Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder,
2015
Rose-Hulman Institute of Technology
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Rose-Hulman Undergraduate Research Publications
From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …
On The Coupling Of Dpg And Bem,
2015
Pontifical Catholic University of Chile
On The Coupling Of Dpg And Bem, Thomas Führer, Norbert Heuer, Michael Karkulik
Mathematics and Statistics Faculty Publications and Presentations
We develop and analyze strategies to couple the discontinuous Petrov-Galerkin method with optimal test functions to (i) least-squares boundary elements and (ii) various variants of standard Galerkin boundary elements. An essential feature of our method is that, despite the use of boundary integral equations, optimal test functions have to be computed only locally. We apply our findings to a standard transmission problem in full space and present numerical experiments to validate our theory.
Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere,
2015
AAR Aerospace Consulting, LLC
Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere, Nihad E. Daidzic, Ph.D.,
International Journal of Aviation, Aeronautics, and Aerospace
Both, a global isothermal temperature model and a nonlinear quadratic temperature model of the ISA was developed and presented here. Constrained optimization techniques in conjunction with the least-square-root approximations were used to design best-fit isothermal models for ISA pressure and density changes up to 47 geopotential km for NLPAM, and 86 orthometric km for ISOAM respectively. The mass of the dry atmosphere and the relevant fractional-mass scale heights have been computed utilizing the very accurate eight-point Gauss-Legendre numerical quadrature for both ISOAM and NLPAM. Both, the ISOAM and the NLPAM represent viable alternatives to ISA in many practical applications and …
Mathematical Studies Of The Glucose-Insulin Regulatory System Models.,
2015
University of Louisville
Mathematical Studies Of The Glucose-Insulin Regulatory System Models., Minghu Wang
Electronic Theses and Dissertations
Three dynamic models are proposed to study the mechanism of glucose-insulin regulatory system and the possible causes of diabetes mellitus. The progression of diabetes comes along with the apoptosis of pancreatic beta-cells. A dynamical system model is formulated based on physiology and studied by geometric singular perturbation theory. The analytical studies reveal rich analytical features, such as persistence of solutions, Hopf bifurcation and backward bifurcation, while numerical studies successfully fit available longitudinal T2DM data of Pima Indian tribe. These studies together not only validate our model, but also point out key intrinsic factors leading to the development of T2DM. We …
Order Automorphisms On The Lattice Of Residuated Maps Of Some Special Nondistributive Lattices.,
2015
University of Louisville
Order Automorphisms On The Lattice Of Residuated Maps Of Some Special Nondistributive Lattices., Erika D. Foreman
Electronic Theses and Dissertations
The residuated maps from a lattice L to itself form their own lattice, which we denote Res(L). In this dissertation, we explore the order automorphisms on the lattice Res(L) where L is a finite nondistributive lattice. It is known that left and right composition of f ∈ Res(L) with automorphisms of L yields an order automorphism of Res(L). It begs the question, then, if all order automorphisms of Res(L) can be classified as such.
Infographics And Mathematics: A Mechanism For Effective Learning In The Classroom,
2015
University of Dayton
Infographics And Mathematics: A Mechanism For Effective Learning In The Classroom, Ivan Sudakov, Thomas Bellsky, Svetlana Usenyuk, Victoria V. Polyakova
Physics Faculty Publications
This work discusses the creation and use of infographies in an undergraduate mathematics course. Infographies are a visualization of information combining data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from undergraduate students on both the general use of infographics and on the specific infographics designed by the authors.
Comparison Of Two Parameter Estimation Techniques For Stochastic Models,
2015
East Tennessee State University
Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker
Electronic Theses and Dissertations
Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …
The Pc-Tree Algorithm, Kuratowski Subdivisions, And The Torus.,
2015
University of Louisville
The Pc-Tree Algorithm, Kuratowski Subdivisions, And The Torus., Charles J. Suer
Electronic Theses and Dissertations
The PC-Tree algorithm of Shih and Hsu (1999) is a practical linear-time planarity algorithm that provides a plane embedding of the given graph if it is planar and a Kuratowski subdivision otherwise. Remarkably, there is no known linear-time algorithm for embedding graphs on the torus. We extend the PC-Tree algorithm to a practical, linear-time toroidality test for K3;3-free graphs called the PCK-Tree algorithm. We also prove that it is NP-complete to decide whether the edges of a graph can be covered with two Kuratowski subdivisions. This greatly reduces the possibility of a polynomial-time toroidality testing algorithm based solely on edge-coverings …
Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions,
2015
University of Southern Mississippi
Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica
Dissertations
Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits …
On The Selection Of A Good Shape Parameter For Rbf Approximation And Its Application For Solving Pdes,
2015
University of Southern Mississippi
On The Selection Of A Good Shape Parameter For Rbf Approximation And Its Application For Solving Pdes, Lei-Hsin Kuo
Dissertations
Meshless methods utilizing Radial Basis Functions~(RBFs) are a numerical method that require no mesh connections within the computational domain. They are useful for solving numerous real-world engineering problems. Over the past decades, after the 1970s, several RBFs have been developed and successfully applied to recover unknown functions and to solve Partial Differential Equations (PDEs).
However, some RBFs, such as Multiquadratic (MQ), Gaussian (GA), and Matern functions, contain a free variable, the shape parameter, c. Because c exerts a strong influence on the accuracy of numerical solutions, much effort has been devoted to developing methods for determining shape parameters which provide …
On A Convex Set With Nondifferentiable Metric Projection,
2015
Portland State University
On A Convex Set With Nondifferentiable Metric Projection, Shyan S. Akmal, Nguyen Mau Nam, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with smooth boundary which possesses the same property.
Chaos In Semiflows.,
2015
University of Louisville
Chaos In Semiflows., Chad Money
Electronic Theses and Dissertations
All the common notions about dynamics in cascades - topological transitivity, periodic points, sensitive dependence, and so forth - can be formulated in the context of a general abelian semiflow. Many intricate results, such as the redundancy of Devaney chaos, remain true (with very minor qualifications) in this wider context. However, when we examine general monoid actions on a product space, it turns out that the topological and algebraic structure of N0 plays a large role in the preservation of chaotic properties. In order to obtain meaningful results in that arena, new ideas such as “directional” and “synnrec” are introduced, …
Strong Quota Pair Systems And May's Theorem On Median Semilattices.,
2015
University of Louisville
Strong Quota Pair Systems And May's Theorem On Median Semilattices., Lucas Hoots
Electronic Theses and Dissertations
Kenneth May [16], in 1952, characterized simple majority rule in terms of three conditions: anonymity, neutrality, and positive responsiveness. In this thesis, we remove the condition of neutrality and obtain a characterization of the class of voting rules that satisfy anonymity and positive responsiveness. The key concept in this characterization is the notion of a strong quota pair system. The situation with two alternatives studied by May can be thought of as a very simple example of a finite median semilattice. The main result of this thesis is an extension of May’s theorem to the domain of all finite median …
How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’,
2015
Northern Michigan University
How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’, Don Faust, Judith Puncochar
Conference Presentations
Collaboration, if to occur successfully at all, needs to be based on careful representation and communication of each stakeholder’s knowledge. In this paper, we investigate, from a foundational logical and epistemological point of view, how such representation and communication can be accomplished. What we tentatively conclude, based on a careful delineation of the logical technicalities necessarily involved in such representation and communication, is that a complete representation is not possible. This inference, if correct, is of course rather discouraging with regard to what we can hope to achieve in the knowledge representations that we bring to our collaborations. We suggest …
Interdisciplinary Modeling For Water-Related Issues Graduate Course,
2015
New Mexico State University
Interdisciplinary Modeling For Water-Related Issues Graduate Course, Laurel Saito, Alexander Fernald, Timothy Link
All ECSTATIC Materials
The science and management of aquatic ecosystems is inherently interdisciplinary, with issues associated with hydrology, atmospheric science, water quality, geochemistry, sociology, economics, environmental science, and ecology. Addressing water resources issues in any one discipline invariably involves effects that concern other disciplines, and attempts to address one issue often have consequences that exacerbate existing issues or concerns, or create new ones (Jørgensen et al. 1992; Lackey et al. 1975; Straskraba 1994) due to the strongly interactive nature of key processes (Christensen et al. 1996). Thus, research and management of aquatic ecosystems must be interdisciplinary to be most effective, but such truly …
Good Stein Neighborhood Bases For Nonsmooth Pseudoconvex Domains,
2015
University of Arkansas, Fayetteville
Good Stein Neighborhood Bases For Nonsmooth Pseudoconvex Domains, Chizuko Iwaki
Graduate Theses and Dissertations
In 1979, Dufresnoy showed that the existence of a good Stein neighborhood base for Ω ⊂ℂⁿ implies that one can solve the inhomogeneous Cauchy-Riemann equations in C^∞(Ω̄), even if the boundary of Ω is only Lipschitz. In my thesis, I will show sufficient conditions for the existence of a good Stein neighborhood base on a Lipschitz domain satisfying Property (P).
Local And Nonlocal Models In Thin-Plate And Bridge Dynamics,
2015
University of Nebraska-Lincoln
Local And Nonlocal Models In Thin-Plate And Bridge Dynamics, Jeremy Trageser
Department of Mathematics: Dissertations, Theses, and Student Research
This thesis explores several models in continuum mechanics from both local and nonlocal perspectives. The first portion settles a conjecture proposed by Filippo Gazzola and his collaborators on the finite-time blow-up for a class of fourth-order differential equations modeling suspension bridges. Under suitable assumptions on the nonlinearity and the initial data, a finite-time blowup is demonstrated as a result of rapid oscillations with geometrically growing amplitudes. The second section introduces a nonlocal peridynamic (integral) generalization of the biharmonic operator. Its action converges to that of the classical biharmonic as the radius of nonlocal interactions---the ``horizon"---tends to zero. For the corresponding …
Accuracy Comparison Of Numerical Integration Algorithms For Real-Time Hybrid Simulations,
2015
Old Dominion University
Accuracy Comparison Of Numerical Integration Algorithms For Real-Time Hybrid Simulations, Ganesh Anant Reddy
Civil & Environmental Engineering Theses & Dissertations
The use of accurate numerical integration algorithms is one of the key factors for a successful real-time hybrid simulation (RTHS). In RTHSs, explicit integration algorithms are preferred more than implicit methods since all calculations need to be completed within a given time step during simulation. Explicit methods require the use of effective stiffness and damping for experimental substructures, which are incorporated into the calculation of the integration parameters. In general, those values that are greater than the expected stiffness and damping of the experimental substructure are used to ensure the stability of simulation. If a rate-dependent and nonlinear experimental substructure …
A Tent Pitching Scheme Motivated By Friedrichs Theory,
2015
Portland State University
A Tent Pitching Scheme Motivated By Friedrichs Theory, Jay Gopalakrishnan, Peter Monk, Paulina Sepulveda
Mathematics and Statistics Faculty Publications and Presentations
Certain Friedrichs systems can be posed on Hilbert spaces normed with a graph norm. Functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet. Motivated by this continuity property, an explicit space-time finite element scheme of the tent pitching type, with spaces that conform to the continuity property, is designed. Numerical results for a model one-dimensional wave propagation problem are presented.
Isometries Of Besov Type Spaces Among Composition Operators,
2015
University of Arkansas, Fayetteville
Isometries Of Besov Type Spaces Among Composition Operators, Melissa Ann Shabazz
Graduate Theses and Dissertations
Let Bp,alpha for p >1 and alpha >1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space Ap,alpha. We then characterize isometries among composition operators in Bp,alpha in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,alpha, except on B 2,0, are induced by rotations. This extends known results by …
