Physical Sciences and Mathematics Commons^™

Weighted Inequalities For Dyadic Operators Over Spaces Of Homogeneous Type, David Edward Weirich

Mathematics & Statistics ETDs

A so-called space of homogeneous type is a set equipped with a quasi-metric and a doubling measure. We give a survey of results spanning the last few decades concerning the geometric properties of such spaces, culminating in the description of a system of dyadic cubes in this setting whose properties mirror the more familiar dyadic lattices in R^n . We then use these cubes to prove a result pertaining to weighted inequality theory over such spaces. We develop a general method for extending Bellman function type arguments from the real line to spaces of homogeneous type. Finally, we uses this …

An Application Of M-Matrices To Preserve Bounded Positive Solutions To The Evolution Equations Of Biofilm Models, Richard S. Landry Jr.

University of New Orleans Theses and Dissertations

In this work, we design a linear, two step implicit finite difference method to approximate the solutions of a biological system that describes the interaction between a microbial colony and a surrounding substrate. Three separate models are analyzed, all of which can be described as systems of partial differential equations (PDE)s with nonlinear diffusion and reaction, where the biological colony grows and decays based on the substrate bioavailability. The systems under investigation are all complex models describing the dynamics of biological films. In view of the difficulties to calculate analytical solutions of the models, we design here a numerical technique …

Underwater Acoustic Signal Analysis Toolkit, Kirk Bienvenu Jr

University of New Orleans Theses and Dissertations

This project started early in the summer of 2016 when it became evident there was a need for an effective and efficient signal analysis toolkit for the Littoral Acoustic Demonstration Center Gulf Ecological Monitoring and Modeling (LADC-GEMM) Research Consortium. LADC-GEMM collected underwater acoustic data in the northern Gulf of Mexico during the summer of 2015 using Environmental Acoustic Recording Systems (EARS) buoys. Much of the visualization of data was handled through short scripts and executed through terminal commands, each time requiring the data to be loaded into memory and parameters to be fed through arguments. The vision was to develop …

Mathematical Formulation Of Fusion Energy Magnetohydrodynamics, Nikolaos I. Xiros

University of New Orleans Theses and Dissertations

Chapter 1 presents the basic principles of Controlled Thermonuclear Fusion, and the approaches to achieve nuclear fusion on Earth. Furthermore, the basic components of the Tokamak, the reactor which will house the fusion reaction, are analyzed. Finally, the chapter ends with a discussion on how the present thesis is related to the Controlled Thermonuclear Fusion. Chapter 2 introduces briefly the basic concepts of the Electromagnetic and Magnetohydrodynamic theories as well as MHD turbulence. Chapter 3 presents a first glance in OpenFOAM CFD library. Chapter 4 introduces the Orszag-Tang vortex flow, which is a benchmark test case for MHD numerical models. …

Feasible Computation In Symbolic And Numeric Integration, Robert H.C. Moir

Electronic Thesis and Dissertation Repository

Two central concerns in scientific computing are the reliability and efficiency of algorithms. We introduce the term feasible computation to describe algorithms that are reliable and efficient given the contextual constraints imposed in practice. The main focus of this dissertation then, is to bring greater clarity to the forms of error introduced in computation and modeling, and in the limited context of symbolic and numeric integration, to contribute to integration algorithms that better account for error while providing results efficiently.

Chapter 2 considers the problem of spurious discontinuities in the symbolic integration problem, proposing a new method to restore continuity …

A Statistical Study Of Student Success In The Bgsu Honors College, Sarah Hercules

Honors Projects

Higher education has long tried to find the best measures to predict student success. Different colleges often have different guidelines, requiring different criteria to be evaluated. The BGSU Honors College has struggled with retention and recruitment of underrepresented students with their current admission criteria. This analysis studies different measures of student success such as BGSU GPA and number of completed Honors credits for high-achieving BGSU students who enrolled from Fall 2013 through Fall 2016 to find the best predictors of student success through regression analysis. Throughout this paper, the impact of ethnicity, gender, the college of a student’s program, high …

Heterogeneous Anisotropy Index And Scaling In Multiphase Random Polycrystals, Muhammad Ridwan Murshed

Theses and Dissertations

Under consideration is the finite-size scaling of elastic properties in single and two-phase random polycrystals with individual grains belonging to any crystal class (from cubic to triclinic). These polycrystals are generated by Voronoi tessellations with varying grain sizes and volume fractions. By employing variational principles in elasticity, we introduce the notion of a 'Heterogeneous Anisotropy Index' and investigate its role in the scaling of elastic properties at finite mesoscales. The index turns out to be a function of 43 variables, 21 independent components for each phase and the volume fraction of either phase. Furthermore, the relationship between Heterogeneous Anisotropy Index …

Statistical Analysis Of Momentum In Basketball, Mackenzi Stump

Honors Projects

The “hot hand” in sports has been debated for as long as sports have been around. The debate involves whether streaks and slumps in sports are true phenomena or just simply perceptions in the mind of the human viewer. This statistical analysis of momentum in basketball analyzes the distribution of time between scoring events for the BGSU Women’s Basketball team from 2011-2017. We discuss how the distribution of time between scoring events changes with normal game factors such as location of the game, game outcome, and several other factors. If scoring events during a game were always randomly distributed, or …

God's Number In The Simultaneously-Possible Turn Metric, Andrew James Gould

Theses and Dissertations

In 2010 it was found that God’s number is 20 in the face turn metric. That is, if the Rubik’s cube hasn’t been disassembled, it can always be solved in 20 twists or fewer, but sometimes requires 20 twists. However, the face turn metric only allows one face to be turned at a time for a total of 18 generators, or 18 possible twists at any time. This dissertation allows opposing, parallel faces to be twisted independent amounts at the same time and still get counted as 1 twist for a total of 45 generators. A new optimal-solving program was …

On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin

MSU Graduate Theses

In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens bifurcations.

Graph Analytics Methods In Feature Engineering, Theophilus Siameh

Electronic Theses and Dissertations

High-dimensional data sets can be difficult to visualize and analyze, while data in low-dimensional space tend to be more accessible. In order to aid visualization of the underlying structure of a dataset, the dimension of the dataset is reduced. The simplest approach to accomplish this task of dimensionality reduction is by a random projection of the data. Even though this approach allows some degree of visualization of the underlying structure, it is possible to lose more interesting underlying structure within the data. In order to address this concern, various supervised and unsupervised linear dimensionality reduction algorithms have been designed, such …

Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett

Mechanical Engineering

This paper describes the design process from ideation to test validation for a singular robotic joint to be configured into a myriad of system level of robots.

Making Models With Bayes, Pilar Olid

Electronic Theses, Projects, and Dissertations

Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects …

Structures Of Derived Graphs, Khawlah Hamad Alhulwah

Dissertations

One of the most familiar derived graphs are line graphs. The line graph L(G) of a graph G is the graph whose vertices are the edges of G where two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. One of the best- known results on the structure of line graphs deals with forbidden subgraphs by Beineke. A characterization of graphs whose line graph is Hamiltonian is due to Harary and Nash-Williams. Iterated line graphs of almost all connected graphs were shown to be Hamiltonian by Chartrand. The girth of a graph G …

Color-Connected Graphs And Information-Transfer Paths, Stephen Devereaux

Dissertations

The Department of Homeland Security in the United States was created in 2003 in response to weaknesses discovered in the transfer of classied information after the September 11, 2001 terrorist attacks. While information related to national security needs to be protected, there must be procedures in place that permit access between appropriate parties. This two-fold issue can be addressed by assigning information-transfer paths between agencies which may have other agencies as intermediaries while requiring a large enough number of passwords and rewalls that is prohibitive to intruders, yet small enough to manage. Situations such as this can be represented by …

Mathematical Modeling Of Mixtures And Numerical Solution With Applications To Polymer Physics, John Timothy Cummings

Doctoral Dissertations

We consider in this dissertation the mathematical modeling and simulation of a general diffuse interface mixture model based on the principles of energy dissipation. The model developed allows for a thermodynamically consistent description of systems with an arbitrary number of different components, each of which having perhaps differing densities. We also provide a mathematical description of processes which may allow components to source or sink into other components in a mass conserving, energy dissipating way, with the motivation of applying this model to phase transformation. Also included in the modeling is a unique set of thermodynamically consistent boundary conditions which …

Radial Basis Function Differential Quadrature Method For The Numerical Solution Of Partial Differential Equations, Daniel Watson

Dissertations

In the numerical solution of partial differential equations (PDEs), there is a need for solving large scale problems. The Radial Basis Function Differential Quadrature (RBFDQ) method and local RBF-DQ method are applied for the solutions of boundary value problems in annular domains governed by the Poisson equation, inhomogeneous biharmonic equation, and the inhomogeneous Cauchy-Navier equations of elasticity. By choosing the collocation points properly, linear systems can be obtained so that the coefficient matrices have block circulant structures. The resulting systems can be efficiently solved using matrix decomposition algorithms (MDAs) and fast Fourier transforms (FFTs). For the local RBFDQ method, the …

Nonspreading Solutions In Integro-Difference Models With Allee And Overcompensation Effects., Garrett Luther Otto

Electronic Theses and Dissertations

Previous work in Integro-Difference models have generally considered Allee effects and over-compensation separately, and have either focused on bounded domain problems or asymptotic spreading results. Some recent results by Sullivan et al. (2017 PNAS 114(19), 5053-5058) combining Allee and over-compensation in an Integro-Difference framework have shown chaotic fluctuating spreading speeds. In this thesis, using a tractable parameterized growth function, we analytically demonstrate that when Allee and over-compensation are present solutions which persist but essentially remain in a compact domain exist. We investigate the stability of these solutions numerically. We also numerically demonstrate the existence of such solutions for more general …

Which Factors Influence Student Success In Intermediate Algebra, Math 101-102-103?, Linh T. Ward

Mathematics & Statistics ETDs

At The University of New Mexico (UNM), Intermediate Algebra (MATH 120 and MATH 101-102-103) has historically been a so-called “killer course”, with very low pass rates: approximately 40% in Fall 2009 to Spring 2011 and about 50% from Fall 2011 to Spring 2013. Furthermore, many students failed the class multiple times. Since 2013, a computer system called ALEKS has been used to teach the course and, along with some additional interventions, on Albuquerque/Main campus success rates for MATH 101 have increased to roughly 80% and MATH 102 to about 70%. This thesis provides a strategy to identify those 20-30% as-risk …

Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry

LSU Doctoral Dissertations

In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure is perturbed, this embedded eigenvalue moves into the complex plane and becomes a “complex resonance” frequency. The real and imaginary parts of this complex frequency have physical meaning. They lie behind anomalous scattering behaviors known collectively as “Fano resonance”, and people are interested in tuning them to specific values in optical devices. The mathematics involves spectral theory and analytic perturbation theory and is well understood [16], at least on a theoretical …

Non-Equispaced Fast Fourier Transforms In Turbulence Simulation, Aditya M. Kulkarni

Masters Theses

Fourier pseudo-spectral method on equispaced grid is one of the approaches in turbulence simulation, to compute derivative of discrete data, using fast Fourier Transform (FFT) and gives low dispersion and dissipation errors. In many turbulent flows the dynamically important scales of motion are concentrated in certain regions which requires a coarser grid for higher accuracy. A coarser grid in other regions minimizes the memory requirement. This requires the use of Non-equispaced Fast Fourier Transform (NFFT) to compute the Fourier transform, by solving a system of linear equations.

To achieve similar accuracy, the NFFT needs to return more Fourier coefficients than …

Spatiotemporal Subspace Feature Tracking By Mining Discriminatory Characteristics, Richard D. Appiah

Doctoral Dissertations

Recent advancements in data collection technologies have made it possible to collect heterogeneous data at complex levels of abstraction, and at an alarming pace and volume. Data mining, and most recently data science seek to discover hidden patterns and insights from these data by employing a variety of knowledge discovery techniques. At the core of these techniques is the selection and use of features, variables or properties upon which the data were acquired to facilitate effective data modeling. Selecting relevant features in data modeling is critical to ensure an overall model accuracy and optimal predictive performance of future effects. The …

Computational Strategies In Uncertainty Quantification For Hazard Mapping, Regis Rutarindwa

Dissertations (1934 -)

There are many hazards associated with volcanic activities. Amongst them are Pyroclastic flows; a mixture of rock fragments, debris and hot gases that flow down the slope of actives volcanoes at high velocities. These flows have proven to be devastating, and at the same time more than 500 millions people in the world live within potential exposure to such a hazard. A few approaches have been used to try to mitigate the impact of volcanic hazard in general. These include remote sensing technology and developing hazard maps – a graphic representation of safe and risky zones for a given volcanic …

High-Order Relaxed Multirate Infinitesimal Step Methods For Multiphysics Applications, Jean Sexton

Mathematics Theses and Dissertations

In this work, we consider numerical methods for integrating multirate ordinary differential equations. We are interested in the development of new multirate methods with good stability properties and improved efficiency over existing methods. We discuss the development of multirate methods, particularly focusing on those that are based on Runge-Kutta theory. We introduce the theory of Generalized Additive Runge-Kutta methods proposed by Sandu and Günther. We also introduce the theory of Recursive Flux Splitting Multirate Methods with Sub-cycling described by Schlegel, as well as the Multirate Infinitesimal Step methods this work is based on. We propose a generic structure called Flexible …

Modelling Walleye Population And Its Cannibalism Effect, Quan Zhou

Electronic Thesis and Dissertation Repository

Walleye is a very common recreational fish in Canada with a strong cannibalism tendency, such that walleyes with larger sizes will consume their smaller counterparts when food sources are limited or a surplus of adults is present. Cannibalism may be a factor promoting population oscillation. As fish reach a certain age or biological stage (i.e. biological maturity), the number of fish achieving that stage is known as fish recruitment. The objective of this thesis is to model the walleye population with its recruitment and cannibalism effect. A matrix population model has been introduced to characterize the walleye population into three …

Nonlinear Waves, Instabilities And Singularities In Plasma And Hydrodynamics, Denis Albertovich Silantyev

Mathematics & Statistics ETDs

This work concentrates on Langmuir wave filamentation instability in the kinetic regime of plasma and computation of Stokes wave with high precision using conformal maps.

Nonlinear effects are present in almost every area of science as soon as one tries to go beyond the first order approximation. In particular, nonlinear waves emerge in such areas as hydrodynamics, nonlinear optics, plasma physics, quantum physics, etc. The results of this work are related to nonlinear waves in two areas, plasma physics and hydrodynamics, united by concepts of instability, singularity and advanced numerical methods used for their investigation.

The first part of this …

Numerical Methods For Nonlinear Optimal Control Problems And Their Applications In Indoor Climate Control, Runxin He

McKelvey School of Engineering Theses & Dissertations

Efficiency, comfort, and convenience are three major aspects in the design of control systems for residential Heating, Ventilation, and Air Conditioning (HVAC) units. In this dissertation, we study optimization-based algorithms for HVAC control that minimizes energy consumption while maintaining a desired temperature, or even human comfort in a room. Our algorithm uses a Computer Fluid Dynamics (CFD) model, mathematically formulated using Partial Differential Equations (PDEs), to describe the interactions between temperature, pressure, and air flow. Our model allows us to naturally formulate problems such as controlling the temperature of a small region of interest within a room, or to control …

Information Theoretic Study Of Gaussian Graphical Models And Their Applications, Ali Moharrer

LSU Doctoral Dissertations

In many problems we are dealing with characterizing a behavior of a complex stochastic system or its response to a set of particular inputs. Such problems span over several topics such as machine learning, complex networks, e.g., social or communication networks; biology, etc. Probabilistic graphical models (PGMs) are powerful tools that offer a compact modeling of complex systems. They are designed to capture the random behavior, i.e., the joint distribution of the system to the best possible accuracy. Our goal is to study certain algebraic and topological properties of a special class of graphical models, known as Gaussian graphs. First, …

On The Ramberg-Osgood Stress-Strain Model And Large Deformations Of Cantilever Beams, Ronald J. Giardina Jr

University of New Orleans Theses and Dissertations

In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many different materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to finding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are …

Simulation Of Driven Elastic Spheres In A Newtonian Fluid, Shikhar M. Dwivedi

Electronic Thesis and Dissertation Repository

Simulations help us test various restrictions/assumptions placed on physical systems that would otherwise be difficult to efficiently explore experimentally. For example, the Scallop Theorem, first stated in 1977, places limitations on the propulsion mechanisms available to microscopic objects in fluids. In particular, the theorem states that when the viscous forces in a fluid dominate the inertial forces associated with a physical body, such a physical body cannot generate propulsion by means of reciprocal motion. The focus of this thesis is to firstly, explore an adaptive Multiple-timestep(MTS) scheme for faster molecular dynamics(MD) simulations, and secondly, use hybrid MD-LBM(Lattice-Boltzman Method) to test …