Syntheses, Structures, and Nonlinear Optical Properties of Two Crown-like Heteroselenometallic Compounds [Et4N]4[(μ5-WSe4)(CuX)5(μ-X)2] (X = Cl, Br)

Two isostructural crown-like heteroselenometallic cluster compounds, [Et₄N]₄[(μ₅-WSe₄)(CuX)₅(μ-X)₂] (X = Cl 1, Br 2), were prepared from the reactions of [Et₄N]₂[WSe₄] with CuX and [Et₄N]X· xH₂O in the presence of 2-picoline and characterized by single-crystal diffraction analysis. The [(μ₅-WSe₄)(Cu-X)₅(μ-X)₂]⁴⁻ anions in the cluster compounds consists of five CuX fragments coordinated to the five edges of the tetrahedral [WSe₄]²⁻ moiety along with two bridging halides connected to each of the two pairs of the symmetric copper atoms, exhibiting a novel crown-like core structure. The nonlinear optical absorption and refraction of cluster compound 2 were determined to be α₂ = 6.15 × 10⁻¹⁰ m/W and n ₂ = 4.18 × 10⁻¹¹ esu, respectively.     

取代苯体系的二阶非线性光学性质:动力学李代数方法

提出了一种动力学李代数方法来研究取代苯体系的非线性光学性质. 对于给定的PPP模型(Pariser-Parr-Pople)哈密顿量, 生成了一个动力学李代数. 依据这些代数元构造出演化算子作为群参数的函数, 通过求解一组非线性微分方程能够得到这些群参数. 再按照统计力学中的密度算子公式给出取代苯分子体系偶极矩的统计平均值. 于是导出二阶极化率的表达式. 与其他量子力学计算结果比较, 表明这种动力学李代数方法在预言有机共轭分子的非线性光学性质上同样有用.     

金属团簇MoS4Cu4(SCN)2(NC5H5)6的皮秒光学非线性特性和光限幅特性研究

由于激光技术的快速发展，新型超快可调谐波长的高功率激光器更多的在民用和军事上应用。快速的非线性光学器件的需求越来越多。近10年，人们投入大量研究寻找超快光学非线性材料，同时寻找快速响应、高线性透过率和低非线性透过率以及高损伤阈值的光限幅材料，研究发现金属酞菁化合物、金属卟啉化合物以及富勒烯衍生物具有良好的光限幅效果和强的光学非线性特性。     

Mo(W)-Cu(Ag)-S簇合物的非线性光学性能研究

本文介绍了非线性光学性测试中的Ｚ－扫描方法。总结了Ｍｏ（Ｗ）－Ｃｕ（Ａｇ）－Ｓ簇合物的光限制效应、非线性吸收和非线性折射等光学性质。讨论了簇合物结构与光学性能的关系。     

Shock waves for the hyperbolic balance laws with discontinuous sources

In this paper, we are concerned with the behavior of shock waves in a 2 × 2 balance law with discontinuous source terms. We obtain the existence of a local shock wave solution of this problem and deduce that the discontinuous source terms create a weak discontinuity in this solution. Copyright © 2013 John Wiley & Sons, Ltd.     

A numerical analysis of a class of generalized Boussinesq‐type equations using continuous/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time‐dependent varying seabed are included. Thus, high‐order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher‐order models, an extra O(μ²ⁿ⁺²) term (n ∈ ?) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth‐order models. The discretization of the spatial variables is made using continuous P₂ Lagrange elements. A predictor‐corrector scheme with an initialization given by an explicit Runge–Kutta method is also used for the time‐variable integration. Moreover, a CFL‐type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.     

Compressive advection and multi‐component methods for interface‐capturing

This paper develops methods for interface‐capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi‐component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P₁DG‐P₂(linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface‐capturing scheme based on compressive control volume advection methods and high‐order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many‐material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows. Copyright © 2015 John Wiley & Sons, Ltd.     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.