Global Analysis Of The Shadow Gierer-Meinhardt System With General Linear Boundary Conditions In A Random Environment, 2020 Samford University

#### Global Analysis Of The Shadow Gierer-Meinhardt System With General Linear Boundary Conditions In A Random Environment, Kwadwo Antwi-Fordjour, Seonguk Kim, Marius Nkashama

*Mathematics Faculty Publications*

The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper. For this reaction-diffusion system, we employ a fixed point argument to prove local existence and uniqueness. Our results on global existence are based on a priori estimates of solutions.

Diagonalization Of 1-D Schrodinger Operators With Piecewise Constant Potentials, 2020 The University of Southern Mississippi

#### Diagonalization Of 1-D Schrodinger Operators With Piecewise Constant Potentials, Sarah Wright

*Master's Theses*

In today's world our lives are very layered. My research is meant to adapt current inefficient numerical methods to more accurately model the complex situations we encounter. This project focuses on a specific equation that is used to model sound speed in the ocean. As depth increases, the sound speed changes. This means the variable related to the sound speed is not constant. We will modify this variable so that it is piecewise constant. The specific operator in this equation also makes current time-stepping methods not practical. The method used here will apply an eigenfunction expansion technique used in ...

Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, 2020 The University of Southern Mississippi

#### Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, Bailey Rester

*Master's Theses*

Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale effectively to higher spatial resolution. This thesis will present a stability analysis of a first-order KSS method applied to the wave equation in inhomogeneous media.

Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, 2020 National University of Uzbekistan

#### Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva

*Acta of Turin Polytechnic University in Tashkent*

В работе установлены критические и двойные критические случаи, обусловленные представлением двойного нелинейного параболического уравнения с переменной плотностью с поглощением в "радиально-симметричной" форме.Такое представление исходного уравнения дало возможность легко построить решения типа Зельдовоч-Баренбатт-Паттл для критических случаев в виде функций сравнения.

Cover Song Identification - A Novel Stem-Based Approach To Improve Song-To-Song Similarity Measurements, 2020 Southern Methodist University

#### Cover Song Identification - A Novel Stem-Based Approach To Improve Song-To-Song Similarity Measurements, Lavonnia Newman, Dhyan Shah, Chandler Vaughn, Faizan Javed

*SMU Data Science Review*

Music is incorporated into our daily lives whether intentional or unintentional. It evokes responses and behavior so much so there is an entire study dedicated to the psychology of music. Music creates the mood for dancing, exercising, creative thought or even relaxation. It is a powerful tool that can be used in various venues and through advertisements to influence and guide human reactions. Music is also often "borrowed" in the industry today. The practices of sampling and remixing music in the digital age have made cover song identification an active area of research. While most of this research is focused ...

Matrix Low Rank Approximation At Sublinear Cost, 2020 The Graduate Center, City University of New York

#### Matrix Low Rank Approximation At Sublinear Cost, Qi Luan

*Dissertations, Theses, and Capstone Projects*

A matrix algorithm runs at sublinear cost if the number of arithmetic operations involved is far fewer than the number of entries of the input matrix. Such algorithms are especially crucial for applications in the field of Big Data, where input matrices are so immense that one can only store a fraction of the entire matrix in memory of modern machines. Typically, such matrices admit Low Rank Approximation (LRA) that can be stored and processed at sublinear cost. Can we compute LRA at sublinear cost? Our counter example presented in Appendix C shows that no sublinear cost algorithm can compute ...

Binary Neutron Star Mergers: Testing Ejecta Models For High Mass-Ratios, 2020 Purdue University - North Central Campus

#### Binary Neutron Star Mergers: Testing Ejecta Models For High Mass-Ratios, Allen Murray

*The Journal of Purdue Undergraduate Research*

Neutron stars are extremely dense stellar corpses which sometimes exist in orbiting pairs known as binary neutron star (BNS) systems. The mass ratio (q) of a BNS system is defined as the mass of the heavier neutron star divided by the mass of the lighter neutron star. Over time the neutron stars will inspiral toward one another and produce a merger event. Although rare, these events can be rich sources of observational data due to their many electromagnetic emissions as well as the gravitational waves they produce. The ability to extract physical information from such observations relies heavily on numerical ...

Advection-Reaction-Diffusion Model Of Drug Concentration In A Lymph Node, 2020 Southern Methodist University

#### Advection-Reaction-Diffusion Model Of Drug Concentration In A Lymph Node, Ting Yan

*Mathematics Theses and Dissertations*

It is recognized that there exist reservoirs of HIV located outside the bloodstream, and that these reservoirs hinder the efficacy of antiretroviral medication regimens in combating the virus. The prevailing theories regarding these reservoirs point to the lymphatic system. In this work, we discuss a novel computational model of viral dynamics in the lymph node, to allow numerical studies of viral “reservoirs” causing reinfection. Our model consists of a system of advection-reaction-diffusion partial differential equations (PDEs), where the diffusion coefficients vary between species (virus, drugs, lymphocytes) and include discontinuous jumps to capture differing properties of internal lymph node structures. We ...

Combating Covid On College Campuses: The Impact Of Structural Changes On Viral Transmissions, 2020 University of Oregon

#### Combating Covid On College Campuses: The Impact Of Structural Changes On Viral Transmissions, Jared Knofczynski, Aria Killebrew Bruehl, Ben Warner, Ryne Shelton

*altREU Projects*

One of the most significant issues in the COVID-19 pandemic is the reopening of schools while minimizing the transmission of coronavirus. Opportunities for evaluating the effectiveness of policies that might be utilized at such institutions are limited, as the necessary empirical data has not been gathered yet. Agent-based modeling, where various entities within an environment are simulated as agents, offers an opportunity to examine the effectiveness of various policies in a way that drastically minimizes the health and economic risks involved. Agent-based modeling is common within biology, ecology and other fields; and has seen some use within the coronavirus literature ...

Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, 2020 Reed College

#### Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson

*altREU Projects*

A Distributed Denial of Service (DDoS) is a cyber attack, which is capable of triggering a cascading failure in the victim network. While DDoS attacks come in different forms, their general goal is to make a network's service unavailable to its users. A common, but risky, countermeasure is to blackhole or null route the source, or the attacked destination. When a server becomes a blackhole, or referred to as the sink in the paper, the data that is assigned to it "disappears" or gets deleted. Our research shows how mathematical modeling can propose an alternative blackholing strategy that could ...

Exploring Food Deserts And Environmental Impacts On Health In Chicago And Oregon, 2020 Emory University

#### Exploring Food Deserts And Environmental Impacts On Health In Chicago And Oregon, Sivasomasundari Arunarasu, Paulina Grzybowicz

*altREU Projects*

Food deserts are defined as, “an impoverished area where residents lack access to healthy foods”. This lack of access can be due to a combination of socioeconomic, geographic, and food-related variables, and has been proven to impact the health of residents in the area. In this project, several statistical and machine learning techniques are used to model the impact of food desserts and various other factors on health outcomes, including diabetes and obesity rates, in both the different neighborhoods in the City of Chicago and the various counties in the state of Oregon. The models are then used to determine ...

Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, 2020 Utah State University

#### Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, Colby Wight

*All Graduate Plan B and other Reports*

Designing numerical algorithms for solving partial differential equations (PDEs) is one of the major research branches in applied and computational mathematics. Recently there has been some seminal work on solving PDEs using the deep neural networks. In particular, the Physics Informed Neural Network (PINN) has been shown to be effective in solving some classical partial differential equations. However, we find that this method is not sufficient in solving all types of equations and falls short in solving phase-field equations. In this thesis, we propose various techniques that add to the power of these networks. Mainly, we propose to embrace the ...

Hybrid Symbolic-Numeric Computing In Linear And Polynomial Algebra, 2020 The University of Western Ontario

#### Hybrid Symbolic-Numeric Computing In Linear And Polynomial Algebra, Leili Rafiee Sevyeri

*Electronic Thesis and Dissertation Repository*

In this thesis, we introduce hybrid symbolic-numeric methods for solving problems in linear and polynomial algebra. We mainly address the approximate GCD problem for polynomials, and problems related to parametric and polynomial matrices. For symbolic methods, our main concern is their complexity and for the numerical methods we are more concerned about their stability. The thesis consists of 5 articles which are presented in the following order:

Chapter 1, deals with the fundamental notions of conditioning and backward error. Although our results are not novel, this chapter is a novel explication of conditioning and backward error that underpins the rest ...

Variable Compact Multi-Point Upscaling Schemes For Anisotropic Diffusion Problems In Three-Dimensions, 2020 The University of Southern Mississippi

#### Variable Compact Multi-Point Upscaling Schemes For Anisotropic Diffusion Problems In Three-Dimensions, James Quinlan

*Dissertations*

Simulation is a useful tool to mitigate risk and uncertainty in subsurface flow models that contain geometrically complex features and in which the permeability field is highly heterogeneous. However, due to the level of detail in the underlying geocellular description, an upscaling procedure is needed to generate a coarsened model that is computationally feasible to perform simulations. These procedures require additional attention when coefficients in the system exhibit full-tensor anisotropy due to heterogeneity or not aligned with the computational grid. In this thesis, we generalize a multi-point finite volume scheme in several ways and benchmark it against the industry-standard routines ...

Dynamics Of Discontinuities In Elastic Solids, 2020 Tallinn University of Technology

#### Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski

*Publications*

The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples.

An Adaptive Approach To Gibbs’ Phenomenon, 2020 The University of Southern Mississippi

#### An Adaptive Approach To Gibbs’ Phenomenon, Jannatul Ferdous Chhoa

*Master's Theses*

Gibbs’ Phenomenon, an unusual behavior of functions with sharp jumps, is encountered while applying the Fourier Transform on them. The resulting reconstructions have high frequency oscillations near the jumps making the reconstructions far from being accurate. To get rid of the unwanted oscillations, we used the Lanczos sigma factor to adjust the Fourier series and we came across three cases. Out of the three, two of them failed to give us the right reconstructions because either it was removing the oscillations partially but not entirely or it was completely removing them but smoothing out the jumps a little too much ...

Optimal Allocation Of Two Resources In Annual Plants, 2020 University of Nebraska - Lincoln

#### Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris

*Dissertations, Theses, and Student Research Papers in Mathematics*

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant ...

Multigrid Methods For Elliptic Optimal Control Problems, 2020 Louisiana State University and Agricultural and Mechanical College

#### Multigrid Methods For Elliptic Optimal Control Problems, Sijing Liu

*LSU Doctoral Dissertations*

In this dissertation we study multigrid methods for linear-quadratic elliptic distributed optimal control problems.

For optimal control problems constrained by general second order elliptic partial differential equations, we design and analyze a $P_1$ finite element method based on a saddle point formulation. We construct a $W$-cycle algorithm for the discrete problem and show that it is uniformly convergent in the energy norm for convex domains. Moreover, the contraction number decays at the optimal rate of $m^{-1}$, where $m$ is the number of smoothing steps. We also prove that the convergence is robust with respect to a regularization parameter ...

Basins Of Convergence In The Collinear Restricted Four-Body Problem With A Repulsive Manev Potential, 2020 Aristotle University of Thessaloniki

#### Basins Of Convergence In The Collinear Restricted Four-Body Problem With A Repulsive Manev Potential, Euaggelos E. Zotos, Md Sanam Suraj, Rajiv Aggarwal, Charanpreet Kaur

*Applications and Applied Mathematics: An International Journal (AAM)*

The Newton-Raphson basins of convergence, related to the equilibrium points, in the collinear restricted four-body problem with repulsive Manev potential are numerically investigated. We monitor the parametric evolution of the position as well as of the stability of the equilibrium points, as a function of the parameter *e*. The multivariate Newton-Raphson optimal method is used for revealing the basins of convergence, by classifying dense grids of initial conditions in several types of two-dimensional planes. We perform a systematic and thorough analysis in an attempt to understand how the parameter *e* affects the geometry as well as the basin entropy of ...

Dynamic Optimal Control For Multi-Chemotherapy Treatment Of Dual Listeriosis Infection In Human And Animal Population, 2020 Cross River University of Technology

#### Dynamic Optimal Control For Multi-Chemotherapy Treatment Of Dual Listeriosis Infection In Human And Animal Population, B. Echeng Bassey

*Applications and Applied Mathematics: An International Journal (AAM)*

Following the rising cases of high hospitalization versa-vise incessant fatality rates and the close affinity of listeriosis with HIV/AIDS infection, which often emanates from food-borne pathogens associated with listeria monocytogenes infection, this present paper seek and formulated as penultimate model, an 8-Dimensional classical mathematical Equations which directly accounted for the biological interplay of dual listeriosis virions with dual set of population (human and animals). The model was studied under multiple chemotherapies (trimethoprim-sulphamethoxazole with a combination of penicillin or ampicillin and/or gentamicin). Using ODE’s, the positivity and boundedness of system solutions was investigated with model presented as an ...