一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

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.     

Comparison of implicit and explicit AUSM‐family schemes for compressible multiphase flows

This paper makes the first attempt of extending implicit AUSM‐family schemes to multiphase flow simulations. Water faucet, air–water shock tube and oscillating manometer problems are used as benchmark tests with the generic four‐equation two‐fluid model. For solving the equations implicitly, Newton's method along with a sparse matrix solver (UMFPACK solver) is employed, and the numerical Jacobian matrix is calculated. Comparison between implicit and explicit AUSM‐family schemes is presented, indicating that similarly accurate results are obtained with both schemes. Furthermore, the water faucet problem is solved using both staggered and collocated grids. This investigation helps integrate high‐resolution schemes into staggered‐grid‐based computational algorithms. The influence of the interface pressure correction on the simulation results is also examined. Results show that the interfacial pressure correction introduces numerical dissipation. However, this dissipation cannot eliminate the overshoots because of the incompatibility of numerical discretization of the conservative and non‐conservative terms in the governing equations. The comparison of CPU time between implicit and explicit schemes is also studied, indicating that the implicit scheme is capable of improving the computational efficiency over its explicit counterpart. Copyright © 2014 John Wiley & Sons, Ltd.     

Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions

In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type. An explicit L² norm estimate for the gradient of the solution of this problem is established. This leads to an explicit bound of the H¹ norm of this solution. Note that the obtained upper-bound is not optimal.     

基于显示连通贝叶斯网络的机场塔台地震易损性分析

将基于性能的多维易损性分析方法,结合显示连通贝叶斯网络,应用于机场塔台的多维易损性分析。考虑地震激励的不确定性,通过非线性时程分析获得结构响应数据;将塔台结构分为三个层次,每个层次按包含的层数分为相应的子层次。根据功能特性确定子层次的评价指标和极限状态,建立服从多元对数正态分布的概率地震需求模型;考虑各种极限状态之间的相关性,建立极限状态方程,确定失效域,通过蒙特卡洛法求得构件的超越概率;建立塔台结构的显示连通贝叶斯网络模型,利用层次分析法获得中间节点的条件概率表,利用MATLAB进行贝叶斯网络的推理计算,实现从单一层次的易损性到整体易损性的推理。     

Comprehensive Mechanism for CO Electroreduction on Dual-Atom-Catalyst-Anchored N-Doped Graphene

Carbon neutrality has drawn increasing attention for realizing the carbon cyclization and reducing the greenhouse effect. Although the C1 products, such as CO, can be achieved with a high Faraday efficiency, the targeted production of C2 fuels as well as the mechanism have not been systematically investigated. In this work, we carry out a first-principles study to screen dual-atom catalysts (DACs) for producing C2 fuels through the electrocatalytic carbon monoxide reduction reaction (e-CORR). We find that methanol, ethanol and ethylene can be produced on both DAC−Co and DAC−Cu, while acetate can be achieved on DAC−Cu only. Importantly, methanol and ethylene are preferred on DAC−Co, while acetate and ethylene on DAC−Cu. Furthermore, we show that the explicit solvent can enhance the adsorption and influence the protonation steps, which subsequently affects the protonation and dimerization behavior as well as the performance and selectivity of e-CORR on DACs. We further demonstrate that the C−C coupling is easy to be formed and stabilized if the Integrated Crystal Orbital Hamilton Population (ICOHP) is low because of the low energy barrier. Our findings provide not only guidance on the design of novel catalysts for e-CORR, but an insightful understanding on the reduction mechanism.     

Stability of ion triplets in ionic liquid/lithium salt solutions: Insights from implicit and explicit solvent models and molecular dynamics simulations

Binding energies of ion triplets formed in ionic liquids by Li⁺ with two anions have been studied using quantum‐chemical calculations with implicit and explicit solvent supplemented by molecular dynamics (MD) simulations. Explicit solvent approach confirms variation of solute‐ionic liquid interactions at distances up to 2 nm, resulting from structure of solvation shells induced by electric field of the solute. Binding energies computed in explicit solvent and from the polarizable continuum model approach differ largely, even in sign, but relative values generally agree between these two models. Stabilities of ion triplets obtained in quantum‐chemical calculations for some systems disagree with MD results; the discrepancy is attributed to the difference between static optimized geometries used in quantum chemical modeling and dynamic structures of triplets in MD simulations. © 2015 Wiley Periodicals, Inc.     

“三端合一”显隐结合的无机化学课程思政方法*

基于本校无机化学的课程特色,拟定课程思政目标,将思政元素与教学内容对应。在无机化学课程的资源端(MOOC平台)、教学端(超星学习通)、服务端(微信公众号)等均融入思政元素,创新教学方法,构建“三端合一”显隐结合的课程思政方法,为其他专业课的课程思政提供参考。