Applied Mathematics Commons^™

Analysis And Implementation Of Numerical Methods For Solving Ordinary Differential Equations, Muhammad Sohel Rana

Masters Theses & Specialist Projects

Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number of practical fields such as equations arising in population dynamics and astrophysics. It …

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 …

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 …

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 …

Parabolic Classical Curvature Flows, Brendan Guilfoyle, Wilhelm Klingenberg

Publications

We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space, which evolve by an arbitrary (nonhomogeneous) function of the radii of curvature (RoC). We determine conditions for parabolic flows that ensure the boundedness of various geometric quantities and investigate some examples. As a new tool, we introduce the RoC diagram of a surface and its hyperbolic or anti-de Sitter metric. The relationship between the RoC diagram and the properties of Weingarten surfaces is also discussed.

Evolution Of Superoscillations For Schrödinger Equation In A Uniform Magnetic Field, Fabrizio Colombo, Jonathan Gantner, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

Aharonov-Berry superoscillations are band-limited functions that oscillate faster than their fastest Fourier component. Superoscillations appear in several fields of science and technology, such as Aharonov’s weak measurement in quantum mechanics, in optics, and in signal processing. An important issue is the study of the evolution of superoscillations using the Schrödinger equation when the initial datum is a weak value. Some superoscillatory functions are not square integrable, but they are real analytic functions that can be extended to entire holomorphic functions. This fact leads to the study of the continuity of a class of convolution operators acting on suitable spaces of …

Filtered Subspace Iteration For Selfadjoint Operators, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall

Portland Institute for Computational Science Publications

We consider the problem of computing a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space. A rational function of the operator is constructed such that the eigenspace of interest is its dominant eigenspace, and a subspace iteration procedure is used to approximate this eigenspace. The computed space is then used to obtain approximations of the eigenvalues of interest. An eigenvalue and eigenspace convergence analysis that considers both iteration error and dis- cretization error is provided. A realization of the proposed approach for a model second-order elliptic operator is based on a …

Convergence Of Media Attention Across 129 Countries, Jisun An, Hassan Aldarbesti, Haewoon Kwak

Research Collection School Of Computing and Information Systems

The objective of this study is to assess the longitudinal trends of media similarity and dissimilarity on the international scale. As news value has well-established political, cultural, and economic consequences, the degree to which media coverage and content is converging across countries has implications for international relations. To study this convergence, we use the daily data of the 100 topics that were over-reported in each country, compared to other countries, from March 7 to October 9, 2016. The results of this analysis indicate that two complementary patterns–globalization and domestication–explain the media attention across the countries. We conclude that this attention …

A Regression Model To Predict Stock Market Mega Movements And/Or Volatility Using Both Macroeconomic Indicators & Fed Bank Variables, Timothy A. Smith, Alcuin Rajan

Publications

In finance, regression models or time series moving averages can be used to determine the value of an asset based on its underlying traits. In prior work we built a regression model to predict the value of the S&P 500 based on macroeconomic indicators such as gross domestic product, money supply, produce price and consumer price indices. In this present work this model is updated both with more data and an adjustment in the input variables to improve the coefficient of determination. A scheme is also laid out to alternately define volatility rather than using common tools such as the …

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 …

Interplay Of Quantum Size Effect, Anisotropy And Surface Stress Shapes The Instability Of Thin Metal Films, Mikhail Khenner

Mathematics Faculty Publications

Morphological instability of a planar surface ([111], [011], or [001]) of an ultra-thin metal film is studied in a parameter space formed by three major effects (the quantum size effect, the surface energy anisotropy and the surface stress) that influence a film dewetting. The analysis is based on the extended Mullins equation, where the effects are cast as functions of the film thickness. The formulation of the quantum size effect (Z. Zhang et al., PRL 80, 5381 (1998)) includes the oscillation of the surface energy with thickness caused by electrons confinement. By systematically comparing the effects, their contributions into the …

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

McKelvey School of Engineering Graduate Student 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

LSU 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 …

Thermodynamics Of Coherent Structures Near Phase Transitions, Julia M. Meyer, Ivan Christov

The Summer Undergraduate Research Fellowship (SURF) Symposium

Phase transitions within large-scale systems may be modeled by nonlinear stochastic partial differential equations in which system dynamics are captured by appropriate potentials. Coherent structures in these systems evolve randomly through time; thus, statistical behavior of these fields is of greater interest than particular system realizations. The ability to simulate and predict phase transition behavior has many applications, from material behaviors (e.g., crystallographic phase transformations and coherent movement of granular materials) to traffic congestion. Past research focused on deriving solutions to the system probability density function (PDF), which is the ground-state wave function squared. Until recently, the extent to which …

Fluid Dynamics Of Watercolor Painting : Experiments And Modelling, David Edward Baron

Theses, Dissertations and Culminating Projects

In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington's experiments has now been clarified. One specific set of such recent studies, which motivates this thesis, concerns the fluid dynamics behind Jackson Pollock's drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and have made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of …

Math Department Newsletter, 2017, University Of Dayton. Department Of Mathematics

Department of Mathematics Newsletters

No abstract provided.

A Stable Algorithm For Divergence-Free And Curl-Free Radial Basis Functions In The Flat Limit, Kathryn Primrose Drake

Boise State University Theses and Dissertations

Radial basis functions (RBFs) were originally developed in the 1970s for interpolating scattered topographic data. Since then they have become increasingly popular for other applications involving the approximation of scattered, scalar-valued data in two and higher dimensions, especially data collected on the surface of a sphere. In the late 2000s, matrix-valued RBFs were introduced for approximating divergence-free and curl-free vector fields on the surface of a sphere from scattered samples, which arise naturally in atmospheric and oceanic sciences. The intriguing property of these RBFs is that the resulting vector-valued approximations analytically preserve the divergence-free or curl-free properties of the field. …

Multi-Rate Runge-Kutta-Chebyshev Time Stepping For Parabolic Equations On Adaptively Refined Meshes, Talin Mirzakhanian

Boise State University Theses and Dissertations

In this thesis, we develop an explicit multi-rate time stepping method for solving parabolic equations on a one dimensional adaptively refined mesh. Parabolic equations are characterized by their stiffness and as a result are usually solved using implicit time stepping schemes [16]. However, implicit schemes have the disadvantage that they can be expensive in higher dimensions or complicated to implement on adaptive or otherwise non-uniform meshes. Moreover, for coupled systems of parabolic equations, it can be difficult to achieve the expected order of accuracy without using sophisticated operator splitting techniques. For these reasons, we seek to exploit the properties of …

Joint Inversion Of Compact Operators, James Ford

Boise State University Theses and Dissertations

The first mention of joint inversion came in [22], where the authors used the singular value decomposition to determine the degree of ill-conditioning in inverse problems. The authors demonstrated in several examples that combining two models in a joint inversion, and effectively stacking discrete linear models, improved the conditioning of the problem. This thesis extends the notion of using the singular value decomposition to determine the conditioning of discrete joint inversion to using the singular value expansion to determine the well-posedness of joint linear operators. We focus on compact linear operators related to geophysical, electromagnetic subsurface imaging.

The operators are …