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Experiments on Random Packings of Ellipsoids

Physical Review Letters 2005年第19期94卷 198001-198001页

作者： Weining Man Aleksandar Donev Frank H. Stillinger Matthew T. Sullivan William B. Russel David Heeger Souheil Inati Salvatore Torquato P. M. Chaikin Department of Physics and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemistry and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemical Engineering and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Psychology and Center for Neural Science New York University New York New York 10003 USA

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25∶1∶0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We have fabricated ellipsoids and show that, in a sphere, the radial packing fraction ϕ(r) can be obtained from V(h), the volume of added fluid to fill the sphere to height h. We also obtain ϕ(r) from a magnetic resonance imaging scan. The measurements of the overall density ϕavr, ϕ(r) and the core density ϕ0=0.74±0.005 agree with simulations.

关键词： .ellipsoids Princeton New Jersey

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An Exponential Matrix Product Based Representation for Generalized Hypergeometric Functions of TypepFp

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Applied Numerical Analysis & computational Mathematics 2005年第1期2卷

作者： N. A. Baykara İrem Yaman Metin Demiralp Mathematics Department Faculty of Sciences and Letters Marmara University Göztepe 34722 İstanbul Turkey Group for Science and Methods of Computing Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 34469 İstanbul Turkey Phone: +90 212 285 70 77 Fax: +90 212 285 70 73 Phone: +90 212 285 70 82 Fax: +90 212 285 70 73

In this work, a new representation is developed for generalized hypergeometric functions of type p F p . To this end a first order vector differential equation is constructed in a way such that the derivative of the unknown vector has unit matrix coefficient. The solution vector differential equation is rewritten in the form of a series expansion. An infinite process of factor extractions and annihilations is employed to construct finally a vector differential equation that can be easily solved. Truncation of this scheme can be used to get approximations to hypergeometric functions of type p F p . A simple, yet meaningful, implementation seems to give quite promising results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： Exponential matrix factorization generalized hypergemetric function

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Weighted Eigenvalue Problem Approach To The Critical Value Determination Of Screened Coulomb Potential Systems

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： Metin Demiralp Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 80626 İstanbul Turkey

In this work, the radial time-independent Schrödinger equation of a screened Coulomb potential system at the zero energy limit is first converted to a weighted eigenvalue problem of an ordinary differential operator. Then, by using an appropriate coordinate transformation, the differential equation is transformed into a form whose first and second order derivative related terms become same as the Extended Jacobi Polynomials' differential equation's corresponding terms. Only difference is the appearance of a multiplicative operator which can be considered as an effective potential. Work focuses on the point whether the solution is obtained easily depending on the structure of this potential. In this direction a screened Coulomb potential with a specific rational screening function is considered. The analytical solutions for the critical values of the screening parameter and the form of the wave function at the threshold of the continous spectrum are obtained. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： Screened Coulomb Potentials Extended Jacobi Polynomials Energy Spectrum

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High Dimensional Model Representation Approximation of an Evolution Operator with a First Order Partial Differential Operator Argument

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： İrem Yaman Metin Demiralp Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 34469 İstanbul Turkey Phone: +90 212 285 70 82 Fax: +90 212 285 70 73

In this work, a novel approximation scheme based on a recently developed representation, called the High Dimensional Model Representation (HDMR), is proposed to approximate evolution operators. The approximation is not developed at the operator level, instead the effect of the operator on an arbitrary function is approximated. The purpose of the work is to investigate how HDMR can be applied for the approximation of evolution operator and its efficiency. Although the approximation can be constructed for any order of multivariance, only the constant and univariate components of HDMR are considered in this work. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： Lie algebraic exponential operator High Dimensional Model Representation

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A Parametric Sensitivity Analysis for the Solution of Extrema Evaluation Problems via a Dimensionality Reducing Approximation Method

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： Tülin Kaman Metin Demiralp Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 34469 İstanbul Turkey Phone: +90 212 285 70 82 Fax: +90 212 285 70 73

This work aims to apply High Dimensional Model Representation (HDMR) to the sensitivity coefficient determination of the solutions of a multivariate extrema problem. The derivations are made for general functional structure and the illustrative applications are related to structures where the resulting extrema equations are matrix eigenvalue problems. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： High Dimensional Model Representation Extrema Finding Matrix Inversion Matrix Eigenvalue

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Optimally Controlled Dynamics of One Dimensional Harmonic Oscillator: Linear Dipole Function and Quadratic Penalty

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： Burcu Tunga Metin Demiralp Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 34469 İstanbul Turkey Phone: +90 212 285 70 82 Fax: +90 212 285 70 73

This work deals with the optimal control of one dimensional quantum harmonic oscillator under an external field characterized by a linear dipole function. The penalty term is taken as kinetic energy. The objective operator whose expectation value is desired to get a prescribed target value is taken as the square of the position operator. The dipole function hypothesis in the external field is valid only for weak fields otherwise hyperpolarizability terms which contain powers of the field amplitude higher than 1 should be considered. The weak field assumption enables us to develop a first order perturbation approach to get approximate solutions to the wave and costate equations. These solutions contain the field amplitude and another unknown, so-called deviation constant, through some certain integrals. By inserting these expressions into the connection equation which functionally relates the field amplitude to the wave and costate function it is possible to produce an integral equation. Same manipulations on the objective equation results in an algebraic equation to determine the deviation parameter. The algebraic deviation equation produces incompatibility which can be relaxed by including second order perturbative term of wave function. The integral and algebraic equations mentioned above are asymptotically solved. Their global solutions are left to future works since the main purpose of this work is to obtain the so-called field and deviation equations. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： Optimal control quantum mechanics harmonic oscillator weak field interaction perturbation

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A Factorized High Dimensional Model Representation on the Partitioned Random Discrete Data

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： M. Alper Tunga Metin Demiralp Department of Computer Science and Engineering Engineering Faculty Işįk University Maslak 34398 İstanbul Turkey Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 80626 İstanbul Turkey Phone: +90 212 285 70 82 Fax: +90 212 285 70 73

The main purpose of this work is to obtain the general structure of a product type of multivariate function when the values of the function are given randomly at the nodes of a hyperprism. When the dimensionality of multivariate interpolation and the number of the data sets increase unboundedly, many problems can be encountered in the standard numerical methods. Factorized High Dimensional Model Representation (FHDMR) is used to obtain the general structure of this given multivariate function. The components of FHDMR are determined by using the components of the Generalized High Dimensional Model Representation (GHDMR).The given random discrete data is partitioned by GHDMR method. This partitioned data produces a structure for the multivariate function by using single variable Lagrange interpolation formula including only the constant term and the univariate terms of the GHDMR components. Finally, a general structure is obtained via FHMDR by using these components. By this way, the multidimensionality of a multivariate interpolation is approximated by lower dimensional interpolations like univariate ones. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： Multivariate functions multivariate representations approximation factor analysis interpolation multidimensional problems

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Optimal Control of One Dimensional Quantum Harmonic Oscillator Under an External Field With Quadratic Dipole Function and Penalty on Momentum: Construction of the Linearised Field Amplitude Integral Equation

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： A. Kurşunlu İrem Yaman Metin Demiralp Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 34469 İstanbul Turkey Phone: +90 212 285 70 77 Fax: +90 212 285 70 73 Phone: +90 212 285 70 82 Fax: +90 212 285 70 73

In this work, the optimal control of an harmonic oscillator is considered. The external field is assumed to be weak and hence is represented by only dipole interaction. The dipole function is taken as a second degree polynomial in spatial coordinate. The objective term is composed of the expectation value of algebraic position operator. Penalty term related operator is taken as momentum. Some specific structures for spatial dependence is assumed and temporal equations are obtained for unknowns. The equations represent forward and backward evolution. The connection is provided by an algebraic equation coming from field amplitude related equation. The key unknown is the field amplitude since its determination leads us to evaluate all unknowns without remarkable difficulty. The purpose is not to determine field amplitude at the most general case but to construct an equation which involves this unknown only. The equation obtained via the linearisation of the field amplitude dependence is shown to be a linear integral equation. We do not attempt to solve it but discuss how to use appropriate methods for the solution. The equation is analytically solved at the zero interaction time limit. The real comprehensive implementation is left for future work. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： Optimal Control Quantum Mechanics Weak Field Interaction Perturbations Harmonic Oscillator

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Publisher’s Note: “Polymer-specific effects of bulk relaxation and stringlike correlated motion in the dynamics of a supercooled polymer melt” [J. Chem. Phys. 119, 5290 (2003)]

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The Journal of Chemical Physics 2004年第14期120卷 6798-6798页

作者： M. Aichele Y. Gebremichael F. W. Starr J. Baschnagel S. C. Glotzer Institut Charles Sadron 6 rue Boussingault 67083 Strasbourg France Institut für Physik Johannes Gutenberg-Universität 55099 Mainz Germany Department of Chemical Engineering University of Michigan Ann Arbor Michigan 48109 Chemical Physics Program Institute for Physical Sciences and Technology University of Maryland College Park Maryland 20742 Center for Theoretical and Computational Materials Science and Polymers Division National Institute of Standards and Technology Gaithersburg Maryland 20899 Departments of Chemical Engineering and Materials Science and Engineering University of Michigan Ann Arbor Michigan 48109

M. Aichele, Y. Gebremichael, F. W. Starr, J. Baschnagel, S. C. Glotzer; Publisher’s Note: “Polymer-specific effects of bulk relaxation and stringlike correlated

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RJSSim: A reconfigurable job scheduling simulator for parallel processing learning 33

RJSSim: A reconfigurable job scheduling simulator for parall...

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33rd Annual Frontiers in Education, FIE 2003

作者： Góes, Luís F.W. Martins, Carlos A.P.S. Pontifical Catholic University of Minas Gerais Post-Graduation Program in Electrical Engineering Computational and Digital Systems Laboratory Belo HorizonteMG Brazil Pontifical Catholic University of Minas Gerais Computer Science Department Post-Graduation Program in Electrical Engineering Computational and Digital Systems Laboratory Belo HorizonteMG Brazil

ISBN: (纸本)0780379616

In this work, we present and analyze the use of a reconfigurable job scheduling simulator called RJSSim as an aid tool for parallel processing learning. This software is a functional and performance Java-based simulator of job scheduling policies. Our objectives are: to present RJSSim;to show the use of RJSSim and reconfigurability concepts for parallel processing learning. First, we present a prototype of RJSSim and the reconfigurability concept. Then we describe two case studies remarking the main parallel processing concepts and skills students can learn. In the first case study, we analyze two parallel algorithm models. In the second, we do some performance tests among parallel (reconfigurable) scheduling policies and architectures. Then, we analyze the performance through some metrics like response time, idle time etc. Finally we discuss and analyze the use of RJSSim for parallel processing learning. Our main contribution is: an implementation of RJSSim for parallel processing learning. © 2003 IEEE.

关键词： Parallel algorithms

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