Out-of-plane deformation of the azulene ring in crystal structures of simply substituted azulene derivatives

The crystal structures of 1,3-bis(4-bromophenyl)- and 1,3-di(2-thienyl)azulenes (5 and 6) were elucidated by X-ray analysis. Two aryl groups connect to the azulenyl core with dihedral angles of 34.9-41.6° and the two aryl planes of the groups slant against the azulene ring toward different ways in their crystal structures. It was also found that the azulene rings of 5 and 6 showed a slight out-of-plane deformation in the way that the hydrogen atoms at the 4- and 8-positions are apart from the neighboring aryl ortho-hydrogen atoms to fill in the vacant space made by the slanting aryl planes.     

Cyclic quaternary ammonium ionic liquids with perfluoroalkyltrifluoroborates: synthesis, characterization, and properties

New cyclic quaternary ammonium salts, composed of N-alkyl(alkyl ether)-N-methylpyrrolidinium, -oxazolidinium, -piperidinium, or -morpholinium cations (alkyl = nC4H9, alkyl ether = CH3OCH2, CH3OCH2CH2) and a perfluoroalkyltrifluoroborate anion ([R(F)BF3]-, R(F) = CF3, C2F5, nC3F7, nC4F9), were synthesized and characterized. Most of these salts are liquids at room temperature. The key properties of these salts--phase transitions, thermal stability, density, viscosity, conductivity, and electrochemical windows--were measured and compared to those of their corresponding [BF4]- and [(CF3SO2)2N]- salts. The structural effect on all the above properties was intensively studied in terms of the identity of the cation and anion, variation of the side chain in the cation (i.e., alkyl versus alkyl ether), and change in the length of the perfluoroalkyl group (R(F)) in the [R(F)BF3]- ion. The reduction of Li+ ions and reoxidation of Li metal took place in pure N-butyl-N-methylpyrrolidinium pentafluoroethyltrifluoroborate as the supporting electrolyte. Such comprehensive studies enhance the knowledge necessary to design and optimize ionic liquids for many applications, including electrolytes. Some of these new salts show desirable properties, including low melting points, high thermal stabilities, low viscosities, high conductivities, and wide electrochemical windows, and may thus be potential candidates for use as electrolytes in high-energy storage devices. In addition, many salts are ionic plastic crystals.     

Highly sensitive optical humidity probe

A highly sensitive optical humidity probe based on reflectance measurements has been developed using Nafion^®-crystal violet (CV) films. This sensor can be used to calibrate relative humidity (RH) in the range 0-0.25% with a detection limit (blank signal + 3σ_b, where σ_b = the standard deviation (S.D.) of the blank signal) of 0.018% RH (∼4.37 ppm) and exhibited low hysteresis. The sensor films were fully reversible in dry nitrogen and reversal times were shown to be dependent on exposure time and % RH. The response to 1% RH was highly reproducible (S.D. = 1.67%, number of samples (n) = 5). Hydrogen chloride gas did not interfere with the response of the sensor to RH but did reduce sensor reversal times. This sensor displayed sufficient sensitivity that it could be used to detect ppm levels of moisture in process gases such as nitrogen and HCl.     

Diffuse interface model of surfactant adsorption onto flat and droplet interfaces

For applications where droplet breakup and surfactant adsorption are strongly coupled, a diffuse interface model is developed. The model is based on a free energy functional, partly adapted from the sharp interface model of [Diamant and Andelman 34(8):575–580, (1996)]. The model is implemented as a 2D Lattice Boltzmann scheme, similar to existing microemulsion models, which are coupled to hydrodynamics. Contrary to these microemulsion models, we can describe realistic adsorption isotherms, such as the Langmuir isotherm. From the free energy, functional analytical expressions of equilibrium properties are derived, which compare reasonably with numerical results. Interfacial tension lowering scales with the logarithm of the area fraction of the interface unloaded with a surfactant: . Furthermore, we show that adsorption kinetics are close to the classical relations of Ward and Tordai. Prelimary simulations of droplets in shear flow show promising results, with surfactants migrating to interfacial regions with highest curvature. We conclude that our diffuse interface model is very promising for apprehending the above-mentioned applications as membrane emulsification. Paper presented at the Annual European Rheology Conference (AERC) 2005, April 21–23, Grenoble, France.     

SU(d)-Biinvariant Random Walks on SL\,{\left( {d,\,\mathbb{C}} \right)} and their Euclidean Counterparts

We establish a deformation isomorphism between the algebras of -biinvariant compactly supported measures on and -conjugation invariant measures on the Euclidean space of all Hermitian -matrices with trace . This isomorphism concisely explains a close connection between the spectral problem for sums of Hermititan matrices on one hand and the singular spectral problem for products of matrices from on the other, which has recently been observed by Klyachko [13]. From this deformation we further obtain an explicit, probability preserving and isometric isomorphism between the Banach algebra of bounded -biinvariant measures on and a certain (non-invariant) subalgebra of the bounded signed measures on . We demonstrate how this probability preserving isomorphism leads to limit theorems for the singular spectrum of -biinvariant random walks on in a simple way. Our construction relies on deformations of hypergroup convolutions and will be carried out in the general setting of complex semisimple Lie groups.Margit Rösler was partially supported by the Netherlands Organisation for Scientific Research (NWO), project nr. B 61-544.     

Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0, p). As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic (0, p) of integral canonical models of projective Shimura varieties of Hodge type with respect to h-hyperspecial subgroups as pro-étale covers of Néron models; this forms progress towards the proof of conjectures of Milne and Reimann. Though the second application was known before in some cases, its proof is new and more of a principle.     

基于分子动力学模拟的金属构件的弹-塑性分解方法

针对金属多晶材料构件的分子动力学（MD）模拟,本文提出了一种新的弹-塑性分解方法.文章将MD运动轨迹分解为结构变形和热振动,给出了计算结构变形的方法和近似公式;针对金属多晶材料构件的当前构型,给出了基于FCC|BCC晶胞和四原子占位的四面体单元相组合的连续变形函数及计算变形梯度的算法;利用原子-连续关联模型,发展了计算当前构型应力场和弹性张量的算法.分析了当构件承受过大载荷后在材料内部所产生的微观缺陷,并将其分类标定为位错、层错、挛晶界、晶界和空位等;对于层错和挛晶界讨论了在弹性卸载过程中应满足的刚体运动约束方程;利用极小势能原理构造了基于当前构型的弹性卸载算法,进而给出了完整的基于MD模拟的计算弹-塑性应变的算法.最后,针对单晶铜纳米线拉伸的MD模拟,计算了弹-塑性应变场,验证了本文方法的合理性.
本文提出的基于MD模拟的弹-塑性分解方法,为从微观到宏观的多尺度和多模型耦合计算提供了算法支撑.     

构造上正交各向异性半球形凸起凹凸板等效刚度研究

根据半球形凹凸板周期性将其划分得到代表性体元结构.首先研究代表性体元的刚度特性,利用变形等效原理、均质化和刚度组合法得到半球形凹凸板的等效刚度.然后将得到的三个主向刚度代入四边简支板Navier解中求解板中心挠度.通过有限元数值模拟解和Navier解进行对比分析,从而验证该文得到的主向刚度的准确性.然后讨论了代表性体元的材料尺寸对所得等效刚度的影响.随着代表性体元边长与凸起半径的比值逐渐增大,所得结果精度越来越高,且等效刚度公式适用于不同厚度的半球形凹凸板.最后给出了较为简洁的工程应用公式,并给出了凸起半径的近似取值范围和工程应用算例.     

基于曲梁弹性理论的弯曲覆岩变形及应力分析

引入适用于极坐标下曲梁的位移函数,通过理论分析得出用位移函数表示的曲梁控制方程和位移分量、应力分量.在此基础上,采用差分原理给出曲梁控制方程、位移分量和应力分量的差分代数方程.最后,采用数值计算方法,分析了煤层开采后弯曲覆岩的位移和应力分布特征,结果表明:1)煤层开采后弯曲覆岩产生下沉变形;弯曲岩层环向位移既有拉伸也有压缩.2)离开切眼不远处径向应力将达到峰值,径向应力由内边界向外逐渐增大;工作面后方不远处环向应力将达到峰值,环向应力较容易引起压缩破断;离开切眼不远处剪应力将达到峰值,对于小角度截面上的剪应力由内边界向外逐渐增大.研究结果为煤矿工程提供了科学依据与参考.     

Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion

This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic – perfectly plastic materials obeying a Drucker–Prager or Mohr–Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress.