On Publications on the Brittle Fracture Mechanics of Prestressed Materials

The paper analyzes new publications on the brittle fracture mechanics of prestressed materials. It is found out that new scientific results published in the International Journal of Solids and Structures in 2002 are a particular case of the results obtained at the Institute of Mechanics 20 years ago     

非保守力和非完整约束对Hamilton系统Lie对称性的影响

研究非保守力和非完整约束对Hamilton系统的Lie对称性和守恒量的影响.分别研究了Hamilt on系统受到非保守力和非完整约束作用时，系统的Lie对称性保持不变的条件，同时给出了 系统的结构方程和守恒量保持不变的条件.以著名的Emden方程和Appell-Hamel模型为例进行 了分析讨论. 关键词： 分析力学 Hamilton系统 非保守力 非完整约束 对称性 守恒量     

A Reality Proof in PT-Symmetric Quantum Mechanics

We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral equivalences inspired by the correspondence are also discussed.     

Classical Limit of Expectation Values in a Wave Packet Involving Few Stationary States

Expectation values of physical quantities in a wave packet involving few stationary states in an infinite square well are calculated. Explicit results show that the expectation values in the classical limit go over to the corresponding classical quantity in the form of the arithmetic mean (in mathematical term, the Fejér's average) of the partial Fourier series converging to the classical quantity. The number of the stationary states is that of the partial Fourer series in the Fejér's average. The quantum uncertainty is then demonstrated to have a classical counterpart.     

转动系统的相对论性分析力学理论

本文讨论了转动相对论力学理论，主要是建立转动系统的相对论性分析力学理论·构造转动系统的相对论性广义动能函数Ｔｒ＝∑ｎｉ＝１Ｉ０ｉΓｉ２（１－１－θ·２ｉ／Γｉ２）和广义加速度能量函数Ｓｒ＝１２∑ｎｉ＝１Ｉｉ（θ·ｉ·θ¨ｉ）２Γｉ２－θ·２ｉ＋θ¨２ｉ，给出其Ｈａｍｉｌｔｏｎ原理和三种不同形式的Ｄ′Ａｌｅｍｂｅｒｔ原理；对于完整约束系统，建立了转动系统的相对论性Ｌａｇｒａｎｇｅ方程、Ｎｉｅｌｓｅｎ方程、Ａｐｐｅｌ方程和Ｈａｍｉｌｔｏｎ正则方程；对于非完整约束系统，建立了转动系统的相对论性Ｒｏｕｔｈ方程、Чаплыгин方程、Ｎｉｅｌｓｅｎ方程和Ａｐｐｅｌ方程；并给出转动系统的相对论性Ｎｏｅｔｈｅｒ守恒律     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.     

Relativistic Dynamics in Basic Chemistry

This paper revisits the historical sequence in which some of the major developments of 20th-century physics occurred, and explores how theories could have turned out differently, if the sequence of developments had been different. It shows how a delay in founding special relativity theory until after (1) at least one puzzling problem in electromagnetic theory could be acknowledged, and (2) sat least some of the experimental observations pertinent to the development of quantum mechanics had become well known, could have resulted in a larger theory that covers both domains in a manner quite different from that of any of the theories we use today. The revised theory dispenses with a separate postulate introducing Planck’s constant h, identifying instead a physical mechanism that implies the constant. Some important aspects of quantum chemistry then follow. Editor, Galilean Electrodynamics, Proceedings of the Natural Philosophy Alliance; Visiting Industry Professor, Tufts University, retired     

The role of binder mobility in spontaneous adhesive contact and implications for cell adhesion

The standard view of mechanical adhesive contact is as a competition between a reduction in free energy when surfaces with bonding potential come into contact and an increase in free energy due to elastic deformation that is required to make these surfaces conform. An equilibrium state is defined by an incremental balance between these effects, akin to the Griffith crack growth criterion. In the case of adhesion of biological cells, the molecules that tend to form surface-to-surface bonds are confined to the cell wall but they are mobile within the wall, adding a new phenomenon of direct relevance to adhesive contact. In this article, the process of adhesive contact of an initially curved elastic plate to a flat surface is studied for the case in which the binders that account for adhesion are able to migrate within the plate. This is done by including entropic free energy of the binder distribution in the total free energy of the system. By adopting a constitutive assumption that binders migrate at a speed proportional to the local gradient in chemical potential, the transient growth of an adhesion zone due to binder transport is analyzed. For the case of a plate of very large extent, the problem can be solved in closed form, whereas numerical methods are invoked for the case of a plate of limited extent. Results are presented on the rate of growth of an adhesion zone in terms of system parameters, on the evolution of the distribution of binders and, in the case of a plate of limited extent, on the long-term limiting size of the adhesion zone.     

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997     

复合结构丝中的电流密度分布和巨磁阻抗效应

提出了由中间为高电导率的非铁磁性金属丝外面包裹一层铁磁材料组成的复合结构丝的电流 密度分布和巨磁阻抗(GMI)效应模型，并对Cu/FeCoNi复合丝进行了数值模拟. 结果表明：在 相同的磁性材料几何尺寸和磁特性时，Cu/FeCoNi复合丝铁磁层内的电流随频率的升高比匀 质FeCoNi铁磁丝内的电流更趋于表面分布，而且开始出现趋肤效应时对应的频率明显降低. 当在比较低的频率下就可以观察到明显的MI变化时，复合结构丝中的电阻和电抗变化主要是 由趋肤效应引起，趋肤效应仍然是引起复合结构材料(包括多层薄膜结构) 关键词： 电流密度 巨磁阻抗效应 趋肤效应