Fast tensor method for summation of long‐range potentials on 3D lattices with defects

In this paper, we present a method for fast summation of long‐range potentials on 3D lattices with multiple defects and having non‐rectangular geometries, based on rank‐structured tensor representations. This is a significant generalization of our recent technique for the grid‐based summation of electrostatic potentials on the rectangular L × L × L lattices by using the canonical tensor decompositions and yielding the O(L) computational complexity instead of O(L³) by traditional approaches. The resulting lattice sum is calculated as a Tucker or canonical representation whose directional vectors are assembled by the 1D summation of the generating vectors for the shifted reference tensor, once precomputed on large N × N × N representation grid in a 3D bounding box. The tensor numerical treatment of defects is performed in an algebraic way by simple summation of tensors in the canonical or Tucker formats. To diminish the considerable increase in the tensor rank of the resulting potential sum, the ?‐rank reduction procedure is applied based on the generalized reduced higher‐order SVD scheme. For the reduced higher‐order SVD approximation to a sum of canonical/Tucker tensors, we prove the stable error bounds in the relative norm in terms of discarded singular values of the side matrices. The required storage scales linearly in the 1D grid‐size, O(N), while the numerical cost is estimated by O(NL). The approach applies to a general class of kernel functions including those for the Newton, Slater, Yukawa, Lennard‐Jones, and dipole‐dipole interactions. Numerical tests confirm the efficiency of the presented tensor summation method; we demonstrate that a sum of millions of Newton kernels on a 3D lattice with defects/impurities can be computed in seconds in Matlab implementation. The tensor approach is advantageous in further functional calculus with the lattice potential sums represented on a 3D grid, like integration or differentiation, using tensor arithmetics of 1D complexity. Copyright © 2015 John Wiley & Sons, Ltd.     

On defected colourings of graphs

Abstract A k-edge-coloring f of a connected graph G is a （A1, A2, , A）-defected k-edge-coloring if there is a smallest integer/ with 1 _ /3 _〈 k - i such that the multiplicity of each color j E {1,2,... ,/3} appearing at a vertex is equal to Aj _〉 2, and each color of {/3 -}- 1,/3 - 2, - , k} appears at some vertices at most one time. The （A1, A2,, A/）-defected chromatic index of G, denoted as X （A1, A2,, A/; G）, is the smallest number such that every （A1,A2,-.., A/）-defected t-edge-coloring of G holds t _〉 X（A1, A2 A;; G）. We obtain A（G） X（A1, ）2, , A/; G） ＋ -- （Ai - 1） _〈 /k（G） 1, and introduce two new chromatic indices of G i=1 as： the vertex pan-biuniform chromatic index X pb （G）, and the neighbour vertex pan-biuniform chromatic index Xnpb（G）, and furthermore find the structure of a tree T having X pb （T） =1.     

SIMULATION OF THE INTERFACED STRUCTURAL COMPONENT BASED ON A MULTIPLE-TIME-SCALE ALGORITHM

A multiple-time-scale algorithm is developed to numerically simulate certain structural components in civil structures where local defects inevitably exist. Spatially, the size of local defects is relatively small compared to the structural scale. Different length scales should be adopted considering the efficiency and computational cost. In the principle of physics, different length scales are stipulated to correspond to different time scales. This concept lays the foundation of the framework for this multiple-time-scale algorithm. A multiple-time-scale algorithm, which involves different time steps for different regions, while enforcing the compatibility of displacement, force and stress fields across the interface, is proposed. Furthermore, a defected beam component is studied as a numerical sample. The structural component is divided into two regions： a coarse one and a fine one; a micro-defect exists in the fine region and the finite element sizes of the two regions are diametrically different. Correspondingly, two different time steps are adopted. With dynamic load applied to the beam, stress and displacement distribution of the defected beam is investigated from the global and local perspectives. The numerical sample reflects that the proposed algorithm is physically rational and computationally efficient in the potential damage simulation of civil structures.     

Vibration analysis of defected and pristine triangular single-layer graphene nanosheets

This paper investigates the vibration behavior of pristine and defected triangular graphene sheets; which has recently attracted the attention of researchers and compare these two types in natural frequencies and sensitivity. Here, the molecular dynamics method has been employed to establish a virtual laboratory for this purpose. After measuring the different parameters obtained by the molecular dynamics approach, these data have been analyzed by using the frequency domain decomposition (FDD) method, and the dominant frequencies and mode shapes of the system have been extracted. By analyzing the vibration behaviors of pristine triangular graphene sheets in four cases (right angle of 45-90-45 configuration, right angle of 60-90-30 configuration, equilateral triangle and isosceles triangle), it has been demonstrated that the natural frequencies of these sheets are higher than the natural frequency of a square sheet, with the same number of atoms, by a minimum of 7.6% and maximum of 26.6%. Therefore, for increasing the resonance range of sensors based on 2D materials, non-rectangular structures, and especially the triangular structure, can be considered as viable candidates. Although the pristine and defective equilateral triangular sheets have the highest values of resonance, the sensitivity of defective (45,90,45) triangular sheet is more than other configurations and then, defective (45,90,45) sheet is the worst choice for sensor applications.     

局域表面等离子体共振效应在光催化技术中的应用

表面等离子激元是物理效应在光催化技术应用中的典型代表之一,作为新型光场调控技术为光催化技术的发展开辟了新的方向和思路,能够从全新的角度解决光催化技术的发展瓶颈,在过去十年来得到了广泛的研究。局域表面等离子体共振效应能够通过调节纳米颗粒的组成、形貌和介质环境等因素调控光催化体系的光谱响应范围。除此之外还能够通过增强光散射、热电子注入、诱导产生强烈的局域电场、加热周围环境等方法来增加光催化剂的氧化-还原反应速度、物质传输以及极化光催化材料表面的吸附分子,从而进一步增强材料的光催化性能。将这些优势集成到光催化材料体系中,能够显著提高传统光催化材料的太阳能转换效率,这是一个非常值得关注的发展方向。本文综述了局域表面等离子体共振效应在光催化技术中应用的基本原理、调控规律和应用等方面的研究进展,着重讨论了热电子的产生和迁移过程,贵金属中带间跃迁和表面等离子体共振效应的制约关系。最后,总结了表面等离子体光催化剂所面临的问题和挑战,并进行了相应的研究展望。     

Density functional theory study on the adsorption of alkali metal ions with pristine and defected graphene sheet

The graphene-based materials along with the adsorption of alkali metal ions are suitable for energy conversion and storage applications. Hence in the present work, we have investigated the structural and electronic properties of pristine and defected graphene sheet upon the adsorption of alkali metal ions (Li⁺, Na⁺, and K⁺) using density functional theory (DFT) calculations. The presence of vacancies or vacancy defects enhances the adsorption of alkali ions than the pristine sheet. From the obtained results, it is found that the adsorption energy of Li⁺ on the vacancies defected graphene sheet is higher (3.05?eV) than the pristine (2.41?eV) and Stone–Wales (2.50?eV) defected sheets. Moreover, the pore radius of the pristine and defected graphene sheets are less affected by metal ions adsorption. The increase in energy gap upon the adsorption of metal ions is found to be high in the vacancy defected graphene than that of other sheets. The metal ions adsorption in the defective vacancy sheets has high charge transfer from metal ions to the graphene sheet. The bonding characteristic between the metal ions and graphene sheet are analysed using QTAIM analysis. The influence of alkali ions on the electronic properties of the graphene sheet is examined from the Total Density of States (TDOS) and Partial Density of States (PDOS).     

The catalytic performance of metal-free defected carbon catalyst towards acetylene hydrochlorination revealed from first-principles calculation

Defected carbon materials as a metal-free catalyst have shown superior stability and catalytic performance in the acetylene hydrochlorination reaction. Through density functional theory (DFT) calculations, for the first time, several different defected configurations comprising mono and divacancies and Stone Wales defect on single-walled carbon nanotubes (SWCNTs) have been used as a direct catalyst for acetylene hydrochlorination reaction. These defective sites on SWCNTs are the most active site for acetylene hydrochlorination reaction compare to pristine SWCNT. The different configurations of defects have different electronic structures, which specify that monovacancy defects have more states adjacent to the Fermi level. The reactant acetylene (C₂H₂) adsorbed strongly compared to hydrogen chloride (HCl) and expected to be the initial step of the reaction. Acetylene adsorbed strongly at monovacancy defected SWCNT compared to other investigated defects. Reaction pathway analysis revealed that mono- and divacancy defected SWCNTs have minimum energy barriers and show extraordinary performance toward acetylene hydrochlorination. This work suggests the potential of metal-free defected carbon in catalyzing acetylene hydrochlorination and provides a solid base for future developments in acetylene hydrochlorination.     

一种采用互补结构的宽阻带共模缺陷地滤波器

为了抑制高速差分信号传输中的共模噪声, 提出了一种基于低成本FR4材料制作的互补型缺陷地结构(defected ground structure, DGS)共模阻带滤波器. 滤波器两边采用对称性酒杯形DGS结构, 中间采用对称伞形DGS结构. 由于这两种DGS 结构互补, 整个滤波器结构紧凑, 可以实现小面积设计目的; 另外, 由于三个DGS结构相邻较近, 相互之间存在互感, 可以通过改变相互之间的距离来调节相互之间的互感, 从而实现宽阻带滤波的目的. 仿真和测试结果表明, 该DGS滤波器的差模信号损耗小, 在抑制共模噪声20 dB条件下其阻带范围为4.8–11.4 GHz, 而且面积仅为10 mm×10 mm. 与周期性DGS结构相比, 本方法在相同共模噪声抑制深度下, 具有占用面积不到30%、阻带宽度增加约50%等优点.