Vorticity: Simplifying the analysis of the current density

The induced current density ( J ( r )) provides useful information about the electronic structure of molecules under a magnetic field ( B ). However, the analysis of its topology is cumbersome because of its vectorial nature. We show that its tropicity (direction of rotation) and its strength can be compressed in the triple product B ⋅ ∇ × J ( r ) (tp J ( r )) that is a scalar field. The topology of tp J ( r ) has clear similarities to the Laplacian of the electron density. Additionally, the topology of aromatic and antiaromatic compounds is notoriously different. The vorticity of J ( r ) is helpful to define the circulation of the current density, C, that contrary to other methods, can be easily defined for individual rings in polycyclic molecules. This allows tp J ( r ) to clearly reproduce the Clar's structure of polycyclic aromatic hydrocarbons. © 2019 Wiley Periodicals, Inc.     

安培环路定理的拓扑学描述

近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用.     

基于相场描述的拉压不对称强度结构拓扑优化

运用了基于相场描述的拓扑优化方法，来寻找在拉伸和压缩中表现出不对称强度行为的连续体结构的最优布局。依据Drucker-Prager屈服准则和幂率插值方案，优化问题可以描述为在局部应力约束下的最小化结构的体积。用qp放松法来解决应力约束的奇异性，并采用基于P-norm函数的聚合方法对应力约束进行凝聚，该方法实现了约束个数的降低，同时引入了稳定转化法来处理大量的局部应力约束和高度非线性的应力行为，以修正应力，提高优化收敛的稳定性。在优化问题求解时，使用拉格朗日乘子法对目标函数和应力约束进行处理。利用伴随变量法进行灵敏度分析，并通过求解Allen-Cahn方程更新相场函数设计变量。数值算例证明了该优化模型和相应数值技术的有效性，相关算例还揭示了考虑拉压不同强度和考虑同拉压强度约束时得到的结构优化拓扑构型具有显著的差异。     

Rational Topological Design for Fluorescence Enhancement upon Aggregation of Distyrylfuran Derivatives

A series of 2,5‐distyrylfuran derivatives bearing pentafluorophenyl‐ and cyanovinyl units have been synthesized for aggregation‐induced emission (AIE). The effect of the type and extent of the supramolecular connections on the AIE of the furan derivatives were examined and correlated with their X‐ray crystal structures. It was found that the simultaneous presence of cyano and perfluorophenyl units strongly enhances the fluorescence upon aggregation. Single‐crystal X‐ray diffraction analysis confirmed that C?H???F, F???F, C?H???nitrile, Ar???Ar_F (Ar=aryl, Ar_F=fluoroaryl), and nitrile???Ar_F intra‐ and intermolecular interactions drive the topology of the molecule and that solid‐state supramolecular contacts favor AIE of the furan derivatives.     

Enhanced Property of Thin Cuprous Oxide Film Prepared through Green Synthetic Route

Thin cuprous oxide films have been prepared by chemical vapor deposition (pulsed spray evaporation-chemical vapor deposition) method without post-treatment. The synthesis ofcuprous oxide was produced by applying a water strategy effect. Then, the effect of water on the morphology, topology, structure, optical properties and surface composition of the obtained films has been comprehensively investigated. The results reveal that a pure phase of Cu₂O was obtained. The introduction of a small quantity of water in the liquid feedstock lowers the band gap energy from 2.16 eV to 2.04 eV. This finding was mainly related to the decrease of crystallite size due to the effect of water. The topology analyses, by using atomic force microscope, also revealed that surface roughness decreases with water addition, namely more uniform covered surface. Moreover, theoretical calculations based on density functional theory method were performed to understand the adsorption and reaction behaviors of water and ethanol on the Cu₂O thin film surface. Formation mechanism of the Cu₂O thin film was also suggested and discussed.     

Time‐periodic solution to the compressible nematic liquid crystal flows in periodic domain

In this paper, we consider the time‐periodic solution to a simplified version of Ericksen‐Leslie equations modeling the compressible hydrodynamic flow of nematic liquid crystals with a time‐periodic external force in a periodic domain in . By using an approach of parabolic regularization and combining with the topology degree theory, we establish the existence of the time‐periodic solution to the model under some smallness and symmetry assumptions on the external force. Then, we give the uniqueness of the periodic solution of this model.     

演化算法求解桁架多目标拓扑优化的收敛速度研究

演化算法能够同时满足结构拓扑优化的前沿领域对全局优化、黑箱函数优化、组合优化和多目标优化的需求,但采用此类算法的可行性与必要性由其收敛性与计算效率决定。本文以应力约束桁架多目标拓扑优化问题为求解对象,致力于揭示在收敛性与计算效率两方面具有竞争力的算法。首先提出评估演化算法求解拓扑优化问题收敛性与计算效率的通用方法,采用穷举法严格推导了典型桁架多目标拓扑优化问题的全局最优解,并采用超体积指标定义了多层次收敛性能准则。最后通过比较研究得到不同收敛性需求下具有最快收敛速度的演化算法,并揭示了具有竞争力的算法机制。本研究为演化算法求解多目标拓扑优化问题的收敛速度奠定了理论基础,同时为高效求解实际工程拓扑优化问题提供算法支持。