Discontinuous Galerkin Methods For Compressible Miscible Displacements And Applications In Reservoir Simulation,
2024
Michigan Technological University
Discontinuous Galerkin Methods For Compressible Miscible Displacements And Applications In Reservoir Simulation, Yue Kang
Dissertations, Master's Theses and Master's Reports
This dissertation contains research on discontinuous Galerkin (DG) methods applied to the system of compressible miscible displacements, which is widely adopted to model surfactant flooding in enhanced oil recovery (EOR) techniques. In most scenarios, DG methods can effectively simulate problems in miscible displacements.
However, if the problem setting is complex, the oscillations in the numerical results can be detrimental, with severe overshoots leading to nonphysical numerical approximations. The first way to address this issue is to apply the bound-preserving
technique. Therefore, we adopt a bound-preserving Discontinuous Galerkin method
with a Second-order Implicit Pressure Explicit Concentration (SIPEC) time marching
method to …
Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders,
2024
Wilfrid Laurier University
Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen
Theses and Dissertations (Comprehensive)
The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …
Last Passage Time And Excursion Theory For Solvable Diffusions With Applications In Mathematical Finance,
2024
Wilfrid Laurier University
Last Passage Time And Excursion Theory For Solvable Diffusions With Applications In Mathematical Finance, Yaode Sui
Theses and Dissertations (Comprehensive)
In this dissertation, we investigate the properties of last passage times and excursion theory in one-dimensional solvable diffusions, emphasizing their applications in financial modeling, particularly in option pricing. We derive closed-form formulas for the marginal distribution of last passage times and their joint distribution with process values, including the maximum and minimum of the process value. The focus is on time-homogeneous diffusions with various boundaries and imposed killing. Employing spectral expansion theory, we derive explicit formulas for distributions of last passage times in common processes such as Drifted Brownian Motion (BM), Squared Bessel (SQB), Ornstein-Uhlenbeck (OU), and Cox-Ingersoll-Ross (CIR) models. …
Long-Wave Modeling Of Viscous Film Dynamics Inside A Tube With Time-Dependent Radius,
2024
Virginia Commonwealth University
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 …
Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model,
2024
Georgia Southern University
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 …
Numerical Modeling Of Thermal Runaway In Lithium-Ion Batteries Using Decomposition Kinetics And Inter-Cell Contact Resistance,
2024
Georgia Southern University
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 …
Mathematical Modeling Of Coupled Heat And Mass Transfer In Metal-Hydride Hydrogen Storage Systems,
2024
Georgia Southern University
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 …
Hamiltonian Models For The Propagation Of Long Gravity Waves, Higher-Order Kdv-Type Equations And Integrability,
2024
Technological University Dublin
Hamiltonian Models For The Propagation Of Long Gravity Waves, Higher-Order Kdv-Type Equations And Integrability, Rossen Ivanov
Book chapter/book
A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to a KdV approximation with higher order nonlinearities and dispersion (higher-order KdV-type equation, or HKdV). The HKdV is related to the known integrable PDEs with an explicit nonlinear and nonlocal transformation.
Effects Of A Protection Zone In A Reaction-Diffusion Model With Strong Allee Effect.,
2023
University of Louisville
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 …
(R2064) Analytical Approximations In Short Times Of Exact Operational Solutions To Reaction-Diffusion Problems On Bounded Intervals,
2023
University of Lomé
(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 …
An Exposition Of The Curvature Of Warped Product Manifolds,
2023
California State University - San Bernardino
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 …
Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells,
2023
George Mason University
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.
Lnksc Method On Pde-Constrained Optimization For Mcf-7 Breast Cancer Cell Growth Predictions And Treatment Response With Gold Nanoparticles,
2023
Jarvis Christian College
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.
Helices In Fluids And Applications To Modeling In Biology,
2023
James Madison University
Helices In Fluids And Applications To Modeling In Biology, Eva M. Strawbridge
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Effects Of Slip On Highly Viscous Thin-Film Flows Inside A Vertical Tube Of Constant Radius,
2023
Illinois State University
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.
A Tale Of Two Diagonalizations: Methods To Diagonalize A 1-D Piecewise Constant Indefinite Schrödinger Operator,
2023
The University of Southern Mississippi
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 …
A Robust Model Reduction For The Optimal Boundary Feedback Stabilization Of Magnetizable Piezoelectric Beams,
2023
Western Kentucky University
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 …
Null Space Removal In Finite Element Discretizations,
2023
Clemson University
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 …
Recovering Coefficients Of Second-Order Hyperbolic And Plate Equations Via Finite Measurements On The Boundary,
2023
Clemson University
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, …
Neural Network Learning For Pdes With Oscillatory Solutions And Causal Operators,
2023
Southern Methodist University
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 …
