Synthesis, structure and conformation of 1,3-difluorotetraphenyl benzene

The compound trifluoroiodomethane can be activated to react with the electron donor,1,4-dilithiotetraphenyl butadiene,by means of electron transfer catalysis (ETC).The structure of the product,1,3-difluorotetraphenyl,benzene (1),was determined by MS,NMR,and X-ray single crystal diffraction.The conformations of compound 1 and its derivatives were analysized by molecular mechanics.     

The statistical mechanical resolution of a thermodynamic “paradox”

We discuss a thermodynamic paradox suggested by Fallows and Greenleaf. Using quantum statistical mechanics, we analyze the problem in detail, showing why no paradox arises.This work was carried out some time ago, circulated as a MIT internal report, and has since enjoyed a modest popularity. We are pleased to publish it more broadly in this volume dedicated to the memory of such an outstanding researcher as Prof. P. Résibois. (MOS)     

核压力容器防止辐照脆化的安全评定

本文结合我国核动力反应堆的实例,首先介绍了设计规范中采用的断裂分析图的评定方法,然后着重讨论一种新的断裂力学的评定方法。结合对容器材料断裂韧性的实验测定,给出了计算结果,绘制了全寿期的安全运行工况图,并对两种方法的结果作了比较讨论。     

消干效应和量子力学新解释的意义

简单介绍了消干 (decoherence)效应以及量子力学的一种新解释———由Griffiths,Gell Mann和Omn埁ｓ等独立提出的“消干历史解释”的由来和要点 ,评述了这一进展在量子理论发展中的意义 .     

Adiabatic waves along interfacial layers near the critical pointOndes adiabatiques le long des interfaces près du point critique

Near the critical point, isothermal interfacial zones are investigated starting from a non-local density of energy. From the equations of motion of thermocapillary fluids, we point out a new kind of adiabatic waves propagating along the interfacial layers. The waves are associated with the second derivatives of densities and propagate with a celerity depending on the proximity of the critical point. To cite this article: H. Gouin, C. R. Mecanique 332 (2004).     

On Some Nonclassical Problems of Fracture Mechanics Taking into Account the Stresses Along Cracks

The paper reports on the results from analysis of some nonclassical fracture problems that allow for stresses along cracks. The results have been obtained by the author and his collaborators at the Institute of Mechanics (Kiev) since 1980     

Application of Discrete Element Method for Continuum Dynamic Problems

A new method based on the principle of minimum potential energy is presented, aiming to overcome some weakness of the present discrete element method (DEM). Our primary research is to put forward the DEM with a tight theory base and a fit technique for treating continuum dynamic problems. By using this method, we can not only extend the existing seven-disc model, but also establish a new nine-disc model in a general way. Moreover, the equivalences of two kinds of models have been verified. In addition, three numerical examples of stress wave propagation problems are given in order to validate accuracy and efficiency of the present DEM models and their algorithms. Finally, the dynamic stress concentration problem of a square plate with a circular hole is analyzed.This work was supported by Nation Natural Science Foundation of China (nos. 10232040 and 10572002).     

The motion of rigid rod-like particles suspended in non-homogeneous flow fields

Equations are written for the velocities of rotation and translation of rigid rod-like particles suspended in arbitrary Stokes flows. These make use of the first approximation from slender body theory for the evaluation of drag forces parallel and transverse to the particle axis, and neglect couples induced by shear stress at the particle surface. They are therefore asymptotically valid as the particle axis ratio becomes large. Simple forms of the equations, applying in constant viscosity flows, are solved, where possible analytically and otherwise numerically, and results obtained for particle motion in planar Poiseuille and sink flows. These are discussed and displayed in terms of appropriate dimensionless groups in a comprehensive set of plots, that can conveniently be used to provide information on translational and rotational velocities, and orientation and displacement as a function of time, including particle slip along and across streamlines, for a wide range of cases. In this way the effects of non-homogeneity in the flow fields are quantified.     

Complex differential games of pursuit-evasion type with state constraints,part 1: Necessary conditions for optimal open-loop strategies

Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.This paper is dedicated to the memory of Professor John V. Breakwell.The authors would like to express their sincere and grateful appreciation to Professors R. Bulirsch and K. H. Well for their encouraging interest in this work.     

New Semiclassical and Numerical Approaches to Locate Zeros of Wave Functions Asiri Nanayakkara

A new semiclassical method is presented for evaluating zeros of wave functions. In this method, locating zeros of the wave functions of Schrodinger equation is converted to finding roots of a polynomial. The coefficients of this polynomial are evaluated using WKB and semi quantum action variable methods. For certain potentials WKB expressions for moments are obtained exactly. Almost explicit formulae for moments are obtained for the potential V (x) = xN. Examples are given to illustrate both methods. Using semi quantum action variable method, complex zeros of the wave functions of the PT symmetric complex system V(x) = x4 iAx are obtained. These zeros exhibit complex version of interlacing.