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Articles 121 - 150 of 811

Full-Text Articles in Applied Mathematics

Mathematical Modeling Of Coupled Heat And Mass Transfer In Metal-Hydride Hydrogen Storage Systems, Muhammad Hasnain Jan 2024

Mathematical Modeling Of Coupled Heat And Mass Transfer In Metal-Hydride Hydrogen Storage Systems, Muhammad Hasnain

College of Graduate Studies: Theses & Dissertations

As a promising clean energy carrier hydrogen has recently gained significant interest, but its efficient and safe storage is a major challenge. Compared to the gaseous state and liquid state, metal hydrides (MH) offer a potentially more effective storage approach for hydrogen. However, the main challenge in this approach is the low thermal conductivity of the MH bed that leads to low heat transfer and ultimately to higher charging and discharging times. The purpose of this work is to develop an in-house comprehensive heat and mass transfer model for hydrogen sorption in MH reactors to simulate the dynamic behavior of …

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Numerical Modeling Of Thermal Runaway In Lithium-Ion Batteries Using Decomposition Kinetics And Inter-Cell Contact Resistance, Shehzad Khan Jan 2024

Numerical Modeling Of Thermal Runaway In Lithium-Ion Batteries Using Decomposition Kinetics And Inter-Cell Contact Resistance, Shehzad Khan

College of Graduate Studies: Theses & Dissertations

Lithium-ion batteries (LIBs) are central in numerous high-demand applications due to their high energy density and prolonged cycle life. Despite these advantages, their susceptibility to thermal runaway (TR) poses a significant safety risk, with the potential for catastrophic failures. This study focuses on the thermal behavior of prismatic lithium-ion cells, using a finite volume-based partial differential equation (PDE) solver developed in MATLAB and JULIA to model TR behavior. This solver accurately simulates transient behaviors, convection, diffusion, and source terms across various coordinate systems. By engaging in a series of increasing complex case studies, this research aims to identify the critical …

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Linear Topological Space, Vi Nguyen Jan 2024

Linear Topological Space, Vi Nguyen

UNF Graduate Theses and Dissertations

This thesis begins with an introduction to linear and topological spaces and then defines linear topological spaces. It studies key properties such as neighborhoods, convexity, reflexivity, and weak and weak* topologies. Finally, it concludes with solving non-linear partial differential equations.

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Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, Syed Tahmid Hussan Jan 2024

Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, Syed Tahmid Hussan

College of Graduate Studies: Theses & Dissertations

The understanding of Bender Element mechanism and utilization of Particle Flow Code (PFC) to simulate the seismic wave behavior is important to test the dynamic behavior of soil particles. Both discrete and finite element methods can be used to simulate wave behavior. However, Discrete Element Method (DEM) is mostly suitable, as the micro scaled soil particle cannot be fully considered as continuous specimen like a piece of rod or aluminum. Recently DEM has been widely used to study mechanical properties of soils at particle level considering the particles as balls. This study represents a comparative analysis of Voigt and Best …

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Long-Wave Modeling Of Viscous Film Dynamics Inside A Tube With Time-Dependent Radius, Robert E. Hicks Jan 2024

Long-Wave Modeling Of Viscous Film Dynamics Inside A Tube With Time-Dependent Radius, Robert E. Hicks

Theses and Dissertations

Lung fluid dynamics is a well studied topic and relevant in the field of research surrounding patients with Chronic Obstructive Pulmonary Disease (COPD) and cystic fibrosis. However, the literature on the mathematical description of the net pulmonary fluid transport in the case of constricting and expanding airways is scarce. In this paper we aim to address how breathing contributes to airways clearance in patients with pulmonary diseases such as COPD and CF in which cilia do not function properly. We begin with the flow of a fluid-filled tube with rigid walls of fixed radius and the effects of gravity being …

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(R2064) Analytical Approximations In Short Times Of Exact Operational Solutions To Reaction-Diffusion Problems On Bounded Intervals, Kwassi Anani Dec 2023

(R2064) Analytical Approximations In Short Times Of Exact Operational Solutions To Reaction-Diffusion Problems On Bounded Intervals, Kwassi Anani

Applications and Applied Mathematics: An International Journal (AAM)

This paper aims to provide an exact solution in the Laplace domain and related analytic approximations in short time limits for the class of boundary value problems of the one-dimensional linear parabolic equation with constant coefficients. The problem’s most general form involves a parameterized equation on a bounded interval, with unified specification of the three classical types of boundary conditions: Dirichlet, Neumann, and Robin. Under certain integrability assumptions, we have proven that a unique solution exists in the Laplace domain. This operational solution can be obtained in a closed form by using classical integral transforms. Four distinct cases have been …

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An Exposition Of The Curvature Of Warped Product Manifolds, Angelina Bisson Dec 2023

An Exposition Of The Curvature Of Warped Product Manifolds, Angelina Bisson

Electronic Theses, Projects, and Dissertations

The field of differential geometry is brimming with compelling objects, among which are warped products. These objects hold a prominent place in differential geometry and have been widely studied, as is evident in the literature. Warped products are topologically the same as the Cartesian product of two manifolds, but with distances in one of the factors in skewed. Our goal is to introduce warped product manifolds and to compute their curvature at any point. We follow recent literature and present a previously known result that classifies all flat warped products to find that there are flat examples of warped products …

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Effects Of A Protection Zone In A Reaction-Diffusion Model With Strong Allee Effect., Isaac Johnson Dec 2023

Effects Of A Protection Zone In A Reaction-Diffusion Model With Strong Allee Effect., Isaac Johnson

Electronic Theses and Dissertations

A protection zone model represents a patchy environment with positive growth over the protection zone and strong Allee effect growth outside the protection zone. Generally, these models are considered through the corresponding eigenvalue problem, but that has certain limitations. In this thesis, a general protection zone model is considered. This model makes no assumption on the direction of the traveling wave solution over the Strong Allee effect patch. We use phase portrait analysis of this protection zone model to draw conclusions about the existence of equilibrium solutions. We establish the existence of three types of equilibrium solutions and the necessary …

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Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells, Arkaprovo Ghosal, Padmanabhan Seshaiyar Dr., Adriana Dawes Dr., General Genomics Inc. Nov 2023

Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells, Arkaprovo Ghosal, Padmanabhan Seshaiyar Dr., Adriana Dawes Dr., General Genomics Inc.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Lnksc Method On Pde-Constrained Optimization For Mcf-7 Breast Cancer Cell Growth Predictions And Treatment Response With Gold Nanoparticles, Widodo Samyono, Shakhawat Bhuiyan Nov 2023

Lnksc Method On Pde-Constrained Optimization For Mcf-7 Breast Cancer Cell Growth Predictions And Treatment Response With Gold Nanoparticles, Widodo Samyono, Shakhawat Bhuiyan

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Helices In Fluids And Applications To Modeling In Biology, Eva M. Strawbridge Nov 2023

Helices In Fluids And Applications To Modeling In Biology, Eva M. Strawbridge

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Effects Of Slip On Highly Viscous Thin-Film Flows Inside A Vertical Tube Of Constant Radius, Mark S. Schwitzerlett Nov 2023

Effects Of Slip On Highly Viscous Thin-Film Flows Inside A Vertical Tube Of Constant Radius, Mark S. Schwitzerlett

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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A Tale Of Two Diagonalizations: Methods To Diagonalize A 1-D Piecewise Constant Indefinite Schrödinger Operator, Sarah Wright Aug 2023

A Tale Of Two Diagonalizations: Methods To Diagonalize A 1-D Piecewise Constant Indefinite Schrödinger Operator, Sarah Wright

Dissertations

We present two numerical methods for computing the solution of a partial differential equation (PDE) for modeling acoustic pressure, known as an extra-wide angle parabolic equation, that features the square root of a differential operator. The differential operator is the negative of an indefinite Schrödinger operator with a piecewise constant potential. This work primarily deals with the 3-piece case; however, a generalization is made to the case of an arbitrary number of pieces. In the first method, the Rayleigh-Secant Method, through restriction to a judiciously chosen lower-dimensional subspace, approximate eigenfunctions are used to obtain estimates for the eigenvalues of the …

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A Robust Model Reduction For The Optimal Boundary Feedback Stabilization Of Magnetizable Piezoelectric Beams, Md Rafi As Sadeq Ibn Emran Aug 2023

A Robust Model Reduction For The Optimal Boundary Feedback Stabilization Of Magnetizable Piezoelectric Beams, Md Rafi As Sadeq Ibn Emran

Masters Theses & Specialist Projects

The one-dimensional Partial Differential Equation (PDE) model of the wave equation, which describes wave dynamics of a wide-range of controlled mechanical systems, with a state feedback controller at its boundary is known to have exponentially stable solutions. Moreover, it is also reported that the several model reductions of the wave equation by the standard Finite Differences and Finite Elements approximations suffer from the lack of exponential stability (and exact observability without a state feedback controller) uniformly as the discretization parameter tends to zero. This is due to the loss of a uniform gap among the high-frequency eigenvalues as the discretization …

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Null Space Removal In Finite Element Discretizations, Pengfei Jia Aug 2023

Null Space Removal In Finite Element Discretizations, Pengfei Jia

All Theses

Partial differential equations are frequently utilized in the mathematical formulation of physical problems. Boundary conditions need to be applied in order to obtain the unique solution to such problems. However, some types of boundary conditions do not lead to unique solutions because the continuous problem has a null space. In this thesis, we will discuss how to solve such problems effectively. We first review the foundation of all three problems and prove that Laplace problem, linear elasticity problem and Stokes problem can be well posed if we restrict the test and trial space in the continuous and discrete finite element …

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Recovering Coefficients Of Second-Order Hyperbolic And Plate Equations Via Finite Measurements On The Boundary, Scott Randall Scruggs Aug 2023

Recovering Coefficients Of Second-Order Hyperbolic And Plate Equations Via Finite Measurements On The Boundary, Scott Randall Scruggs

All Dissertations

Abstract In this dissertation, we consider the inverse problem for a second-order hyperbolic equation of recovering n + 3 unknown coefficients defined on an open bounded domain with a smooth enough boundary. We also consider the inverse problem of recovering an unknown coefficient on the Euler- Bernoulli plate equation on a lower-order term again defined on an open bounded domain with a smooth enough boundary. For the second-order hyperbolic equation, we show that we can uniquely and (Lipschitz) stably recover all these coefficients from only using half of the corresponding boundary measurements of their solutions, and for the plate equation, …

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Neural Network Learning For Pdes With Oscillatory Solutions And Causal Operators, Lizuo Liu Jul 2023

Neural Network Learning For Pdes With Oscillatory Solutions And Causal Operators, Lizuo Liu

Mathematics Theses and Dissertations

In this thesis, we focus on developing neural networks algorithms for scientific computing. First, we proposed a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wave equations. Several linearized learning schemes have been proposed for neural networks solving nonlinear Navier-Stokes equations. We also proposed a causality deep neural network (Causality-DeepONet) to learn the causal response of a physical system. An extension of the Causality-DeepONet to time-dependent PDE systems is also proposed. The PhaseDNN makes use of the fact that common DNNs often achieve convergence in the low frequency …

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On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson Jul 2023

On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson

Rose-Hulman Undergraduate Mathematics Journal

We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.

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(R1966) Semi Analytical Approach To Study Mathematical Model Of Atmospheric Internal Waves Phenomenon, Patel Yogeshwari, Jayesh M. Dhodiya Jun 2023

(R1966) Semi Analytical Approach To Study Mathematical Model Of Atmospheric Internal Waves Phenomenon, Patel Yogeshwari, Jayesh M. Dhodiya

Applications and Applied Mathematics: An International Journal (AAM)

This research aims to study atmospheric internal waves which occur within the fluid rather than on the surface. The mathematical model of the shallow fluid hypothesis leads to a coupled nonlinear system of partial differential equations. In the shallow flow model, the primary assumption is that vertical size is smaller than horizontal size. This model can precisely replicate atmospheric internal waves because waves are dispersed over a vast horizontal area. A semi-analytical approach, namely modified differential transform, is applied successfully in this research. The proposed method obtains an approximate analytical solution in the form of convergent series without any linearization, …

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(R2052) Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe, Erick Sanchez, Dambaru Bhatta Jun 2023

(R2052) Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe, Erick Sanchez, Dambaru Bhatta

Applications and Applied Mathematics: An International Journal (AAM)

A fully developed laminar steady flow of an incompressible, viscous fluid in a horizontal cylindrical pipe is considered here. Flow patterns for an incompressible, viscous fluid for both Newtonian and non-Newtonian fluids such as shear-thinning, shear-thickening and Bingham plastic fluids are analyzed in this study. Assuming that the flow is only due to the wall shear stress and the pressure drop, the velocity component in the axial direction for these cases is derived. Computational results of the velocity profiles for various cases are obtained using MATLAB and presented in graphical forms. It is observed that the velocity profile is parabolic …

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Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe Jun 2023

Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe

Master's Theses

In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …

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(R2028) A Brief Note On Space Time Fractional Order Thermoelastic Response In A Layer, Navneet Lamba, Jyoti Verma, Kishor Deshmukh Jun 2023

(R2028) A Brief Note On Space Time Fractional Order Thermoelastic Response In A Layer, Navneet Lamba, Jyoti Verma, Kishor Deshmukh

Applications and Applied Mathematics: An International Journal (AAM)

In this study, a one-dimensional layer of a solid is used to investigate the exact analytical solution of the heat conduction equation with space-time fractional order derivatives and to analyze its associated thermoelastic response using a quasi-static approach. The assumed thermoelastic problem was subjected to certain initial and boundary conditions at the initial and final ends of the layer. The memory effects and long-range interaction were discussed with the help of the Caputo-type fractional-order derivative and finite Riesz fractional derivative. Laplace transform and Fourier transform techniques for spatial coordinates were used to investigate the solution of the temperature distribution and …

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Pde Model For Protocell Evolution And The Origin Of Chromosomes Via Multilevel Selection, Daniel B. Cooney, Fernando W. Rossine, Dylan H. Morris, Simon A. Levin May 2023

Pde Model For Protocell Evolution And The Origin Of Chromosomes Via Multilevel Selection, Daniel B. Cooney, Fernando W. Rossine, Dylan H. Morris, Simon A. Levin

Biology and Medicine Through Mathematics Conference

No abstract provided.

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Reaction-Diffusion System On Irregular Boundaries Reproduces Multiple Generations Of Petal Spot Patterns In Monkeyflower Hybrids, Emily Simmons May 2023

Reaction-Diffusion System On Irregular Boundaries Reproduces Multiple Generations Of Petal Spot Patterns In Monkeyflower Hybrids, Emily Simmons

Biology and Medicine Through Mathematics Conference

No abstract provided.

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Helices In Fluids And Their Applications, Eva M. Strawbridge May 2023

Helices In Fluids And Their Applications, Eva M. Strawbridge

Biology and Medicine Through Mathematics Conference

No abstract provided.

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Monolithic Multiphysics Simulation Of Hypersonic Aerothermoelasticity Using A Hybridized Discontinuous Galerkin Method, William Paul England May 2023

Monolithic Multiphysics Simulation Of Hypersonic Aerothermoelasticity Using A Hybridized Discontinuous Galerkin Method, William Paul England

Theses and Dissertations

This work presents implementation of a hybridized discontinuous Galerkin (DG) method for robust simulation of the hypersonic aerothermoelastic multiphysics system. Simulation of hypersonic vehicles requires accurate resolution of complex multiphysics interactions including the effects of high-speed turbulent flow, extreme heating, and vehicle deformation due to considerable pressure loads and thermal stresses. However, the state-of-the-art procedures for hypersonic aerothermoelasticity are comprised of low-fidelity approaches and partitioned coupling schemes. These approaches preclude robust design and analysis of hypersonic vehicles for a number of reasons. First, low-fidelity approaches limit their application to simple geometries and lack the ability to capture small scale flow …

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U-No: U-Shaped Neural Operators, Md Ashiqur Rahman, Zachary E Ross, Kamyar Azizzadenesheli May 2023

U-No: U-Shaped Neural Operators, Md Ashiqur Rahman, Zachary E Ross, Kamyar Azizzadenesheli

Department of Computer Science Faculty Publications

Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented success in learning solution operators of partial differential equations. Due to their close proximity to fully connected architectures, these models mainly suffer from high memory usage and are generally limited to shallow deep learning models. In this paper, we propose U-shaped Neural Operator (U-NO), a U-shaped memory enhanced architecture that allows for deeper neural operators. U-NOs exploit the problem structures in function predictions and demonstrate fast training, data …

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Advancements In Fluid Simulation Through Enhanced Conservation Schemes, Sean Ingimarson May 2023

Advancements In Fluid Simulation Through Enhanced Conservation Schemes, Sean Ingimarson

All Dissertations

To better understand and solve problems involving the natural phenomenon of fluid and air flows, one must understand the Navier-Stokes equations. Branching several different fields including engineering, chemistry, physics, etc., these are among the most important equations in mathematics. However, these equations do not have analytic solutions save for trivial solutions. Hence researchers have striven to make advancements in varieties of numerical models and simulations. With many variations of numerical models of the Navier-Stokes equations, many lose important physical meaningfulness. In particular, many finite element schemes do not conserve energy, momentum, or angular momentum. In this thesis, we will study …

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An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones May 2023

An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). The experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory …

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Asymptotic Properties And Separation Rates For Navier-Stokes Flows, Patrick Michael Phelps May 2023

Asymptotic Properties And Separation Rates For Navier-Stokes Flows, Patrick Michael Phelps

Graduate Theses and Dissertations

In this dissertation, we investigate asymptotic properties of local energy solutions to the Navier-Stokes equations and develop an application which controls the separation of non-unique solutions in this class. Specifically, we quantify the rate at which two, possibly unique solutions evolving from the same data may separate pointwise away from a singularity. This is motivated by recent results on non-uniqueness for forced and unforced Navier-Stokes and analytical and numerical evidence suggesting non-uniqueness in the Leray class. Our investigation begins with discretely self-similar solutions known to exist globally in time and to be regular outside a space-time paraboloid. We prove decay …

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