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Generalized Cauchy-Born rules for elastic deformation of sheets, plates, and rods: Derivation of continuum models from atomistic models

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Physical Review B 2006年第18期74卷 184110-184110页

作者： Jerry Z. Yang Weinan E The Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We present an elementary and systematic discussion on the derivation of continuum theories from atomistic models for studying the elastic deformation of plates, sheets, and rods. The derivation is based on various generalizations of the classical Cauchy-Born rule. In particular, we discuss a so-called local Cauchy-Born rule which is very general and particularly easy to use. As an application, we use the atomistically derived continuum models to study the elastic deformation of carbon nanotubes.

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Second-order Sigma-Delta (ΣΔ) quantization of finite frame expansions

Second-order Sigma-Delta (ΣΔ) quantization of finite frame...

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作者： Benedetto, John J. Powell, Alexander M. Yilmaz, Özgür Department of Mathematics University of Maryland College Park MD 20742 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Mathematics University of British Columbia Vancouver BC V6T 1Z2 Canada

The second-order Sigma-Delta (ΣΔ) scheme with linear quantization rule is analyzed for quantizing finite unit-norm tight frame expansions for Rd. Approximation error estimates are derived, and it is shown that for certain choices of frames the quantization error is of order 1/N2, where N is the frame size. However, in contrast to the setting of bandlimited functions there are many situations where the second-order scheme only gives approximation error of order 1/N. For example, this is the case when quantizing harmonic frames of odd length in even dimensions. An important component of the error analysis involves extending existing stability results to yield smaller invariant sets for the linear second-order ΣΔ scheme. © 2005 Elsevier Inc. All rights reserved.

关键词： Estimation

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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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Coarse Graining the Dynamics of Coupled Oscillators

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Physical Review Letters 2006年第14期96卷 144101-144101页

作者： Sung Joon Moon R. Ghanem I. G. Kevrekidis Department of Chemical Engineering & Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA Department of Civil Engineering University of Southern California Los Angeles California 90089 USA

We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observables which account for the (rapidly developing) correlations between phase angles and natural frequencies. Exploiting short bursts of appropriately initialized detailed simulations, we circumvent the derivation of closures for the long-term dynamics of the assembly statistics.

关键词： Oscillators (electronic)

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Coarse molecular-dynamics determination of the onset of structural transitions: Melting of crystalline solids

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Physical Review B 2006年第13期74卷 132201-132201页

作者： Miguel A. Amat Ioannis G. Kevrekidis Dimitrios Maroudas Department of Chemical Engineering University of Massachusetts Amherst Massachusetts 01003 USA Department of Chemical Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach provides a means for constructing effective free-energy landscapes of structural transitions in condensed matter. The predictions of the approach for the thermodynamic melting point of a model silicon system are in excellent agreement with those of “traditional” techniques for melting-point calculations, as well as with literature values.

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Designed interaction potentials via inverse methods for self-assembly

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Physical Review E 2006年第1期73卷 011406-011406页

作者： Mikael Rechtsman Frank Stillinger Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and PRISM Princeton New Jersey 08544 USA

We formulate statistical-mechanical inverse methods in order to determine optimized interparticle interactions that spontaneously produce target many-particle configurations. Motivated by advances that give experimentalists greater and greater control over colloidal interaction potentials, we propose and discuss two computational algorithms that search for optimal potentials for self-assembly of a given target configuration. The first optimizes the potential near the ground state and the second near the melting point. We begin by applying these techniques to assembling open structures in two dimensions (square and honeycomb lattices) using only circularly symmetric pair interaction potentials; we demonstrate that the algorithms do indeed cause self-assembly of the target lattice. Our approach is distinguished from previous work in that we consider (i) lattice sums, (ii) mechanical stability (phonon spectra), and (iii) annealed Monte Carlo simulations. We also devise circularly symmetric potentials that yield chainlike structures as well as systems of clusters.

关键词： THERMAL-EXPANSION MICROSTRUCTURES SYSTEM PORES MODEL

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Virtual Array Processing for Active Radar and Sonar Sensing

Virtual Array Processing for Active Radar and Sonar Sensing

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Asilomar Conference on Signals, Systems & Computers

作者： Louis L. Scharf Ali Pezeshki Departments of Electrical and Computer Engineering and Statistics Colorado State University Fort Collins CO USA Program Applied and Computational Mathematics Princeton University Princeton NJ USA

In this paper, we describe how an active radar/sonar imaging problem may be formulated as a virtual passive sensor array processing problem. We consider an active sensing problem where it is desired to form a range-Doppler image at a slow- time rate, even though the radar/sonar can transmit pulses at a fast time rate. By transmitting pulses at the fast time rate we can estimate the second-order statistics of an ambiguity vector, calculated at a coarse resolution. As we show this ambiguity vector plays the role of an array snapshot vector in passive sensor array processing. The noise free version of this ambiguity vector acts as a signature vector or steering vector, which can be steered around in delay and Doppler at a fine resolution to produce an image. We employ a MVDR-like principle to generate high resolution delay-Doppler images.

关键词： Array signal processing Sonar Sensor arrays Radar imaging Delay Image resolution Passive radar Image sensors Sensor phenomena and characterization Statistics

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Guest editorial nonlinear optimization of communication systems

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IEEE Journal on Selected Areas in Communications 2006年第8期24卷 1421-1423页

作者： Chiang, Mung Low, Steven H. Luo, Zhi-Quan Shroff, Ness B. Yu, Wei Steenstrup, M. Princeton University Department of Electrical Engineering Program in Applied and Computational Mathematics Princeton NJ 08544 United States California Institute of Technology Department of Computer Science Pasadena CA 91125 United States University of Minnesota Department of Electrical and Computer Engineering Minneapolis MN 55455 United States Purdue University School of Electrical and Computer Engineering West Lafayette IN 47907 United States University of Toronto Edward S. Rogers Sr. Department of Electrical and Computer Engineering Toronto Ont. M4S 3G5 Canada

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关键词： Communication systems Design optimization Communication system control Optimization methods Protocols Distributed algorithms Power system modeling Nonlinear control systems Lagrangian functions Surges

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Do Binary Hard Disks Exhibit an Ideal Glass Transition?

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Physical Review Letters 2006年第22期96卷 225502-225502页

作者： Aleksandar Donev Frank H. Stillinger Salvatore Torquato Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA PRISM Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

We demonstrate that there is no ideal glass transition in a binary hard-disk mixture by explicitly constructing an exponential number of jammed packings with densities spanning the spectrum from the accepted amorphous glassy state to the phase-separated crystal. Thus the configurational entropy cannot be zero for an ideal amorphous glass, presumed distinct from the crystal in numerous theoretical and numerical estimates in the literature. This objection parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)].

关键词： .glassy Phys Rev Hard Disks PRL week ending Princeton University Princeton gurational New Jersey USA hard-disk jammed ideal glass exponential number phase-separated crystal

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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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