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Tilings of space and superhomogeneous point processes

Physical Review E 2008年第3期77卷 031125-031125页

作者： A. Gabrielli M. Joyce S. Torquato SMC-INFM Dipartimento di Fisica Università La Sapienza P.le A. Moro 2 I-00185 Rome Italy ISC-CNR Via dei Taurini 19 I-00185 Rome Italy Laboratoire de Physique Nucléaire et de Hautes Energies UMR-7585 Université Pierre et Marie Curie Paris 6 75252 Paris Cedex 05 France Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

We consider the construction of point processes from tilings, with equal-volume tiles, of d-dimensional Euclidean space Rd. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are “superhomogeneous” (or “hyperuniform”)—i.e., for which the structure factor S(k) vanishes when the wave vector k tends to zero. The exponent γ characterizing the leading small-k behavior, S(k→0)∝kγ, depends in a simple manner on the nature of the correlation properties of the specific tiling and on the conservation of the mass moments of the tiles. Assigning one point to the center of mass of each tile gives the exponent γ=4 for any tiling in which the shapes and orientations of the tiles are short-range correlated. Smaller exponents in the range 4−d<γ<4 (and thus always superhomogeneous for d≤4) may be obtained in the case that the latter quantities have long-range correlations. Assigning more than one point to each tile in an appropriate way, we show that one can obtain arbitrarily higher exponents in both cases. We illustrate our results with explicit constructions using known deterministic tilings, as well as some simple stochastic tilings for which we can calculate S(k) exactly. Our results provide an explicit analytical construction of point processes with γ>4. Applications to condensed matter physics, and also to cosmology, are briefly discussed.

关键词： SIMULATIONS CAUSALITY SPECTRUM

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Accelerating the complex Hessenberg QR algorithm with the csx600 floating-point coprocessor

Accelerating the complex Hessenberg QR algorithm with the cs...

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19th IASTED International Conference on Parallel and Distributed Computing and Systems

作者： Yamamoto, Yusaku Miyata, Takafumi Nakamura, Yoshimasa Dept. of Computational Science and Engineering Graduate School of Engineering Nagoya University Nagoya 464-8603 Japan Dept. of Applied Mathematics and Physics Graduate School of Informatics Kyoto University/ JST SORST Kyoto 606-8501 Japan

ISBN: (纸本)9780889867048

In this paper, we show how to speed up the Hessenberg QR algorithm for computing the eigenvalues of a dense complex nonsymmetric matrix using the CSX600 floating-point coprocessor. Our approach is based on the small-bulge multishift QR algorithm proposed by Braman et al. This algorithm can perform a major part of the computation in the form of matrix multiplication and is therefore very suited to high performance architectures. However, to exploit the potential of the CSX600, the number of shifts must be increased to more than two hundred. In that case, the parts other than matrix multiplication begin to occupy a considerable percentage of the execution time, thereby limiting the speedup. To solve this problem, we focus on two most time-consuming parts in the algorithm except for matrix multiplication: accumulation of bulge-chasing transformations and solution of a decoupled small eigenproblem. We reconstruct the former as a recursive algorithm and apply a blocking technique to the latter. This enables these parts to be computed also using matrix multiplication. As a result of these optimizations, we obtained up to 3.8 times speedup with the CSX600 processor over a 3.2GHz Xeon processor when computing the eigenvalues of a 12,000 × 12,000 complex Hessenberg matrix.

关键词： Coprocessor

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An information theoretic framework for eukaryotic gradient sensing 19

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20th Annual Conference on Neural Information Processing Systems, NIPS 2006

作者： Kimmel, Joseph M. Salter, Richard M. Thomas, Peter J. Computer Science Program Oberlin College Oberlin OH 44074 United States Department of Mathematics Biology and Cognitive Science Case Western Reserve University Cleveland OH 44106 United States Computational Neuroscience Graduate Program University of Chicago United States Center for Computation and Modeling United States

ISBN: (纸本)9780262195683

Chemical reaction networks by which individual cells gather and process information about their chemical environments have been dubbed "signal transduction" networks. Despite this suggestive terminology, there have been few attempts to analyze chemical signaling systems with the quantitative tools of information theory. Gradient sensing in the social amoeba Dictyostelium discoideum is a well characterized signal transduction system in which a cell estimates the direction of a source of diffusing chemoattractant molecules based on the spatiotemporal sequence of ligand-receptor binding events at the cell membrane. Using Monte Carlo techniques (MCell) we construct a simulation in which a collection of individual ligand particles undergoing Brownian diffusion in a three-dimensional volume interact with receptors on the surface of a static amoeboid cell. Adapting a method for estimation of spike train entropies described by Victor (originally due to Kozachenko and Leonenko), we estimate lower bounds on the mutual information between the transmitted signal (direction of ligand source) and the received signal (spatiotemporal pattern of receptor binding/unbinding events). Hence we provide a quantitative framework for addressing the question: how much could the cell know, and when could it know it? We show that the time course of the mutual information between the cell's surface receptors and the (unknown) gradient direction is consistent with experimentally measured cellular response times. We find that the acquisition of directional information depends strongly on the time constant at which the intracellular response is filtered.

关键词： Ligands

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Modeling heterogeneous materials via two-point correlation functions: Basic principles

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Physical Review E 2007年第3期76卷 031110-031110页

作者： Y. Jiao F. H. Stillinger S. Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex microstructures, which also make it difficult to model the materials. Yeong and Torquato [Phys. Rev. E 57, 495 (1998)] introduced a stochastic optimization technique that enables one to generate realizations of heterogeneous materials from a prescribed set of correlation functions. In this first part of a series of two papers, we collect the known necessary conditions on the standard two-point correlation function S2(r) and formulate a conjecture. In particular, we argue that given a complete two-point correlation function space, S2(r) of any statistically homogeneous material can be expressed through a map on a selected set of bases of the function space. We provide examples of realizable two-point correlation functions and suggest a set of analytical basis functions. We also discuss an exact mathematical formulation of the (re)construction problem and prove that S2(r) cannot completely specify a two-phase heterogeneous material alone. Moreover, we devise an efficient and isotropy-preserving construction algorithm, namely, the lattice-point algorithm to generate realizations of materials from their two-point correlation functions based on the Yeong-Torquato technique. Subsequent analysis can be performed on the generated images to obtain desired macroscopic properties. These developments are integrated here into a general scheme that enables one to model and categorize heterogeneous materials via two-point correlation functions. We will mainly focus on basic principles in this paper. The algorithmic details and applications of the general scheme are given in the second part of this series of two papers.

关键词： RECONSTRUCTING RANDOM-MEDIA PROBABILITY FUNCTIONS NONLINEAR COMPOSITES POROUS-MEDIA BOUNDS MICROSTRUCTURES OPTIMIZATION SCATTERING

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Oscillator models and collective motion

IEEE Control Systems Magazine

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IEEE Control Systems Magazine 2007年第4期27卷 89-105页

作者： Paley, Derek A. Leonard, Naomi Ehrich Sepulchre, Rodolphe Grünbaum, Daniel Parrish, Julia K. Princeton University Department of Mechanical and Aerospace Engineering Princeton NJ 08544 United States Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department Electrical Engineering and Computer Science University of Liège Liège Belgium School of Oceanography Department of Biology University of Washington Seattle WA United States Biology Department School of Aquatic and Fishery Sciences University of Washington Seattle WA United States

A description of the so called "particles with coupled oscillator dynamics" (PCOD) is presented which is used to model, analyze and synthesize collective motion. An oscillator model with spatial dynamics is presented to help describe how to design steering control laws while it is being used to study biological collectives. Lastly, both engineering and biological analysis were described.

关键词： Oscillators (mechanical)

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Large amplitude electromagnetic solitons in intense laser plasma interaction

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Chinese Physics B 2006年第9期15卷 2046-2052页

作者：李百文 Ishiguro S Skoric M M Institute of Applied Physics and Computational Mathematics Beijing 100088 China The Graduate University/or Advanced Studies and National Institute/or Fusion Science Toki 509-5292 Japan

This paper shows that the standing, backward- and forward-accelerated large amplitude relativistic electromagnetic solitons induced by intense laser pulse in long underdense collisionless homogeneous plasmas can be observed by particle simulations. In addition to the inhomogeneity of the plasma density, the acceleration of the solitons also depends upon not only the laser amplitude but also the plasma length. The electromagnetic frequency of the solitons is between about half and one of the unperturbed electron plasma frequency. The electrostatic field inside the soliton has a one-cycle structure in space, while the transverse electric and magnetic fields have half-cycle and one-cycle structure respectively. Analytical estimates for the existence of the solitons and their electromagnetic frequencies qualitatively coincide with our simulation results.

关键词： particle-in-cell （PIC） Raman cascade photon-condensation relativistic EM soliton

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Instantaneous radar polarimetry with multiple dually-polarized antennas

Instantaneous radar polarimetry with multiple dually-polariz...

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40th Asilomar Conference on Signals, Systems, and Computers, ACSSC '06

作者： Calderbank, A.R. Howard, S.D. Moran, W. Pezeshki, A. Zoltowski, M. Program in Applied and Computational Mathematics Princeton University Princeton NJ United States Defence Science and Technology Organization Edinburgh Australia Electrical Engineering and Computer Science University of Melbourne Melbourne Australia Electrical and Computer Engineering Purdue University West Lafayette IN United States

ISBN: (纸本)1424407850

Fully Polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar transmitter and receiver on a pulse by pulse basis, and can improve the radar detection performance and suppress range sidelobes. In this paper, we extend the use of instantaneous radar polarimetry for radar systems with multiple dually-polarized transmit and receive antennas. Alamouti signal processing is used to coordinate transmission of Golay pairs of phase codes waveforms across polarizations and multiple antennas. The integration of multi-antenna signal processing with instantaneous radar polarimetry can further improve the detection performance, at a computational cost comparable to single channel matched filtering.

关键词： Polarimeters

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An information theoretic framework for eukaryotic gradient sensing 06

An information theoretic framework for eukaryotic gradient s...

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Proceedings of the 20th International Conference on Neural Information Processing Systems

作者： Joseph M. Kimmel Richard M. Salter Peter J. Thomas Computer Science Program Oberlin College Oberlin Ohio and Computational Neuroscience Graduate Program The University of Chicago Computer Science Program Oberlin College Oberlin Ohio and Oberlin Center for Computation and Modeling Departments of Mathematics Biology and Cognitive Science Case Western Reserve University Cleveland Ohio and Oberlin College Research Associate

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Stimulated Raman Cascade into Photon Condensation and Large Amplitude EM Solitons in Laser Plasma Interaction

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AIP Conference Proceedings 2006年第1期827卷 74-85页

作者： Li Baiwen S. Ishiguro M. M. Škorić *Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 People’s Republic of China †The Graduate University for Advanced Studies Toki 509‐5292 Japan ‡National Institute for Fusion Science Toki 509‐5292 Japan

Stimulated Raman scattering, stimulated Raman cascade and the transition from Raman cascade into photon condensation, induced by a linearly‐polarized intense laser interacting with low‐density uniform plasmas, are studied by particle simulations. It is found that, at appropriate laser amplitude and plasma condition, a large amplitude relativistic EM soliton forms due to the strong photon condensation. The standing, backward‐ and forward‐accelerated ultra‐relativistic electromagnetic solitons induced by intense laser pulses are observed. In addition to the inhomogeneity of the plasma density the acceleration of solitons depends upon, both, the laser intensity and the plasma length. The frequency of solitons is about half of the unperturbed electron plasma frequency, while the transverse electric, magnetic and electrostatic field have half‐, one‐ and one‐cycle spatial structure, respectively.

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Instantaneous Radar Polarimetry with Multiple Dually-polarized Antennas

Instantaneous Radar Polarimetry with Multiple Dually-polariz...

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Asilomar Conference on Signals, Systems & Computers

作者： A. R. Calderbank S. D. Howard W. Moran A. Pezeshki M. Zoltowski Program Applied and Computational Mathematics Princeton University Princeton NJ USA Defence Science and Technology Organization Edinburgh Australia Electrical Engineering and Computer Science University of Melbourne Melbourne Australia Electrical and Computer Engineering Purdue University West Lafayette IN USA

Fully polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar transmitter and receiver on a pulse by pulse basis, and can improve the radar detection performance and suppress range sidelobes . In this paper, we extend the use of instantaneous radar polarimetry for radar systems with multiple dually-polarized transmit and receive antennas. Alamouti signal processing is used to coordinate transmission of Golay pairs of phase codes waveforms across polarizations and multiple antennas. The integration of multi- antenna signal processing with instantaneous radar polarimetry can further improve the detection performance, at a computational cost comparable to single channel matched filtering.

关键词： Radar polarimetry Radar antennas Polarization Radar detection Radar signal processing Transmitters Receiving antennas Transmitting antennas computational efficiency Matched filters

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