an all-embracing assortment …

Markov-Modulated Queueing Network For Mobile Traffic Aggregation With Threshold-Controlled Buffers, Anton A. Esin, Elmira Yu. Kalimulina

Mathematical Modelling and Numerical Simulation with Applications

We study the problem of data transmission from mobile platforms operating in high-speed transit between cellular base stations, under conditions of unstable and intermittent connectivity. Conventional queueing and connectivity models often fail to capture the combined effects of rapidly changing signal conditions, finite buffer capacity, and dynamic topology. We aim to develop a tractable yet expressive model that integrates stochastic link availability, queue dynamics, and buffer control. We propose a mathematical framework based on queues whose service intensities are modulated by a continuous-time Markov chain (CTMC) representing signal conditions along a high-speed trajectory. The core subsystem is a two-stage (aggregation …

A Coupled Fractional Thermistor System Demonstrating Existence, Uniqueness, And Simulation Results With Two-Point Boundary Conditions, Yahia Awad, Angela Khattar, Hussein Fakih, Sami Hammoud, Karim Amin

Mathematical Modelling and Numerical Simulation with Applications

This paper studies a coupled system of Caputo fractional differential equations of orders $\alpha, \beta\in(1,2]$, subject to two-point boundary conditions. The model incorporates nonlinear nonlocal integral terms that capture the memory-dependent interactions between thermal and electrical dynamics in thermistor materials. We rigorously establish existence via Schaefer’s fixed-point theorem and uniqueness through Banach’s contraction principle in a Banach space of continuous and continuously differentiable functions. Additionally, we analyze Ulam–Hyers stability to quantify solution sensitivity to initial perturbations. A numerical example highlights the effects of fractional orders and nonlocal feedback on system behavior. This work generalizes classical thermistor models and provides a …

Memory Effects In Many-Body Systems, Jeffrey Beckstrand

Master's Projects

This thesis investigates memory effects in many-body systems through the MoriZwanzig Formalism for projected dynamics of a Hamiltonian System which yields the Generalized Langevin Equation (GLE). The GLE is a stochastic differential equation (SDE) that studies the dynamics of observables under the effects of many other observables in the system. Although satisfying, the GLE has a term called the Memory Kernel that encodes the past of the system and introduces a computational challenge by introducing a non-Markovian property to the equation. The kernel is often approximated by introducing a delta function, which simplifies the computation, but at the loss of …

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 …

Liutex - A Fluid Vortex, Oscar Alvarez

Mathematics Dissertations

Fluid vortices are found everywhere in our universe. A vortex can take the form of almost anything - from the classical spiral vortex to chaotic plumes. Defining a vortex physically and mathematically is absolutely necessary if we desire to study vortices and their interactions with each other as well as our physical world. Fluid vortices are incredibly important in the study of turbulent flows. From determining wear, optimizing design for better flow, efficiency, etc., to even predicting the weather on Earth or other planets, having the ability to measure vortices in fluid flow is invaluable. In this study, I investigate …

A Mathematical Frameworks For Singular, Nonlinear Phenomena: Applications To Nematocyst Firing And Inhomogeneous Nls With Coulomb Potential, Abdulrahman Alharbi

Theses and Dissertations

Nematocysts are specialized cellular organelles found in all cnidarians, including corals and jellyfish, as well as in some single-celled protists such as dinoflagellates. These organelles display remarkable diversity in morphology and function, playing roles in prey capture and defense. The firing of a nematocyst is one of the fastest accelerations in nature, yet the underlying physical mechanisms remain not fully understood. In this work, we address key questions: how sufficient force is generated to overcome the fluid boundary layer, whether fluid–structure interaction models can reproduce observed dynamics, and what mechanisms trigger discharge.

Our research investigates models based on osmotic pressure …

Quantum Mechanics As A Framework For Data Assimilation And Its Application To Atmospheric Parameterization, David Freeman

Dartmouth College Ph.D Dissertations

Quantum mechanics, as a mathematical system, can be understood as a generalization of classical probability theory. Quantum Mechanical Data Assimilation (QMDA) is a method in which classical dynamical systems are embedded into a quantum mechanical setting, with an associated data assimilation scheme leveraging the operator algebraic setting. In this dissertation, the algebraic structure underlying the operator theoretic formulation of QMDA is discussed. A procedure for closure of dynamical systems based on QMDA, known as Quantum Mechanical Closure (QMCl), is then constructed, and the procedures for constructing the quantum embeddings and implementing QMCl in practice are laid out and implemented for …

Entropic Foundation Of Finance And Physics: Securities Price Dynamics And Quantum Theory, Mohammad Abedi

Electronic Theses & Dissertations (2024 - present)

In many scientific and financial contexts, we must reason and make predictions under conditions of incomplete information. This dissertation develops Entropic Dynamics (ED) as a unified framework for deriving dynamical laws directly from principles of inference. Within this approach, probability distributions represent states of knowledge, and their evolution is determined through entropy maximization subject to relevant constraints. This leads to a novel concept of entropic time and a formulation of dynamics as an inferential process. In this talk, I will present how ED provides a common foundation across multiple domains. In physics, quantum dynamics for particles and scalar fields in …