Physics Commons^™

Measures Of Centrality Based On The Spectrum Of The Laplacian, Scott D. Pauls, Daniel Remondini

Dartmouth Scholarship

We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information.

We explore this centrality in the context of several examples. While for sparse unweighted net- works 1-spectral centrality behaves similarly to other standard centralities, for dense weighted net- works they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) …

Modelling Three-Phase Flow In Metallurgical Processes, Christoph Goniva, Gijsbert Wierink, Kari Heiskanen, Stefan Pirker, Christoph Kloss

Gijsbert Wierink

The interaction between gasses, liquids, and solids plays a critical role in many processes, such as coating, granulation and the blast furnace process. In this paper we present a comprehensive numerical model for three phase flow including droplets, particles and gas. By means of a coupled Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) approach the physical core phenomena are pictured at a detailed level. Sub-models for droplet deformation, breakup and coalescence as well as droplet-particle and wet particle-particle interaction are applied. The feasibility of this model approach is demonstrated by its application to a rotating drum coater. The …

Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman

Masters Theses

Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection and radiation as flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration generates a totally node-based algebraic statement for computing. Closure for gray body radiation is a newly derived node-based radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 hour diurnal field experiments for …

Radar Signal Delay In The Dvali-Gabadadze-Porrati Gravity In The Vicinity Of The Sun, Ioannis Haranas, Omiros Ragos, Ioannis Gkigkitzis

Physics and Computer Science Faculty Publications

In this paper we examine the recently introduced Dvali-Gabadadze-Porrati (DGP) gravity model. We use the space time metric in which the local gravitation source dominates the metric over the contributions from the cosmological flow. Anticipating ideal possible solar system effects we derive expressions for the signal time delays in the vicinity of the sun, and for various angles of the signal approach. We use the corresponding numerical value for the parameter r₀ to be equal to 5 Mpc, and from that we calculate that the time contribution due to DGP correction to the metric is proportional to b^{3/2 …}

N-Body Problem’S Global Solution I. Classical Approach, Jorge A. Franco

Jorge A Franco

The prediction of the movement of a group of N gravitationally attracting bodies around its center of mass CM, given their initial positions and velocities, is what has been called the N-body problem, since Isaac Newton formulated it in his magnum work Phylosophiae Naturalis Principia Mathematica, commonly known as his "Principia" published in 1667. So far it has only been fully resolved (Johan Bernoulli in 1710) the problem of two bodies from the classical view, using Newton's laws. For N>2 in some cases only approximate, or not general, solutions exist. In this work the strategy of realizing physical properties …

A Homogeneous Solution Of The Einstein-Maxwell Equations, Charles G. Torre

Research Vignettes

We exhibit and analyze a homogeneous spacetime whose source is a pure radiation electromagnetic field [1]. It was previously believed that this spacetime is the sole example of a homogeneous pure radiation solution of the Einstein equations which admits no electromagnetic field (see [2] and references therein). Here we correct this error in the literature by explicitly displaying the electromagnetic source. This result implies that all homogeneous pure radiation spacetimes satisfy the Einstein-Maxwell equations.

PDF and Maple worksheets can be downloaded from the links below.

How To Create A Lie Algebra, Ian M. Anderson

How to... in 10 minutes or less

We show how to create a Lie algebra in Maple using three of the most common approaches: matrices, vector fields and structure equations. PDF and Maple worksheets can be downloaded from the links below.

Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv

Applications and Applied Mathematics: An International Journal (AAM)

Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.

Estimation And Testing For Spatially Indexed Curves With Application To Ionospheric And Magnetic Field Trends, Oleksandr Gromenko, Piotr Kokoszka, Lie Zhu, Jan Josef Sojka

All Physics Faculty Publications

We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves X(sk;t), t∈[0, T], observed at spatial locations s1,s2, . . . ,sN. We propose several methods, and evaluate them by means of a simulation study. Next, we develop a significance test for the correlation of two such functional spatial fields. After validating the finite sample performance of this test by means of a simulation study, we apply it to determine if there is correlation between long-term trends in the so-called critical ionospheric frequency …

Exact Results In Model Statistical Systems, Peter H. Kleban

University of Maine Office of Research Administration: Grant Reports

Intellectual merit: This project focuses on continued research on the exact study of the statistical mechanics of model systems. The research concentrates on two areas:

1) critical percolation in two dimensions, an important and very extensively studied model system, to which we are bringing new and unexpected approaches, and

2) the thermodynamics of the Farey fraction spin chain, a set of one dimensional models with interesting phase transition behavior and connections to multifractals, and dynamical systems.

This project aims at new results and insights in both these areas. Research on the Farey models illuminates an interesting borderline case in the …

Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda

Department of Math & Statistics Faculty Publications

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …

Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda

Biology Faculty Publications

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …

Average Output Entropy For Quantum Channels, Christopher King, David K. Moser

Christopher King

We study the regularized average Renyi output entropy r reg of quantum channels. This quantity gives information about the average noisiness of the channel output arising from a typical, highly entangled input state in the limit of infinite dimensions. We find a closed expression for βr reg , a quantity which we conjecture to be equal to r reg . We find an explicit form for βr reg for some entanglement-breaking channels and also for the qubit depolarizing channel Δλ as a function of the parameter λ. We prove equality of the two quantities in some cases, in particular, we …

Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard

Articles

We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.

The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun

Xiao-Jun Yang

The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform, used in Yang-Fourier transform in fractal space. This paper points out new standard forms of discrete Yang-Fourier transforms (DYFT) of fractal signals, and both properties and theorems are investigated in detail.

Expression Of Generalized Newton Iteration Method Via Generalized Local Fractional Taylor Series, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a generalized Newton iteration method derived from the generalized local fractional Taylor series with the local fractional derivatives is reviewed. Operators on real line numbers on a fractal space are induced from Cantor set to fractional set. Existence for a generalized fixed point on generalized metric spaces may take place.

Section Abstracts: Astronomy, Mathematics And Physics With Materials Science

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics, and Physics with Material Science Section for the 90th Annual Meeting of the Virginia Academy of Science, May 23-25, 2012, Norfolk State University, Norfolk, Virginia

Parameterized Special Theory Of Relativity (Pstr), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We have parameterized Einstein’s thought experiment with atomic clocks, supposing that we knew neither if the space and time are relative or absolute, nor if the speed of light was ultimate speed or not. We have obtained a Parameterized Special Theory of Relativity (PSTR), first introduced in 1982. Our PSTR generalized not only Einstein’s Special Theory of Relativity, but also our Absolute Theory of Relativity, and introduced three more possible Relativities to be studied in the future. After the 2011 CERN’s superluminal neutrino experiments, we recall our ideas and invite researchers to deepen the study of PSTR, ATR, and check …

The Zero-Mass Renormalization Group Differential Equations And Limit Cycles In Non-Smooth Initial Value Problems, Yang Xiaojun

Xiao-Jun Yang

In the present paper, using the equation transform in fractal space, we point out the zero-mass renormalization group equations. Under limit cycles in the non-smooth initial value, we devote to the analytical technique of the local fractional Fourier series for treating zero-mass renormalization group equations, and investigate local fractional Fourier series solutions.

A Novel Approach To Processing Fractal Dynamical Systems Using The Yang-Fourier Transforms, Yang Xiaojun

Xiao-Jun Yang

In the present paper, local fractional continuous non-differentiable functions in fractal space are investigated, and the control method for processing dynamic systems in fractal space are proposed using the Yang-Fourier transform based on the local fractional calculus. Two illustrative paradigms for control problems in fractal space are given to elaborate the accuracy and reliable results.

The History Of Maxwell's Equations, Lindsay Guilmette (Class Of 2012)

Writing Across the Curriculum

An enormous amount of technology is owed to Maxwell's theory of electromagnetism and his perseverance through cultural obstacles to advocate his talent of mathematical interpretation.

Stability And Clustering Of Self-Similar Solutions Of Aggregation Equations, Hui Sun, David Uminsky, Andrea L. Bertozzi

Mathematics

In this paper we consider the linear stability of a family of exact collapsing similarity solutions to the aggregation equation ρ _t = ∇ · (ρ∇K * ρ) in Rd , d ⩾ 2, where K(r) = r ^γ/γ with γ > 2. It was previously observed [Y. Huang and A. L. Bertozzi, “Self-similar blowup solutions to an aggregation equation in Rn,” J. SIAM Appl. Math.70, 2582–2603 (Year: 2010)]10.1137/090774495 that radially symmetric solutions are attracted to a self-similar collapsing shell profile in infinite time for γ > 2. In this paper we compute the stability of the …

Introduction Aux Méthodes D’Intégrale De Chemin Et Applications, Nour-Eddiine Fahssi

Nour-Eddine Fahssi

These lecture notes are based on a master course given at University Hassan II - Agdal in spring 2012.

Theory And Applications Of Local Fractional Fourier Analysis, Yang Xiaojun

Xiao-Jun Yang

Local fractional Fourier analysis is a generalized Fourier analysis in fractal space. The local fractional calculus is one of useful tools to process the local fractional continuously non-differentiable functions (fractal functions). Based on the local fractional derivative and integration, the present work is devoted to the theory and applications of local fractional Fourier analysis in generalized Hilbert space. We investigate the local fractional Fourier series, the Yang-Fourier transform, the generalized Yang-Fourier transform, the discrete Yang-Fourier transform and fast Yang-Fourier transform.

Heat Transfer In Discontinuous Media, Yang Xiaojun

Xiao-Jun Yang

From the fractal geometry point of view, the interpretations of local fractional derivative and local fractional integration are pointed out in this paper. It is devoted to heat transfer in discontinuous media derived from local fractional derivative. We investigate the Fourier law and heat conduction equation (also local fractional instantaneous heat conduct equation) in fractal orthogonal system based on cantor set, and extent them. These fractional differential equations are described in local fractional derivative sense. The results are efficiently developed in discontinuous media.

A Short Note On Local Fractional Calculus Of Function Of One Variable, Yang Xiaojun

Xiao-Jun Yang

Local fractional calculus (LFC) handles everywhere continuous but nowhere differentiable functions in fractal space. This note investigates the theory of local fractional derivative and integral of function of one variable. We first introduce the theory of local fractional continuity of function and history of local fractional calculus. We then consider the basic theory of local fractional derivative and integral, containing the local fractional Rolle’s theorem, L’Hospital’s rule, mean value theorem, anti-differentiation and related theorems, integration by parts and Taylor’ theorem. Finally, we study the efficient application of local fractional derivative to local fractional extreme value of non-differentiable functions, and give …

A New Successive Approximation To Non-Homogeneous Local Fractional Volterra Equation, Yang Xiaojun

Xiao-Jun Yang

A new successive approximation approach to the non-homogeneous local fractional Valterra equation derived from local fractional calculus is proposed in this paper. The Valterra equation is described in local fractional integral operator. The theory of local fractional derivative and integration is one of useful tools to handle the fractal and continuously non-differentiable functions, was successfully applied in engineering problem. We investigate an efficient example of handling a non-homogeneous local fractional Valterra equation.

Advanced Local Fractional Calculus And Its Applications, Yang Xiaojun

Xiao-Jun Yang

This book is the first international book to study theory and applications of local fractional calculus (LFC). It is an invitation both to the interested scientists and the engineers. It presents a thorough introduction to the recent results of local fractional calculus. It is also devoted to the application of advanced local fractional calculus on the mathematics science and engineering problems. The author focuses on multivariable local fractional calculus providing the general framework. It leads to new challenging insights and surprising correlations between fractal and fractional calculus. Keywords: Fractals - Mathematical complexity book - Local fractional calculus- Local fractional partial …

A Short Introduction To Yang-Laplace Transforms In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The Yang-Laplace transforms [W. P. Zhong, F. Gao, In: Proc. of the 2011 3rd International Conference on Computer Technology and Development, 209-213, ASME, 2011] in fractal space is a generalization of Laplace transforms derived from the local fractional calculus. This letter presents a short introduction to Yang-Laplace transforms in fractal space. At first, we present the theory of local fractional derivative and integral of non-differential functions defined on cantor set. Then the properties and theorems for Yang-Laplace transforms are tabled, and both the initial value theorem and the final value theorem are investigated. Finally, some applications to the wave equation …

Local Fractional Integral Equations And Their Applications, Yang Xiaojun

Xiao-Jun Yang

This letter outlines the local fractional integral equations carried out by the local fractional calculus (LFC). We first introduce the local fractional calculus and its fractal geometrical explanation. We then investigate the local fractional Volterra/ Fredholm integral equations, local fractional nonlinear integral equations, local fractional singular integral equations and local fractional integro-differential equations. Finally, their applications of some integral equations to handle some differential equations with local fractional derivative and local fractional integral transforms in fractal space are discussed in detail.