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.     

Effect of the topology on the antibacterial activity of cationic polythioether synthesized by all-click chemistry

Cationic compounds often serve as antibacterial materials for a wide range of applications. However, the relationship of topology−antibacterial activity has been rarely revealed. Herein, three cationic polythioethers (CPTEs) with hyperbranched topologies are well designed and facilely synthesized via an all-click chemistry strategy (including thiol-ene and epoxy-amine additions). These as-prepared CPTEs were found to exhibited outstanding antibacterial activity against Escherichia coli and Staphylococcus aureus with minimum inhibitory concentrations against E. coli of 7.3, 14.6, and 14.6 μg ml⁻¹, and against S. aureus of 14.6, 29.2, and 29.2 μg ml⁻¹, respectively. The antibacterial activity is coincident with their degree of branching (DB, their DB values of 0.81, 0.48, and 0.27), which is mainly attributed to the inherent three-dimensional structure. The present strategy reveals the relationship of polymer topology and antibacterial activity, providing a novel possibility for designing and/or synthesis of high-efficiency antibacterial agents.     

Organic Cage Dumbbells

Molecular dumbbells with organic cage capping units were synthesised via a multi-component imine condensation between a tri-topic amine and di- and tetra-topic aldehydes. This is an example of self-sorting, which can be rationalised by computational modelling.     

基于移动可变形孔洞方法的超弹性结构拓扑优化

现有隐式拓扑优化方法在进行超弹性结构拓扑优化设计时，具有设计变量多、中间设计有限元分析存在严重的收敛性和设计结果无法直接导入CAD/CAE系统等问题。为解决这些问题，提出了一种基于移动可变形孔洞的显式拓扑优化方法来进行承受大变形的超弹性结构设计，材料本构采用常用的Mooney-Rivlin模型。首先，介绍了移动可变形孔洞方法的基本思想和可变形孔洞的显式描述方法；其次，构造了基于移动可变形孔洞方法的超弹性结构拓扑优化的数学列式，给出了相应的灵敏度结果；最后，通过数值算例验证了本方法的有效性。数值结果表明，该方法可以通过较少的设计变量和非常稳健的优化过程，给出边界由B样条曲线描述且可与CAD/CAE软件无缝连接的超弹性结构设计。     

Shape morphing and topology optimization of fluid channels by explicit boundary tracking

An integrated shape morphing and topology optimization approach based on the deformable simplicial complex methodology is developed to address Stokes and Navier‐Stokes flow problems. The optimized geometry is interpreted by a set of piecewise linear curves embedded in a well‐formed triangular mesh, resulting in a physically well‐defined interface between fluid and impermeable regions. The shape evolution is realized by deforming the curves while maintaining a high‐quality mesh through adaption of the mesh near the structural boundary, rather than performing global remeshing. Topological changes are allowed through hole merging or splitting of islands. The finite element discretization used provides smooth and stable optimized boundaries for simple energy dissipation objectives. However, for more advanced problems, boundary oscillations are observed due to conflicts between the objective function and the minimum length scale imposed by the meshing algorithm. A surface regularization scheme is introduced to circumvent this issue, which is specifically tailored for the deformable simplicial complex approach. In contrast to other filter‐based regularization techniques, the scheme does not introduce additional control variables, and at the same time, it is based on a rigorous sensitivity analysis. Several numerical examples are presented to demonstrate the applicability of the approach.