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Edge-Stress-Induced Warping of Graphene Sheets and Nanoribbons

Physical Review Letters 2008年第24期101卷 245501-245501页

作者： V. B. Shenoy C. D. Reddy A. Ramasubramaniam Y. W. Zhang Division of Engineering Brown University Providence Rhode Island 02912 USA Institute of High Performance Computing Singapore 138632 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Materials Science and Engineering National University of Singapore Singapore 119260

We show that edge stresses introduce intrinsic ripples in freestanding graphene sheets even in the absence of any thermal effects. Compressive edge stresses along zigzag and armchair edges of the sheet cause out-of-plane warping to attain several degenerate mode shapes. Based on elastic plate theory, we identify scaling laws for the amplitude and penetration depth of edge ripples as a function of wavelength. We also demonstrate that edge stresses can lead to twisting and scrolling of nanoribbons as seen in experiments. Our results underscore the importance of accounting for edge stresses in thermal theories and electronic structure calculations for freestanding graphene sheets.

关键词： Nanoribbons

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The Elastic Continuum Limit of the Tight Binding Model

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Chinese Annals of mathematics,Series B 2007年第6期28卷 665-676页

作者： Weinan E Jianfeng LU Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.

关键词： Continuum limit Elasticity theory Cauchy-Born rule Tight binding model

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Rate-achievability strategies for two-hop interference flows

Rate-achievability strategies for two-hop interference flows

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Annual Allerton Conference on Communication, Control, and Computing

作者： P.S. Chandrashekhar Thejaswi Amir Bennatan Junshan Zhang Robert Calderbank Douglas Cochran Department of Electrical Engineering Arizona Stare University Tempe 85287 USA Program in Applied and Computational Mathematics (PACM) at Princeton University Princeton NJ USA Department of Electrical Engineering Arizona State University Tempe AZ USA Department of Electrical Engineering Arizona Stare University Tempe AZ USA

We consider a basic model for two-hop transmissions of two information flows which interfere with each other. In this model, two sources simultaneously transmit to two relays (in the first hop), which then simultaneously transmit to two destinations (in the second hop). While the transmission during the first hop is essentially the transmission over a classical interference channel, the transmission in the second hop enjoys an interesting advantage. Specifically, as a byproduct of the Han-Kobayashi transmission scheme applied to the first hop, each of the relays (in the second hop) has access to some of the data that is intended to the other destination, in addition to its own data. As recently observed by Simeone et al., this opens the door to cooperation between the relays. In this paper, we observe that the cooperation can take the form of distributed MIMO broadcast, thus greatly enhancing its effectiveness at high SNR. However, since each relay is only aware of part of the data beyond its own, full cooperation is not possible. We propose several approaches that combine MIMO broadcast strategies (including ldquodirty paperrdquo) with standard non-cooperative strategies for the interference channel. Numerical results are provided, which indicate that our approaches provide substantial benefits at high SNR.

关键词： Relays Interference channels Decoding MIMO Broadcasting Context Wireless networks mathematics Electronic mail

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Negative Poisson’s Ratio Materials via Isotropic Interactions

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Physical Review Letters 2008年第8期101卷 085501-085501页

作者： Mikael C. Rechtsman Frank H. 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 Princeton Center for Theoretical Science Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, have a negative Poisson’s ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson’s ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, a negative Poisson’s ratio can be exhibited even when the material is constrained to be elastically isotropic.

关键词： Lennard-Jones potential

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Optimal Packings of Superdisks and the Role of Symmetry

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Physical Review Letters 2008年第24期100卷 245504-245504页

作者： Y. Jiao F. H. Stillinger S. Torquato Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA

Almost all studies of the densest particle packings consider convex particles. Here, we provide exact constructions for the densest known two-dimensional packings of superdisks whose shapes are defined by |x1|2p+|x2|2... 详细信息

关键词： Condensed matter physics

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Erratum: Toward the jamming threshold of sphere packings: Tunneled crystals (Journal of applied Physics (2007) 102 (093511))

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Journal of applied Physics 2008年第12期103卷

作者： Torquato, S. Stillinger, F.H. Department of Chemistry Princeton University Princeton NJ 08544 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Princeton Institute for the Science and Technology of Materials Princeton University Princeton NJ 08544 United States Princeton Center for Theoretical Physics Princeton University Princeton NJ 08544 United States

No abstract available

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Modeling heterogeneous materials via two-point correlation functions. II. Algorithmic details and applications

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Physical Review E 2008年第3期77卷 031135-031135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 and School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA

In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media) via two-point correlation functions S2 and introduced an efficient heterogeneous-medium (re)construction algorithm called the “lattice-point” algorithm. Here we discuss the algorithmic details of the lattice-point procedure and an algorithm modification using surface optimization to further speed up the (re)construction process. The importance of the error tolerance, which indicates to what accuracy the media are (re)constructed, is also emphasized and discussed. We apply the algorithm to generate three-dimensional digitized realizations of a Fontainebleau sandstone and a boron-carbide/aluminum composite from the two-dimensional tomographic images of their slices through the materials. To ascertain whether the information contained in S2 is sufficient to capture the salient structural features, we compute the two-point cluster functions of the media, which are superior signatures of the microstructure because they incorporate topological connectedness information. We also study the reconstruction of a binary laser-speckle pattern in two dimensions, in which the algorithm fails to reproduce the pattern accurately. We conclude that in general reconstructions using S2 only work well for heterogeneous materials with single-scale structures. However, two-point information via S2 is not sufficient to accurately model multiscale random media. Moreover, we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two-point correlation functions.

关键词： RECONSTRUCTING RANDOM-MEDIA TOPOLOGY OPTIMIZATION MICROSTRUCTURES COMPOSITES DESIGN TRANSPORT

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Optimized Structures for Photonic Quasicrystals

引用

Physical Review Letters 2008年第7期101卷 073902-073902页

作者： Mikael C. Rechtsman Hyeong-Chai Jeong Paul M. Chaikin Salvatore Torquato Paul J. Steinhardt Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Physics Sejong University Gwangjin-gu Seoul 143-747 Korea Department of Physics and Center for Soft Condensed Matter Research New York University New York 10003 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and PRISM Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

A photonic quasicrystal consists of two or more dielectric materials arranged in a quasiperiodic pattern with noncrystallographic symmetry that has a photonic band gap. We use a novel method to find the pattern with the widest TM-polarized gap for two-component materials. Patterns are obtained by computing a finite sum of density waves, assigning regions where the sum exceeds a threshold to a material with one dielectric constant, ϵ1, and all other regions to another, ϵ0. Compared to optimized crystals, optimized quasicrystals have larger gaps at low constrasts ϵ1/ϵ0 and have gaps that are much more isotropic for all contrasts. For high contrasts, optimized hexagonal crystals have the largest gaps.

关键词： Quasicrystals

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Simulation of Impurity Diffusion in a Strained Nanowire Using Off-Lattice KMC

引用

Communications in computational Physics 2007年第1期2卷 164-176页

作者： Weidong Guo Tim P.Schulze Weinan E Department of Mathematics University of TennesseeKnoxvilleTN 37996-1300USA Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544-1000USA.

Kinetic Monte Carlo(KMC)is a stochastic model used to simulate crystal ***,most KMC models rely on a pre-defined lattice that neglects dislocations,lattice mismatch and strain *** this paper,we investigate the use of a 3D off-lattice KMC *** test this method by investigating impurity diffusion in a strained FCC *** faster than a molecular dynamics simulation,the most general implementation of off-lattice KMC is much slower than a lattice-based *** improved procedure is achieved for weakly strained systems by precomputing approximate saddle point locations based on unstrained lattice *** this way,one gives up some of the flexibility of the general method to restore some of the computational speed of lattice-based *** addition to providing an alternative approach to nano-materials simulation,this type of simulation will be useful for testing and calibrating methods that seek to parameterize the variation in the transition rates for lattice-based KMC using continuum modeling.

关键词： Off-lattice KMC nanowire strain rate impurity diffusion.

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Heterogeneous Multiscale Methods: A Review

引用

Communications in computational Physics 2007年第3期2卷 367-450页

作者： Weinan E Bjorn Engquist Xiantao Li Weiqing Ren Eric Vanden-Eijnden Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA Department of Mathematics The University of Texas at AustinAustinTX 78712USA Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA Department of Mathematics Courant Institute of Mathematical SciencesNew York UniversityNew YorkNY 10012USA.

This paper gives a systematic introduction to HMM,the heterogeneous multiscale methods,including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome when using HMM for a particular *** is illustrated by examples from several application areas,including complex fluids,micro-fluidics,solids,interface problems,stochastic problems,and statistically self-similar *** is given to the technical tools,such as the various constrained molecular dynamics,that have been developed,in order to apply HMM to these *** of mathematical results on the error analysis of HMM are *** review ends with a discussion on some of the problems that have to be solved in order to make HMM a more powerful tool.

关键词： Multi-scale modeling heterogeneous multi-scale method multi-physics models constrained micro-scale solver data estimation.

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