2-(1H-pyrazol-3-yl)pyrazine: a polytopic N-donor ligand used to construct Cu-[2+2] molecular grid: synthesis,structure, and magnetic properties

Herein, we present a new polytopic N-donor, which is used to construct a metal–organic compound. The resulting metal–organic compound, Cu₄(L)₆(NO₃)₂ (HL=(1H-pyrazol-3-yl)pyrazine) (1), is synthesized by the hydrothermal reaction of Cu(NO₃)₂ and HL (ratio: 1?:?1). Single-crystal X-ray diffraction shows that 1 comprises a Cu-[2+2] molecular grid. Magnetic studies reveal antiferromagnetic interactions, interpreted by a simplified dinuclear mode.     

“On–off” switching of dynamically controllable self‐assembly formation of double‐responsive block copolymers with tunable LCSTs

We report here a reversible self‐assembly formation system using block copolymers with thermo‐tunable properties. A series of double‐responsive block copolymers, poly(N‐isopropylacrylamide (NIPAAm))‐block‐poly(NIPAAm‐co‐N‐(isobutoxymethyl)acrylamide (BMAAm)) with two lower critical solution temperatures were synthesized by one‐pot atom transfer radical polymerization via sequential monomer addition. When dissolved in aqueous solution at room temperature, the block copolymers remained unimeric. Upon heating above room temperature, the block copolymers self‐assembled into micellar structures. The micelle formation temperature and the resulting diameter were controlled by varying the BMAAm content. ¹H Nuclear Magnetic Resonance, dynamic light scattering, field‐emission scanning electron microscopy, and fluorescence spectra revealed the presence of a monodisperse nanoassembly, and demonstrated the assembly formation/inversion process was fully reversible. Moreover, a model hydrophobic molecule, pyrene, was successfully loaded into the micelle core by including pyrene in the original polymer solution. Further heating resulted in mesoscopic micelle aggregation and precipitation. This dual micelle and aggregation system will find utility in drug delivery applications as a thermal trigger permits both aqueous loading of hydrophobic drugs and their subsequent release. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.     

基于Navier-Stokes／Kirchhoff方程的悬停旋翼跨声速气动声学计算

研究了Kirchhoff积分面是否有盖有底,以及是否计及旋翼网格上的流场值,这两个因素对噪声预测结果的影响.发展了一种基于重叠网格的计算悬停旋翼远场噪声的数值方法.数值计算过程分为流场模拟和声场模拟两部分.悬停旋翼流场的数值模拟是在两个相互重叠的网格上进行的:在高质量的旋翼网格上求解Navier-Stokes方程,用于模拟旋翼附近的粘性流动和近场尾涡的捕捉;在远离粘性区域处布置符合悬停流场物理特征的圆柱形背景网格,控制方程为Euler方程,用于远场尾涡的捕捉.计算得到的流场信息插值到用于声场计算的Kirchhoff积分面上.观测点处的噪声可以认为是由这个完全包含桨叶的Kirchhoff积分面上的面元(声源)发声得到.远场声波的传播由Kirchhoff积分公式描述.计算结果表明:采用有盖有底的Kirchhoff积分面并且同时计及旋翼网格流场值时,计算得到的HSI噪声与实验值吻合最好.     

Nonsteady flow of groundwater in aquifer system with viscoelastic properties

The transient flow behavior of groundwater in aquifer-aquitard system with viscoelastic properties is studied. On the basis of previous works (Hantush, Neuman, Brutsaert, Corapcioglu), the new partial differential-integral equations are derived. The well-known equations (Hantush, Brutsaert) are the special cases of the new equations. The new equations describe the flow of a slightly compressible groundwater in layers with viscoelastic properties.Analytical solutions of the partial differential-integral equations are obtained by using the method of Laplace transform. The viscoelastic properties enhance the heterogeneities of elastic aquifer system which have delay and feed qualities. The agreements between the numericl inversion results of Laplace transform and the analytical solutions are good. The formulae predict the transient flow behavior of groundwater in this heterogeneous layers.     

电磁热弹性介质的一些基本理论─电磁热动力理论

具有电磁热弹性耦合性质的介质是许多传感器及机敏结构或系统中的关键材料，本文则是力争对这种耦合材料的基本理论进行系统的研究。第一部分基于被推广的经典热动力学理论推导和归纳了电磁热弹性体的几个守恒方程、动力学方程、本构方程和热平衡方程。第二部分则是系统地讨论了在数值计算中具有极重要意义的电磁热弹性变分原理。     

可变形儒可夫斯基翼型亚音速非定常气动力的研究

对于翼面变形速度远小于来流速度情况下的儒可夫斯翼型亚音速绕流问题,通过仿射变换将可压缩流动转换成不可压缩流动,将解析解和离散涡方法相结合计算变形机翼的不可压缩流动速度场,再利用逆变换得到变形机翼的亚音速流动速度场,进而分析非定常气动力特性,建立变形机翼的准定常升力系数和非定常附加升力系数在可压缩和不可压缩两种状态下的简单近似对应关系。计算结果显示变形机翼的非定常气动升力近似等于准定常计算结果叠加上虚拟质量力导致的非定常附加升力,该非定常附加升力随翼型变形速率呈线性关系,由机翼当前时刻飞行姿态、翼型及其变形速率确定,与具体变形历史过程无关。低来流马赫数时虚拟质量力导致的非定常效应显著,高亚音速流动时准定常升力起主导作用。同时还分析了不同马赫数下机翼往复变形过程中升力的变化特性,指出尽管高亚音速变形机翼的气动升力近似等于准定常气动升力,但不能忽视非定常附加升力的影响,非定常附加升力将导致完成往复变形需要外界输入正比于Ma∞/[(1-Ma2∞)]的功。     

Convergence analysis of some high–order time accurate schemes for a finite volume method for second order hyperbolic equations on general nonconforming multidimensional spatial meshes

The present work is an extension of our previous work (Bradji, Numer Methods Partial Differ Equations, to appear) which dealt with error analysis of a finite volume scheme of a first convergence order (both in time and space) for second‐order hyperbolic equations on general nonconforming multidimensional spatial meshes introduced recently in (Eymard et al. IMAJ Numer Anal 30(2010), 1009–1043). We aim in this article to get some higher‐order time accurate schemes for a finite volume method for second‐order hyperbolic equations using the same class of spatial generic meshes stated above. We derive a family of finite volume schemes approximating the wave equation, as a model for second‐order hyperbolic equations, in which the discretization in time is performed using a one‐parameter scheme of the Newmark's method. We prove that the error estimate of these finite volume schemes is of order two (or four) in time and it is of optimal order in space. These error estimates are analyzed in several norms which allow us to derive approximations for the exact solution and its first derivatives whose the convergence order is two (or four) in time and it is optimal in space. We prove in particular, when the discrete flux is calculated using a stabilized discrete gradient, that the convergence order is \begin{align*}k^2+h_\mathcal{D}\end{align*} or \begin{align*}k^4+h_\mathcal{D}\end{align*}, where \begin{align*}h_\mathcal{D}\end{align*} (resp. k) is the mesh size of the spatial (resp. time) discretization. These estimates are valid under the regularity assumption \begin{align*}u\in C^4(\lbrack 0,T\rbrack;C^2(\overline{\Omega}))\end{align*}, when the schemes are second‐order accurate in time, and \begin{align*}u\in C^6(\lbrack 0,T\rbrack;C^2(\overline{\Omega}))\end{align*}, when the schemes are four‐order accurate in time for the exact solution u. The proof of these error estimates is based essentially on a comparison between the finite volume approximate solution and an auxiliary finite volume approximation. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

A two‐grid characteristic finite volume element method for semilinear advection‐dominated diffusion equations

A two‐grid finite volume element method, combined with the modified method of characteristics, is presented and analyzed for semilinear time‐dependent advection‐dominated diffusion equations in two space dimensions. The solution of a nonlinear system on the fine‐grid space (with grid size h) is reduced to the solution of two small (one linear and one nonlinear) systems on the coarse‐grid space (with grid size H) and a linear system on the fine‐grid space. An optimal error estimate in H¹ ‐norm is obtained for the two‐grid method. It shows that the two‐grid method achieves asymptotically optimal approximation, as long as the mesh sizes satisfy h = O(H²). Numerical example is presented to validate the usefulness and efficiency of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013