Surface reorientation dynamics of nematic liquid crystals

In this paper we report an experimental investigation on the dynamics of the azimuthal director reorientation at a nematic-solid interface. Three qualitatively different kinds of substrates have been investigated: I) intrinsically anisotropic SiO-substrates (-evaporation), II) isotropic SiO-substrates (-evaporation) and III) rubbed PVA-substrates. In the case II), an in-plane anisotropy was induced cooling slowly the thermotropic nematic liquid crystal (NLC) from the isotropic phase in the presence of a 0.75 T magnetic field. The reorientation dynamic of the surface azimuthal director angle at the switching-on and off of a magnetic (or electric) field has been investigated. All the substrates show comparable azimuthal anchoring energies and two dynamic regimes: a fast dynamic response, driven by the bulk director reorientation and an extremely slow reorientation. The slow dynamics is explained in terms of anisotropic adsorption of NLC molecules on the solid substrate and is well represented by a stretched exponential. Received 7 December 1998     

Quality assurance in analytical measurement

 The peculiarities of analytical measurement require to check characteristics of the error (its components) of the obtained analysis results to assure the quality of the measurements. This article deals with the various quality assurance procedures and algorithms which are used to check the quality indices, i.e. the accuracy, reproducibility, certainty and repeatability of analytical measurements: These procedures include: laboratory rapid control; Intra-laboratory statistical control (statistical selection control by alternative attribute, statistical selection control by quantity method of periodic check of the analysis procedure for conformity to the specified requirements) and external control (inter-laboratory control checks, inter-laboratory comparison tests, and intra-laboratory control algorithms carried out by the appropriate supervisory body.) in the separately taken laboratory. The respective algorithms, control plans and control requirements, specified according to the different control aims and assurance tasks, enable the quality and certianty of analytical information obtained in laboratories in Russia to be assured. Received: 9 November 1998 / Accepted: 24 November 1998     

一类平面齐次多项式系统的局部相图

平面系统在动力系统的研究中起着重要的和基础的作用．在实系数系统情况下,本文利用奇点指数和牛顿多边形方法,讨论了一类平面齐次多项式系统在其孤立点附近的相图,同时给出一些奇点稳定的充要条件．     

Amann三解定理的改进及其应用

本文对非线性泛函分析中著名的Ａｍａｎｎ三解定理作了本质性的改进,并将其结果应用到核函数不恒为正的Ｈａｍｍｅｒｓｔｅｉｎ型积分方程,得到了新的结论．     

扭化的Atiyah-Singer算子(I)

本文证明黎曼流表上的ｄｅ Ｒｈａｍ以及Ｓｉｇｎａｔｕｒｅ算子都同构于扭化的Ａｔｉｙａｈ－Ｓｉｎｇｅｒ算子。这两类算子的局部指数定理和局部Ｌｅｆｓｃｈｅｔｚ不动点公式都可以从扭化的Ａｔｉｙａｈ－Ｓｉｎｇｅｒ算子得到。     

A mod 2 index theorem for the twisted Signature operator

A mod 2 index theorem for the twisted Signature operator on 4 _q + 1 dimensional manifolds is established. This result generalizes a result of Farber and Turaev, which was proved for the case of orthogonal flat bundles, to arbitrary real vector bundles. It also provides an analytic interpretation of the sign of the Poincare-Reidemeister scalar product defined by Farber and Turaev. Project partially supported by the National Natural Science Foundation of China (Grant No. 19525102), the Fok Ying-Tung Foundation and the Qiu Shi Foundation.     

正交异性体某些断裂动力学问题

首先对具有任意自相似指数的正交异性弹性动力学问题推导了解的一般表示,给出了一般解法,然后用这一方法对若干具体问题进行求解,利用本文方法可以迅速将所论问题化为半平面上的Ｒｉｍａｎｎ－Ｈｉｌｂｅｒｔ问题,并可以相当简单地得到问题的闭合解。     

The conjugacy problem for Dehn twist automorphisms of free groups

A Dehn twist automorphism of a group G is an automorphism which can be given (as specified below) in terms of a graph-of-groups decomposition of G with infinite cyclic edge groups. The classic example is that of an automorphism of the fundamental group of a surface which is induced by a Dehn twist homeomorphism of the surface. For , a non-abelian free group of finite rank n, a normal form for Dehn twist is developed, and it is shown that this can be used to solve the conjugacy problem for Dehn twist automorphisms of . Received: February 12, 1996.     

Spectroscopic Ellipsometry Characterisation and Estimation of the Hamaker Constant of Cellulose

Calculations of Hamaker constants using Lifshitz theory require the availability of accurate dielectric data, especially in the visible-ultraviolet region. We present spectroscopic ellipsometry data on well-defined cellulose films of a limited thickness range (100–140 layers) deposited on an oxidised and hydrophobised silicon substrate. The spectral data, representing measurements from a perpendicular orientation to the fibre deposition direction, was used for estimates of the necessary spectral parameters, i.e. the oscillator strengths and characteristic frequencies in the UV-range. Our calculations show that cellulose has a relatively low Hamaker constant in air (58 zJ) and water (8.0 zJ). The implications for the surface energy estimates of cellulose and colloidal interactions between cellulose and various types of fillers and coating colours are indicated.     

Pore Network Analysis of Resistivity Index for Water-Wet Porous Media

Pore network analysis is used to investigate the effects of microscopic parameters of the pore structure such as pore geometry, pore-size distribution, pore space topology and fractal roughness porosity on resistivity index curves of strongly water-wet porous media. The pore structure is represented by a three-dimensional network of lamellar capillary tubes with fractal roughness features along their pore-walls. Oil-water drainage (conventional porous plate method) is simulated with a bond percolation-and-fractal roughness model without trapping of wetting fluid. The resistivity index, saturation exponent and capillary pressure are expressed as approximate functions of the pore network parameters by adopting some simplifying assumptions and using effective medium approximation, universal scaling laws of percolation theory and fractal geometry. Some new phenomenological models of resistivity index curves of porous media are derived. Finally, the eventual changes of resistivity index caused by the permanent entrapment of wetting fluid in the pore network are also studied.Resistivity index and saturation exponent are decreasing functions of the degree of correlation between pore volume and pore size as well as the width of the pore size distribution, whereas they are independent on the mean pore size. At low water saturations, the saturation exponent decreases or increases for pore systems of low or high fractal roughness porosity respectively, and obtains finite values only when the wetting fluid is not trapped in the pore network. The dependence of saturation exponent on water saturation weakens for strong correlation between pore volume and pore size, high network connectivity, medium pore-wall roughness porosity and medium width of the pore size distribution. The resistivity index can be described succesfully by generalized 3-parameter power functions of water saturation where the parameter values are related closely with the geometrical, topological and fractal properties of the pore structure.