Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

Kinetic model for water/oil absorption of mesquite gum (Prosopis juliflora) and gum arabic (Acacia senegal)

The water and oil uptake of mesquite and arabic gums in powdered form was studied at temperatures of 23, 35 and 45°C. A previously proposed equation to predict osmotic equilibrium was tested using the experimental data with both gums and a good statistical fit was obtained. Mesquite gum showed the highest water and oil absorption at all temperatures studied. Temperature dependence of the reciprocal of the S₁ and WL_∞ were determined using an Arrhenius equation. The activation energy for water and oil absorption for gum arabic was 21.98 and 39.57 kJ mol⁻¹, compared to that of mesquite gum having values of 15.79 and 46.16 kJ mol⁻¹, respectively. A second order kinetic model was obtained for water and oil absorption for both gums.     

Important features of Iris OSQL

OSQL is the object-oriented database language developed for the Iris object-oriented database management system at Hewlett-Packard Laboratories. Its three fundamental constructs are objects, types, and functions. This paper provides an overview of the underlying concepts and some important features of OSQL.     

Application of boundary element method to 3-D problems of coupled thermoelasticity

This paper deals with a new boundary element method for analysis of the quasistatic problems in coupled thermoelasticity. Through some mathematical manipulation of the Navier equation in elasticity, the heat conduction equation is transformed into a simpler form, similar to the uncoupled-type equation with the modified thermal conductivity which shows the coupling effects. This procedure enables us to treat the coupled thermoelastic problems as an uncoupled one, A few examples are computed by the proposed BEM, and the results obtained are compared with the analytical ones available in the literature, whereby the accuracy and versatility of the proposed method are demonstrated.     

Density functional theory studies of Cu-zeolite de-NOx catalysts

Summary Recent progress in the modelling of exchanged Cu sites and their interactions with small molecules, based on DFT cluster calculations, is briefly reviewed.     

A new approach to the decomposition of Boolean functions by the method of <Emphasis Type="Italic">q</Emphasis>-partitions. III. Joint decomposition of a function system

The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean functions of variables specified in different representation forms. The approach is based on the method of q-partitions of conjuncterms and concept of decomposition clones. Theorems on joint decomposition of a system of full and partial functions are formulated. The approach is illustrated by examples. Parts I and II of this article are published in No. 5 (2001) and No. 1 (2002). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 39–58, March–April 2007.     

Studies on fluorinated polyurethanes by X-ray diffraction and density functional theory calculations with periodic boundary conditions

Thin-film wide-angle X-ray diffraction, small-angle X-ray scattering, and density functional theory calculations using B3LYP hybrid functional with the two-dimensional periodic boundary conditions (2D-PBC) have been applied to study the crystal structures of parent and fluorinated polyurethanes. The crystal structures from 2D-PBC-B3LYP calculation and experiments showed the hard-segment chains within crystallites adopted an extended-chain conformation for polyurethanes. Energetically, the parent polyurethane preferred an alternating hydrogen-bonded sheet structure while the fluorinated one adopted a progressive hydrogen-bonded sheet structure.     

小波变换在求解重力测定反问题中的应用

针对重力测定反问题,提出将其离散为线性不适定问题,利用小波变换方法进行数值求解.该方法将小波变换和正则化方法相结合,选取小波函数作为一组基底,将原不适定问题转化为粗子空间上的适定问题,并给出选取粗子空间基的方法.通过数值模拟已有方法和小波变换方法求解结果的比较,表明了小波变换方法的可行性和有效性.     

含氮、磷有机配体对(CdSe)_2量子点结构和电子性质的影响

使用密度泛函理论方法研究了量子点(CdSe)2与配体L(L=PH3、PH2Me、PHMe2、PMe3、NH3、NH2Me、NHMe2、NMe3)之间的相互作用及其产物的结构和性质。配体中的P或N原子与Cd原子上分别形成较强的Cd—P和Cd—N配位键,从而影响(CdSe)2的结构和电子性质。配体作用下,(CdSe)2的几何结构、电荷分布、轨道能级、吸收光谱等均发生变化,但2类配体的影响,尤其是甲基数目的影响,存在较大差异。     

Stability and control of nonlinear systems described by retarded functional equations: a review of recent results

This paper reports on recent results in a series of the work of the authors on the stability and nonlinear control for general dynamical systems described by retarded functional differential and difference equations. Both internal and external stability properties are studied. The corresponding Lyapunov and Razuminkhin characterizations for input-to-state and input-to-output stabilities are proposed. Necessary and sufficient Lyapunov-like conditions are derived for robust nonlinear stabilization. In particular, an explicit controller design procedure is developed for a new class of nonlinear time-delay systems. Lastly, sufficient assumptions, including a small-gain condition, are presented for guaranteeing the input-to-output stability of coupled systems comprised of retarded functional differential and difference equations.