Applied Mathematics Commons^™

Hybrid Algorithm For Singularly Perturbed Delay Parabolic Partial Differential Equations, Imiru T. Daba, Gemechis F. Duressa

Applications and Applied Mathematics: An International Journal (AAM)

This study aims at constructing a numerical scheme for solving singularly perturbed parabolic delay differential equations. Taylor’s series expansion is applied to approximate the shift term. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is an ε−uniformly convergent accuracy of order one. Some test examples are considered to testify …

Correlated Positron-Electron Orbital (Cpeo): A Novel Method That Models Positron-Electron Correlation In Virtual Ps At The Mean-Field Level, Kevin E. Blaine

Theses and Dissertations

The Correlated Positronic-Electronic Orbital (CPEO) method was developed and implemented to capture correlation effects at between the positron and electron in the modeling of systems that involve a bound positron. Methods that effectively model these systems require many hundred basis functions and use a mean field approach as the beginning step. CPEO builds an orbital for virtual Positronium (Ps) that contains a positron in a bound state along with an accompanying electron to the larger system. Assigning the virtual Ps orbital allows for the two particle variational optimization in conjunction with the other particles that compose the whole system. This …

Demailly's Conjecture And The Containment Problem, Sankhaneel Bisui, Eloisa Grifo, Huy Tài Hà, Thái Thành Nguyên

Department of Mathematics: Faculty Publications

We investigate Demailly’s Conjecture for a general set of sufficiently many points. Demailly’s Conjecture generalizes Chudnovsky’s Conjecture in providing a lower bound for the Waldschmidt constant of a set of points in projective space. We also study a containment between symbolic and ordinary powers conjectured by Harbourne and Huneke that in particular implies Demailly’s bound, and prove that a general version of that containment holds for generic determinantal ideals and defining ideals of star configurations.

Novel And Fast Peridynamic Models For Material Degradation And Failure, Siavash Jafarzadeh

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Fracture is one of the main mechanisms of structural failure. Corroded surfaces with chemically-induced damage are, notably, potential sites for crack initiation and propagation in metals, which can lead to catastrophic failure of structures. Despite some progress in simulating fracture and damage using classical models, realistic prediction of complex damage progression and failure has been out of reach for many decades. Peridynamics (PD), a nonlocal theory introduced in 2000, opened up new avenues in modeling material degradation and failure. Existing numerical methods used to discretize PD equations, however, are quite expensive as the PD nonlocal interactions make them unaffordable for …

Intermittent Dynamics Of Dense Particulate Matter, Chao Cheng

Dissertations

Granular particle systems are scattered around the universe, and they can behave like solids when there exist strong force-bearing networks, so that the granular system can resist certain stress without deformation. When such a network is not present, particles yield to small stress and behave like a fluid. A wide range of systems exhibit intermittent dynamics as they are slowly loaded, with different dynamical regimes governing many industrial and natural phenomena. While a significant amount of research on exploring intermittent dynamics of granular systems has been carried out, not much is known about the connection between particle-scale response and the …

Eigenvalue Problems For Fully Nonlinear Elliptic Partial Differential Equations With Transport Boundary Conditions, Jacob Lesniewski

Dissertations

Fully nonlinear elliptic partial differential equations (PDEs) arise in a number of applications. From mathematical finance to astrophysics, there is a great deal of interest in solving them. Eigenvalue problems for fully nonlinear PDEs with transport boundary conditions are of particular interest as alternative formulations of PDEs that require data to satisfy a solvability condition, which may not be known explicitly or may be polluted by noisy data. Nevertheless, these have not yet been well-explored in the literature. In this dissertation, a convergence framework for numerically solving eigenvalue problems for fully nonlinear PDEs is introduced. In addition, existing two-dimensional methods …

An Examination Of Fontan Circulation Using Differential Equation Models And Numerical Methods, Vanessa Maybruck

Honors Student Research

Certain congenital heart defects can lead to the development of only a single pumping chamber, or ventricle, in the heart instead of the usual two ventricles. Individuals with this defect undergo a corrective, three-part surgery, the third step of which is the Fontan procedure, but as the patients age, their cardiovascular health will likely deteriorate. Using computational fluid dynamics and differential equations, Fontan circulation can be modeled to investigate why the procedure fails and how Fontan failure can be maximally prevented. Borrowing from well-established literature on RC circuits, the differential equation models simulate systemic blood flow in a piecewise, switch-like …

Finite Element Modeling Of Underwater Acoustic Environments And Domain Decomposition Methods, General Ozochiawaeze

Theses

Underwater acoustic scattering problems have several important applications ranging from sonar imaging in target detection to providing information for sediment classification and geoacoustic inversion. This work presents numerical methods for time-harmonic acoustic scattering problems, specifically, finite element methods for the Helmholtz equation. Furthermore, an iterative domain decomposition formulation is introduced for acoustic scattering problems where the physical domain consists of multiple layers of different materials.

Stock Markets Performance During A Pandemic: How Contagious Is Covid-19?, Yara Abushahba

Theses and Dissertations

Background and Motivation: The coronavirus (“COVID-19”) pandemic, the subsequent policies and lockdowns have unarguably led to an unprecedented fluid circumstance worldwide. The panic and fluctuations in the stock markets were unparalleled. It is inarguable that real-time availability of news and social media platforms like Twitter played a vital role in driving the investors’ sentiment during such global shock.

Purpose:The purpose of this thesis is to study how the investor sentiment in relation to COVID-19 pandemic influenced stock markets globally and how stock markets globally are integrated and contagious. We analyze COVID-19 sentiment through the Twitter posts and investigate its …

Compare And Contrast Maximum Likelihood Method And Inverse Probability Weighting Method In Missing Data Analysis, Scott Sun

Mathematical Sciences Technical Reports (MSTR)

Data can be lost for different reasons, but sometimes the missingness is a part of the data collection process. Unbiased and efficient estimation of the parameters governing the response mean model requires the missing data to be appropriately addressed. This paper compares and contrasts the Maximum Likelihood and Inverse Probability Weighting estimators in an Outcome-Dependendent Sampling design that deliberately generates incomplete observations. WE demonstrate the comparison through numerical simulations under varied conditions: different coefficient of determination, and whether or not the mean model is misspecified.

Access To Higher Education: Do Schools “Grant” Success?, Nathaniel Jones

Symposium of Student Scholars

University education can lead to upward income mobility for low-income students. Being exposed to other student’s life experiences that are different from their own may highlight activities and actions that they may want to consider aiding their success. According to the U.S. Bureau of Labor Statistics, the median weekly earnings in 2019 for all workers in the U.S. was $969. Of those, U.S. workers who held bachelor’s degrees earned $1,248. In 2016, the Brookings Institute found that Pell Grant recipients and first-generation student loan borrowers attended universities that had lower graduation rates and higher loan default rates in comparison to …

Environmental Impact On Competition In Ecological Communities, Isabel Ouko

Symposium of Student Scholars

We study the effects of environmental feedback on the ecological competition by analyzing the classic Lotka-Volterra model coupled with a simple model of the environment. In particular, we look for ways in which feedback between competing populations and the environment stabilizes or destabilizes coexistence between the species. To do so, we use a combination of mathematical analysis and computer software such as Matlab.

KEYWORDS; mathematical modeling, Lotka-Volterra, ecological competition, environmental feedback

Characterizing The Northern Hemisphere Circumpolar Vortex Through Space And Time, Nazla Bushra

LSU Doctoral Dissertations

This hemispheric-scale, steering atmospheric circulation represented by the circumpolar vortices (CPVs) are the middle- and upper-tropospheric wind belts circumnavigating the poles. Variability in the CPV area, shape, and position are important topics in geoenvironmental sciences because of the many links to environmental features. However, a means of characterizing the CPV has remained elusive. The goal of this research is to (i) identify the Northern Hemisphere CPV (NHCPV) and its morphometric characteristics, (ii) understand the daily characteristics of NHCPV area and circularity over time, (iii) identify and analyze spatiotemporal variability in the NHCPV’s centroid, and (iv) analyze how CPV features relate …

Computational Design Of Nonlinear Stress-Strain Of Isotropic Materials, Askhad M.Polatov, Akhmat M. Ikramov, Daniyarbek Razmukhamedov

Chemical Technology, Control and Management

The article deals with the problems of numerical modeling of nonlinear physical processes of the stress-strain state of structural elements. An elastoplastic medium of a homogeneous solid material is investigated. The results of computational experiments on the study of the process of physically nonlinear deformation of isotropic elements of three-dimensional structures with a system of one- and double-periodic spherical cavities under uniaxial compression are presented. The influence and mutual influence of stress concentrators in the form of spherical cavities, vertically located two cavities and a horizontally located system of two cavities on the deformation of the structure are investigated. Numerical …

Morgan- Voyce Approach For Solution Bratu Problems, Bushra Eesa Kashiem

Emirates Journal for Engineering Research

Bratu equations are substantial in electrostatic and plasma problem. The aim of this paper is design a morgan-voyce approach for solving bratu problem. We present a morgan-voyce polynomial along with significant properties; the effectiveness of the proposed algorithm is demonstrated by considering three numerical examples.

High-Order Flexible Multirate Integrators For Multiphysics Applications, Rujeko Chinomona

Mathematics Theses and Dissertations

Traditionally, time integration methods within multiphysics simulations have been chosen to cater to the most restrictive dynamics, sometimes at a great computational cost. Multirate integrators accurately and efficiently solve systems of ordinary differential equations that exhibit different time scales using two or more time steps. In this thesis, we explore three classes of time integrators that can be classified as one-step multi-stage multirate methods for which the slow dynamics are evolved using a traditional one step scheme and the fast dynamics are solved through a sequence of modified initial value problems. Practically, the fast dynamics are subcycled using a small …

A Survey On Long-Range Wide-Area Network Technology Optimizations, Felipe S. Dantas Silva, Emidio P. Neto, Helder Oliveira, Denis Rosário, Eduardo Cerqueira, Cristiano Both, Sherali Zeadally, Augusto V. Neto

Information Science Faculty Publications

Long-Range Wide-Area Network (LoRaWAN) enables flexible long-range service communications with low power consumption which is suitable for many IoT applications. The densification of LoRaWAN, which is needed to meet a wide range of IoT networking requirements, poses further challenges. For instance, the deployment of gateways and IoT devices are widely deployed in urban areas, which leads to interference caused by concurrent transmissions on the same channel. In this context, it is crucial to understand aspects such as the coexistence of IoT devices and applications, resource allocation, Media Access Control (MAC) layer, network planning, and mobility support, that directly affect LoRaWAN’s …

Higher Order Fourier Finite Element Methods For Hodge Laplacian Problems On Axisymmetric Domains, Nicole E. Stock

Senior Honors Projects, 2020-current

We construct efficient higher order Fourier finite element spaces to approximate the solution of Hodge Laplacian problems on axisymmetric domains. In [16], a new family of Fourier finite element spaces was constructed by using the lowest order finite element methods. These spaces were used to discretize Hodge Laplacian problems in [18]. In this research, we extend the results of [16,18] by constructing higher order Fourier finite element spaces. We demonstrate that these new higher order Fourier finite element methods provide improved computational efficiency as well as increased accuracy.

Sampling Compactness Scores To Detect Gerrymandering In Squaretopia, Joshua Mariz

Honors Thesis

In electoral politics, gerrymandering is the phenomenon of creating electoral district partitionings that are often not geographically compact for the unfair benefit of one political party over another. Researchers have proposed several methods to quantify compactness, but identifying gerrymandering using these measures is an open problem. We analyze the possible distributions of compactness scores by exploring “Squaretopia,” a square n x n grid that we must partition into n equally-sized contiguous districts that each contain n cells. However, even in this simplified model, the number of possible partitions of a Squaretopia of size n = 9 exceeds 700 trillion, rendering …

Research Focus: Pattern Recognition

In The Loop

A CDM health informatics team joins a global race to advance COVID-19 diagnostics through X-ray insights.