The Band-Edge Behavior of the Density of Surfacic States

This paper is devoted to the asymptotics of the density of surfacic states near the spectral edges for a discrete surfacic Anderson model. Two types of spectral edges have to be considered: fluctuating edges and stable edges. Each type has its own type of asymptotics. In the case of fluctuating edges, one obtains Lifshitz tails the parameters of which are given by the initial operator suitably 'reduced' to the surface. For stable edges, the surface density of states behaves like the surface density of states of a constant (equal to the expectation of the random potential) surface potential. Among the tools used to establish this are the asymptotics of the surface density of states for constant surface potentials.Mathematics Subject Classifications (2000) 35P20, 46N50, 47B80.     

Frequency-selective response of FitzHugh-Nagumo neuron networks via changing random edges

We consider a network of FitzHugh-Nagumo neurons; each neuron is subjected to a subthreshold periodic signal and independent Gaussian white noise. The firing pattern of the mean field changes from an internal-scale dominant pattern to an external-scale dominant one when more and more edges are added into the network. We find numerically that (a) this transition is more sensitive to random edges than to regular edges, and (b) there is a saturation length for random edges beyond which the transition is no longer sharpened. The influence of network size is also investigated.     

电网在三种边攻击方式下的级联失效

研究美国西部电网在三种边攻击方式下级联失效差异性.定义边ij的初始负载为(k_ik_j)^θ,k_i,k_j分别表示节点i和j的度,θ为一可调参数.三种边攻击方式分别为:最小负载边攻击方式(LL)、最大负载边攻击方式(HL)和容量比最小边攻击方式(SPC).通过分析电网的拓扑结构,研究三种攻击方式级联失效差异性.研究表明:HL和LL攻击方式下,受攻击边的范围不随θ而改变,HL的攻击效果随θ的增大而增强,LL的攻击效果随θ的增大而减弱.而SPC法选中的被攻击边随θ变化,当θ取值较小时,SPC攻击边是拓扑结构较特殊的一种最小负载边,随着θ的增大,SPC攻击边趋向于高负载边,因此θ较小时,SPC的攻击效果和LL接近,当θ较大时,SPC的攻击效果和HL接近.     

改进的Zernike矩工业CT图像边缘检测

为提高工业计算机断层扫描(CT)图像亚像素边缘检测的精度和速度,研究了一种改进的Zernike矩边缘检测方法。该方法采用Sobel边缘算子快速检测出图像所有可能的边缘,通过Zernike矩算子对所有可能的边缘进行重新检测,最后,检测出图像的亚像素边缘并计算其精确位置。由于采用Sobel算子检测出可能的边缘使后续Zernike矩算子检测范围缩小,从而减小了运算量,提高了运算速度。对实际CT图像进行的实验结果表明:改进的Zernike矩工业CT图像边缘检测精度绝对误差<0.24 pixel,改进算法的运算速度提高了约70%。     

Energy gaps in graphene nanoribbons

Based on a first-principles approach, we present scaling rules for the band gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs considered have either armchair or zigzag shaped edges on both sides with hydrogen passivation. Both varieties of ribbons are shown to have band gaps. This differs from the results of simple tight-binding calculations or solutions of the Dirac's equation based on them. Our ab initio calculations show that the origin of energy gaps for GNRs with armchair shaped edges arises from both quantum confinement and the crucial effect of the edges. For GNRs with zigzag shaped edges, gaps appear because of a staggered sublattice potential on the hexagonal lattice due to edge magnetization. The rich gap structure for ribbons with armchair shaped edges is further obtained analytically including edge effects. These results reproduce our ab initio calculation results very well.     

Anomalous dispersion behavior of multiple-wave X-ray diffraction at absorption edges: determination of phase change at resonance

The effects of anomalous dispersion (resonance) on multiple reflection of x rays and their interference in crystals at atomic absorption edges are studied. Intensity ratios of two inversion-symmetry-related multiple diffractions at or near absorption edges exhibit highly phase-sensitive profiles with strong asymmetric characteristics, unlike those far from the edges. A new resonance perturbation Bethe approach is developed to explain this behavior. This leads to direct determination of the phase change for x-ray reflections at resonance.     

Color image edge detection method using VTV denoising and color difference

The traditional Canny edge uses Gaussian filter to suppress the noise, it also smoothes out the image edges. An improved Canny edge detection method for color image is proposed in this paper, the improved method uses fast vectorial total variation (VTV) minimization model to remove noise in color image, and then calculates the color difference and direction in CIELAB color space, which is used for non-maximal suppression. Finally, the improved method extracts the edges by the double-threshold method. The experimental results show that the proposed method achieves better performance than the traditional Canny edge detector. It can remove noise while preserving the image edges, and effectively detect the image edges.     

Causal Set Dynamics and Elementary Particles

A causal set is considered a finite, acyclic oriented graph with special restrictions: each vertex has two incident edges directed to this vertex and two incident edges directed from this vertex. This graph is called a causal graph. The vertex with incident edges is called an X-structure. Quantum measurements are discussed. A dynamics of the causal graph is a random sequence of elementary interactions of edges that is described by complex amplitudes. These amplitudes correspond to each pair of interacting edges. The edges are elementary particles. The mass of a particle is a probability of the interaction. An equation of particles is proposed. In a simple case this equation for X-structure is the Dirac's equation. The edges are fermions with the spin 1/2.     

误差分散类彩色半调图的边缘检测算法

针对误差分散类彩色半调图提出一种边缘检测算法.首先应用K－L变换,将(R,G,B)空间转换为具有正交特性的彩色特征空间(I1,I2,I3),构造灰度图I使之包含所有单色图像的边缘信息,最后设计多尺度边缘检测模板以获取图像边缘.实验表明,算法较传统方法抗半调噪音的能力强,能快速、准确地提取彩色半调图像的边缘.     

Functionalization of edge reconstructed graphene nanoribbons by H and Fe: A density functional study

In this paper, we have studied functionalization of 5–7 edge-reconstructed graphene nanoribbons by ab initio density functional calculations. Our studies show that hydrogenation at the reconstructed edges is favorable in contrast to the case of unreconstructed 6–6 zigzag edges, in agreement with previous theoretical results. Thermodynamical calculations reveal the relative stability of single and dihydrogenated edges under different temperatures and chemical potential of hydrogen gas. From phonon calculations, we find that the lowest optical phonon modes are hardened due to 5–7 edge reconstruction compared to the 6–6 unreconstructed hydrogenated edges. Finally, edge functionalization by Fe atoms reveals a dimerized Fe chain structure along the edges. The magnetic exchange coupling across the edges varies between ferromagnetic and antiferromagnetic ones with the variation of the width of the nanoribbons.     

Theoretical ELNES using one-particle and multi-particle calculations

One-, two-, and many-particle calculations for electron-energy-loss near-edge structures (ELNES) are reviewed. The most important point for the ELNES calculation is the proper introduction of the core-hole effect. By introducing the core-hole effect in a sufficiently large supercell, one-particle calculations are applicable to the ELNES of many edges. On the other hand, the two-particle interaction between the excited electron and the core-hole, namely the excitonic effect, is significant in the K edges of very light elements and the L_2,3 edges of Mg and Al. Many-particle interactions, including both electron–electron and electron–hole interactions, are indispensable for the L_2,3 edges of transition metals and the M_4,5 edges of lanthanides, namely white lines. In this review, we present the basics, methodologies, and some applications of one-, two-, and many-particle calculations. In addition, importance of momentum transfer vector in the ELNES calculations for comparison with the experiments is discussed.     

Relative stability of armchair,zigzag and reczag graphene edges on the Ru(0001) surface

The relative stability of armchair, zigzag, and the reconstructed zigzag (reczag) graphene edges was studied using density functional theory with the Perdew, Burke, and Ernzerhof (PBE) exchange correlation functional for graphene nanoribbons in vacuo and on the Ru(0001) surface. Although the reczag edge was found to be more stable in vacuo confirming previous predictions of Koskinen et al. [Phys. Rev. Lett. 101 (2008) 115502], the relative stability reverses upon adsorption on the Ru(0001) surface. The zigzag edge is more stable than the reczag edge on the surface by about 0.15 eV/Å and the armchair ribbon was found to be approximately isoenergetic with the zigzag ribbon. For all three types of edges, strong edge–Ru interactions are observed that cause the edges to buckle down. The lowered edge height may facilitate C attachments at graphene edges during graphene synthesis.     

FREE VIBRATION ANALYSIS OF ARBITRARILY SHAPED PLATES WITH A MIXED BOUNDARY CONDITION USING NON-DIMENSIONAL DYNAMIC INFLUENCE FUNCTIONS

A new approach using the non-dimensional dynamic influence functions has been developed for free vibration analysis of arbitrarily shaped plates with a mixed boundary condition involving both simply supported edges and clamped ones. Since the proposed method is based on the collocation method using one-dimensional and wave-type functions, no integration procedure is needed on boundary edges of the plate of interest and numerical calculation schemes are relatively concise. In order to settle the incompleteness of the system matrix, which is due to the discarding of a complex natural boundary condition at simply supported edges, an additional simple equation is devised by means of using a geometric approximation on curved edges. Finally, verification examples show that a complete system matrix formed in this way successfully gives accurate eigenvalues compared with FEM (ANSYS) and other methods.     

Lateral diffusion and percolation in membranes

An algorithm based on Voronoi tessellation and percolation theory is presented to study the diffusion of model membrane components (solutes) in the plasma membrane. The membrane is modeled as a two-dimensional space with integral membrane proteins as static obstacles. The Voronoi diagram consists of vertices, which are equidistant from three matrix obstacles, joined by edges. An edge between two vertices is said to be connected if solute particles can pass directly between the two regions. The percolation threshold, pc, determined using this passage criterion is pc approximately equal to 0.53. This is smaller than if the connectivity of edges were assigned randomly, in which case the percolation threshold pr=2/3, where p is the fraction of connected edges. Molecular dynamics simulations show that diffusion is determined by percolation of clusters of edges.     

The edge state of nanographene and the magnetism of the edge-state spins

Nanographene has unique edge-shape dependence of the electronic structure with non-bonding edge states being created in its zigzag edges. The presence of the edge state is experimentally confirmed in well-defined hydrogen-terminated zigzag edges by scanning tunneling microscopy/spectroscopy (STM/STS) observations. In the three-dimensional (3D) disordered network of nanographite domains in nanoporous carbon (activated carbon fibers), the localized edge-state spins are in a spin-glass-like ordered state at low temperatures with the aid of exchange interactions whose strengths varies randomly in space, when the strengths of inter-nanographene and nanographite interactions are tuned. Chemical and structural modifications of nanographene edges change the magnetism of edge-state spins through covalent bond formation and charge transfer.     

Edge-enhanced spatiotemporal constrained reconstruction of undersampled dynamic contrast-enhanced radial MRI

Dynamic contrast-enhanced magnetic resonance imaging (MRI) is a technique used to study and track contrast kinetics in an area of interest in the body over time. Reconstruction of images with high contrast and sharp edges from undersampled data is a challenge. While good results have been reported using a radial acquisition and a spatiotemporal constrained reconstruction (STCR) method, we propose improvements from using spatially adaptive weighting and an additional edge-based constraint. The new method uses intensity gradients from a sliding window reference image to improve the sharpness of edges in the reconstructed image. The method was tested on eight radial cardiac perfusion data sets with 24 rays and compared to the STCR method. The reconstructions showed that the new method, termed edge-enhanced spatiotemporal constrained reconstruction, was able to reconstruct images with sharper edges, and there were a 36%±13.7% increase in contrast-to-noise ratio and a 24%±11% increase in contrast near the edges when compared to STCR. The novelty of this paper is the combination of spatially adaptive weighting for spatial total variation (TV) constraint along with a gradient matching term to improve the sharpness of edges. The edge map from a reference image allows the reconstruction to trade-off between TV and edge enhancement, depending on the spatially varying weighting provided by the edge map.     

Stationary states of crystal growth in three dimensions

A new Markov process describing crystal growth in three dimensions is introduced. States of the process are configurations of the crystal surface, which has a terrace-edge-kink structure. The states are continuous along edges but discrete across edges, in accordance with the very different rates for the two types of captures of particles. Stationary distributions, describing steady crystal growth, are found in general. To our knowledge, these are the first examples of stationary distributions for layered crystal growth in three dimensions. The steady growth rate and other quantities are obtained explicitly for two interacting edges. For many interacting edges, growth behavior is determined (a) in various asymptotic regimes including thermodynamic limits, (b) via simulations, and (c) using series (cluster) expansions in the slope of the surface, the first three coefficients being computed. The theoretical growth rates show a marked dependence on surface dimensions. This may contribute to the size dependence and dispersion in the observed growth rate of small crystals.     

Aromaticity and cyclic conjugation of three pairs of strongly subspectral series of conjugated molecules as models for graphene armchair and zigzag edges

It is shown that armchair edges possess greater aromaticity and cyclic conjugation than do zigzag edges in model nanoribbons. These results are consistent with the zigzag graphene edges being more prone to rapid oxidation when oxygen is present than armchair graphene edges. These results were obtained using Aihara's BRE and Bosanac and Gutman's CCE methods for measuring aromaticity of individual rings. New numerical results are given for three pairs of strongly subspectral series.     

Structure Dependence of Excitonic Effects in Chiral Graphene Nanoribbons

We explore the excitonic effects in chiral graphene nanoribbons(cGNRs), whose edges are composed alternatively of armchair-edged and zigzag-edged segments. For cGNRs dominated by armchair edges, their energy gaps and exciton energies decrease with increasing chirality angles, and they, as functions of widths, oscillate with the period of three, while the exciton binding energies do not have such distinct oscillation. On the other hand,for cGNRs dominated by zigzag edges, all the energy gaps, exciton energies, and exciton binding energies show oscillation properties with their widths, due to the interactions between the edge states localized at the opposite zigzag edges. In addition, the triplet excitons are energy degenerate when the electrons are spin-unpolarized,while the degeneracy split when the electrons are spin-polarized. All the studied cGNRs show strong excitonic effects with the exciton binding energies of hundreds of meV.