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-pl...
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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.
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 mode...
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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.
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 simultaneou...
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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.
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 condit...
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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.
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...
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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|2p≤1 and thus contain a large family of both convex (p≥0.5) and concave (0
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 eff...
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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.
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 t...
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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.
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 ...
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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.
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 H...
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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.
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