Bose-Einstein transition in a dilute interacting gas

We study the effects of repulsive interactions on the critical density for the Bose-Einstein transition in a homogeneous dilute gas of bosons. First, we point out that the simple mean field approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of various contradictory results in the literature. Then, both within the frameworks of Ursell operators and of Green's functions, we derive self-consistent equations that include correlations in the system and predict the change of the critical density. We argue that the dominant contribution to this change can be obtained within classical field theory and show that the lowest order correction introduced by interactions is linear in the scattering length, a, with a positive coefficient. Finally, we calculate this coefficient within various approximations, and compare with various recent numerical estimates. Received 15 July 2001     

A Model for Spacetime: The Role of Interpretation in Some Grothendieck Topoi

We analyse the proposition that the spacetime structure is modified at short distances or at high energies due to weakening of classical logic. The logic assigned to the regions of spacetime is intuitionistic logic of some topoi. Several cases of special topoi are considered. The quantum mechanical effects can be generated by such semi-classical spacetimes. The issues of: background independence and general relativity covariance, field theoretic renormalization of divergent expressions, the existence and definition of path integral measures, are briefly discussed in the proposal. The connection with some problems in foundations of mathematics and differential topology are also discussed.     

弹丸对钢筋混凝土中钢筋交汇处侵彻效应研究

考虑弹丸在钢筋交汇处与钢筋直接发生作用的情况,提出了弹丸侵彻钢筋混凝土的近似模型。利用该模型得到了弹丸侵彻钢筋混凝土过程中弹丸的加速度时间历程。计算结果与实验结果符合较好。用该模型分析了不同配筋结构、配筋尺寸和网眼尺寸对侵彻深度和侵彻过程的影响,结果表明:弹丸从钢筋交汇处侵彻时,当弹丸动能相对较小时,随着网眼尺寸的减小,弹丸的大部分能量均消耗在侵彻第一层配筋结构中,当弹丸动能较大时,不管网眼尺寸多大,第一层配筋均只消耗掉弹丸的部分能量;配筋直径和网眼尺寸对侵彻深度的影响较大。     

PVDF压电计的动态响应特性及其在橡胶材料SHPB实验中的应用

通过夹心式PVDF(Polyvinylide Fluoride)压电计的动态分离式Hopkinson压杆(SHPB)标定实验,系统地讨论了传感器的动态响应特性,其中包括测量电路、PVDF表面应力集中、压电计的材料及结构特性和同一压电计受多次撞击对测试信号的影响,为PVDF压电计的制作工艺研究提供参考。利用标定好的压电计测试了橡胶材料在SHPB实验中的动态应力均匀过程。结果表明:调节并联电阻值可以提高压电计的传感精度;增大压电计的敏感面积可以减小因应力集中所造成的信号失真;材料的热粘塑性性质、摩擦效应等将使信号振荡幅度偏小;多次撞击对信号的加载与卸载段都将产生影响,但当传感器表面未发生明显损伤时,测试的应力平台平均值与真实信号近似相同。     

物理科学发展史的回顾与聚集力学的创建

本文简单地阐述了物理科学的发展电,在19世纪末期,物珲科学已经有相当发展,并形成了三个科学分支--研究物体运动,有牛顿力学;研究物质热运动,有热力学和统计力学;研究电磁波和光波,有电动力学,可是,这三种经典力学在20世纪初面临着新的挑战(困难),从而,相应地产生了三种新的基础理论,即狭义相对论,广义相对论;聚集理论,聚集力学;量子理论,量子力学,具体实践表明,它们在解决新的难题方面都取得很大成功.     

Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators

We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization.     

Spectrum-Generating Symmetries for the Superpotentials Acot θ and Btanh y

The hierarchy of supersymmetric partner Schrödinger equations for the superpotentials Acot?θ and Btanh?y with A and B as half-integer and negative integer numbers are solved. The number of bound states for given trigonometric and hyperbolic potentials are infinite and finite, respectively. In addition to the spectrum-generating corresponding to the standard supersymmetry which is based on shifting potential parameter, there exist three other different methods for generating the spectrum. The first method is based on supersymmetrizing two given models via infinite and finite number of their bound states. This is realized by the ladder operators which shift only quantum numbers. The second and third methods are based on supersymmetrizing any of the models via all bound states corresponding to hierarchy of their partner potentials. They are respectively realized via simultaneous increasing or decreasing of quantum number and the potential parameter, and also, increasing one of them while decreasing the other. Any of the second and third methods leads to introducing two different classes of the algebraic solutions for both models.     

围压与径向荷载共同作用下巴西盘裂纹应力强度因子的解析解

利用权函数法推导了围压和径向荷载共同作用下,考虑裂纹面摩擦的预制裂纹巴西盘应力强度因子计算公式,从理论上分析了围压、径向荷载和裂纹面摩擦对巴西盘应力强度因子的影响。结果表明,围压对I型应力强度因子有很大影响,I型应力强度因子随围压的增大而减小。当裂纹面闭合后围压和摩擦系数对II型应力强度因子同样具有显著影响,考虑裂纹面有效剪应力的权函数法理论解与有限元数值解相吻合,表明理论分析的正确性。     

遥感技术用于固体力学实验研究的新成果

在岩石、混凝土和钢材加载直到破坏的过程中用红外和微波遥感技术进行了观测研究．发现这些材料在加载过程中其红外和微波辐射温度、红外辐射波谱及红外热像均随应力的变化而变化．材料破坏前这些变化表现出某些前兆性特征．研究表明遥感技术可作为固体力学研究的一种新手段，并可望在工程上得到应用     

离散差分变分Hamilton系统的Lie对称性与Noether守恒量

研究离散差分Hamilton系统的Lie对称性与Noether守恒量. 根据扩展的时间离散力学变分原理构建Hamilton系统的差分动力学方程.定义离散系统运动差分方程在无限小变换群下的不变性为Lie对称性, 导出由Lie对称性得到系统离散Noether守恒量的判据. 举例说明结果的应用. 关键词： 离散力学 差分Hamilton系统 Lie对称性 Noether守恒量