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 …

Les-C Turbulence Models And Fluid Flow Modeling: Analysis And Application To Incompressible Turbulence And Fluid-Fluid Interaction, 2024 Michigan Technological University

#### Les-C Turbulence Models And Fluid Flow Modeling: Analysis And Application To Incompressible Turbulence And Fluid-Fluid Interaction, Kyle J. Schwiebert

*Dissertations, Master's Theses and Master's Reports*

In the first chapter of this dissertation, we give some background on the Navier-Stokes equations and turbulence modeling. The next two chapters in this dissertation focus on two important numerical difficulties arising in fluid flow modeling: poor mass-conservation and nonphysical oscillations. We investigate two different formulations of the Crank-Nicolson method for the Navier-Stokes equations. The most attractive implementation, second order accurate for both velocity and pressure, is shown to introduce non-physical oscillations. We then propose two options which are shown to avoid the poor behavior. Next, we show that grad-div stabilization, previously assumed to have no effect on the target …

Quantification Of Antiviral Drug Tenofovir (Tfv) By Surface-Enhanced Raman Spectroscopy (Sers) Using Cumulative Distribution Functions (Cdfs), 2024 Old Dominion University

#### Quantification Of Antiviral Drug Tenofovir (Tfv) By Surface-Enhanced Raman Spectroscopy (Sers) Using Cumulative Distribution Functions (Cdfs), Marguerite R. Butler, Jana Hrncirova, Meredith Clark, Sucharita Dutta, John B. Cooper

*Chemistry & Biochemistry Faculty Publications*

Surface-enhanced Raman spectroscopy (SERS) is an ultrasensitive spectroscopic technique that generates signal-enhanced fingerprint vibrational spectra of small molecules. However, without rigorous control of SERS substrate active sites, geometry, surface area, or surface functionality, SERS is notoriously irreproducible, complicating the consistent quantitative analysis of small molecules. While evaporatively prepared samples yield significant SERS enhancement resulting in lower detection limits, the distribution of these enhancements along the SERS surface is inherently stochastic. Acquiring spatially resolved SERS spectra of these dried surfaces, we have shown that this enhancement is governed by a power law as a function of analyte concentration. Consequently, by definition, …

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 …

Echolocation On Manifolds, 2024 Bucknell University

#### 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, 2024 Bucknell University

#### 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.

Penalized Interpolating B-Splines And Their Applications, 2024 Virginia Commonwealth University

#### Penalized Interpolating B-Splines And Their Applications, Kylee L. Hartman-Caballero

*Theses and Dissertations*

One of the most studied data analysis techniques in Numerical Analysis is interpolation. Interpolation is used in a variety of fields, namely computer graphic design and biomedical research. Among interpolation techniques, cubic splines have been viewed as the standard since at least the 1960s, due to their ease of computation, numerical stability, and the relative smoothness of the interpolating curve. However, cubic splines have notable drawbacks, such as their lack of local control and necessary knowledge of boundary conditions. Arguably a more versatile interpolation technique is the use of B-splines. B-splines, a relative of Bézier curves, allow local control through …

A New Proper Orthogonal Decomposition Method With Second Difference Quotients For The Wave Equation, 2024 Missouri University of Science and Technology

#### A New Proper Orthogonal Decomposition Method With Second Difference Quotients For The Wave Equation, Andrew Calvin Janes

*Masters Theses*

"Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In \cite {Sarahs}, a new approach to POD with DQs was developed that is more computationally efficient than the standard DQ POD approach and it also retains the guaranteed pointwise in time error bounds of the standard method. In this thesis, we extend the new DQ POD approach from \cite {Sarahs} to the case of second difference quotients (DDQs). Specifically, a new POD method utilizing DDQs and only one snapshot and …

Symmetry Analysis Of The Canonical Connection On Lie Groups:Co-Dimension Two Abelian Nilradical With Abelian And Non Abelian Complement, 2024 Virginia Commonwealth University

#### Symmetry Analysis Of The Canonical Connection On Lie Groups:Co-Dimension Two Abelian Nilradical With Abelian And Non Abelian Complement, Nouf Alrubea Almutiben

*Theses and Dissertations*

We consider the symmetry algebra of the geodesic equations of the canonical

connection on a Lie groups. We mainly consider the solvable indecomposable four,

five and six-dimensional Lie algebras with co-dimension two abelian nilradical, that

have an abelian and not abelian complement. In this particular case, we have only

one algebra in dimension four namely; A4,12 , and three algebras in dimension five

namely; A5,33, A5,34, and A5,35 In dimension six, based on the list of Lie algebras in

Turkowski’s list, there are nineteen such algebras namely; A6,1- A6,19 that have an

abelian complement, and there are eight algebras that …

Mathematical Modeling And Analysis Of Inflammation And Tissue Repair: Lung Inflammation And Wound Healing In Corals Under Stress, 2024 Virginia Commonwealth University

#### Mathematical Modeling And Analysis Of Inflammation And Tissue Repair: Lung Inflammation And Wound Healing In Corals Under Stress, Quintessa Hay

*Theses and Dissertations*

A variety of insults, including tissue injury and/or exposure to pathogen, elicit an immune response in many organisms. An improperly regulated immune response can result in deleterious effects to the organism. Here we present models for lung injury in young and old mice and models for wound healing in coral reefs.

It is well known that the immune response becomes less effective in older individuals. This is of particular interest in pulmonary insults such as ventilator induced lung injury (VILI) or lung infection. We extended a mathematical model for the inflammatory response to VILI and used experimental data to select …

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

*Electronic Theses and 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 …

Automatic Hemorrhage Segmentation In Brain Ct Scans Using Curriculum-Based Semi-Supervised Learning, 2024 The University of Texas at El Paso

#### Automatic Hemorrhage Segmentation In Brain Ct Scans Using Curriculum-Based Semi-Supervised Learning, Solayman H. Emon, Tzu-Liang (Bill) Tseng, Michael Pokojovy, Peter Mccaffrey, Scott Moen, Md Fashiar Rahman

*Mathematics & Statistics Faculty Publications*

One of the major neuropathological consequences of traumatic brain injury (TBI) is intracranial hemorrhage (ICH), which requires swift diagnosis to avert perilous outcomes. We present a new automatic hemorrhage segmentation technique via curriculum-based semi-supervised learning. It employs a pre-trained lightweight encoder-decoder framework (MobileNetV2) on labeled and unlabeled data. The model integrates consistency regularization for improved generalization, offering steady predictions from original and augmented versions of unlabeled data. The training procedure employs curriculum learning to progressively train the model at diverse complexity levels. We utilize the PhysioNet dataset to train and evaluate the proposed approach. The performance results surpass those of …

Uniform Regularity Estimates For The Stokes System In Perforated Domains, 2024 University of Kentucky

#### 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 $\eta$.

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, 2024 Georgia Southern University

#### Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly

*Electronic Theses and Dissertations*

In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, 2024 Department of mathematics and engineering physics, faculty of engineering, Mansoura University, Mansoura, Egypt

#### 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 …

Structured Invariant Subspace And Decomposition Of Systems With Time Delays And Uncertainties, 2024 Southern Illinois University Edwardsville

#### Structured Invariant Subspace And Decomposition Of Systems With Time Delays And Uncertainties, Huan Phan-Van, Keqin Gu

*SIUE Faculty Research, Scholarship, and Creative Activity*

This article discusses invariant subspaces of a matrix with a given partition structure. The existence of a nontrivial structured invariant subspace is equivalent to the possibility of decomposing the associated system with multiple feedback blocks such that the feedback operators are subject to a given constraint. The formulation is especially useful in the stability analysis of time-delay systems using the Lyapunov-Krasovskii functional approach where computational efficiency is essential in order to achieve accuracy for large scale systems. The set of all structured invariant subspaces are obtained (thus all possible decompositions are obtained as a result) for the coupled differential-difference equations …

Basins Of Attraction And Metaoptimization For Particle Swarm Optimization Methods, 2024 Bowdoin College

#### Basins Of Attraction And Metaoptimization For Particle Swarm Optimization Methods, David Ma

*Honors Projects*

Particle swarm optimization (PSO) is a metaheuristic optimization method that finds near- optima by spawning particles which explore within a given search space while exploiting the best candidate solutions of the swarm. PSO algorithms emulate the behavior of, say, a flock of birds or a school of fish, and encapsulate the randomness that is present in natural processes. In this paper, we discuss different initialization schemes and meta-optimizations for PSO, its performances on various multi-minima functions, and the unique intricacies and obstacles that the method faces when attempting to produce images for basins of attraction, which are the sets of …

Reducing Generalization Error In Multiclass Classification Through Factorized Cross Entropy Loss, 2024 Claremont McKenna College

#### Reducing Generalization Error In Multiclass Classification Through Factorized Cross Entropy Loss, Oleksandr Horban

*CMC Senior Theses*

This paper introduces Factorized Cross Entropy Loss, a novel approach to multiclass classification which modifies the standard cross entropy loss by decomposing its weight matrix W into two smaller matrices, U and V, where UV is a low rank approximation of W. Factorized Cross Entropy Loss reduces generalization error from the conventional O( sqrt(k / n) ) to O( sqrt(r / n) ), where k is the number of classes, n is the sample size, and r is the reduced inner dimension of U and V.

Unveiling The Power Of Shor's Algorithm: Cryptography In A Post Quantum World, 2024 Claremont Colleges

#### Unveiling The Power Of Shor's Algorithm: Cryptography In A Post Quantum World, Dylan Phares

*CMC Senior Theses*

Shor's Algorithm is an extremely powerful tool, in utilizing this tool it is important to understand how it works and why it works. As well as the vast implications it could have for cryptography

Bringing Gans To Medieval Times: Manuscript Translation Models, 2024 Georgia Southern University

#### Bringing Gans To Medieval Times: Manuscript Translation Models, Tonilynn M. Holtz

*Electronic Theses and Dissertations*

The Generative Adversarial Networks (GAN) recently emerged as a powerful framework for producing new knowledge from existing knowledge. These models aim to learn patterns from input data then use that knowledge to generate output data samples that plausibly appear to belong to the same set as the input data. Medieval manuscripts study has been an important research area in the humanities field for many decades. These rare manuscripts are often times inaccessible to the general public, including students in scholars, and it is of a great interest to provide digital support (including, but not limited to translation and search) for …