The third law of thermodynamics and the degeneracy of the ground state for lattice systems

The third law of thermodynamics, in the sense that the entropy per unit volume goes to zero as the temperature goes to zero, is investigated within the framework of statistical mechanics for quantum and classical lattice models. We present two main results: (i) For all models the question of whether the third law is satisfied can be decided completely in terms of ground-state degeneracies alone, provided these are computed for all possible boundary conditions. In principle, there is no need to investigate possible entropy contributions from low-lying excited states, (ii) The third law is shown to hold for ferromagnetic models by an analysis of the ground states.Dedicated to Pierre Résibois. Work supported in part by NSF grant PHY-7825390 A01.     

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT’s) is established to describe the nonlinear stress-strain curve of SWCNT’s and to predict both the elastic properties and breaking strain of SWCNT’s during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT’s. The project supported by the National Natural Science Foundation of China (10121202, 90305015 and 10328203), the Key Grant Project of Chinese Ministry of Education (0306) and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7195/04E).     

Recent advances in theoretical models of respiratory mechanics

As an important branch of biomedical engineering, respiratory mechanics helps to understand the physiology of the respiratory system and provides fundamental data for developing such clinical technologies as ventilators. To solve different clinical problems, researchers have developed numerous models at various scales that describe biological and mechanical properties of the respiratory system. During the past decade, benefiting from the continuous accumulation of clinical data and the dramatic progress of biomedical technologies (e.g. biomedical imaging), the theoretical modeling of respiratory mechanics has made remarkable progress regarding the macroscopic properties of the respiratory process, complexities of the respiratory system, gas exchange within the lungs, and the coupling interaction between lung and heart. The present paper reviews the advances in the above fields and proposes potential future projects.     

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。     

基于扫描隧道显微镜的原子电子云结构

本文简要介绍了扫描隧道显微镜的基本工作原理，展示了一些扫描样品（石墨和铜）的电子云图，在简要介绍量子力学关于原子电子云结构基本理论的基础上，通过理论上的电子云结构与扫描结果的比较，在一定程度上验证了量子力学关于原子电子云结构理论的正确性．     

Entanglement and Classical Correlations in the Quantum Frame

The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones. This leads to a frame in which two kinds of correlations emerge: the classical correlation that is coded in the mixed state of the physical system and a new correlation, to be called probabilistic entanglement, which may occur also at pure states. We examine to what extent this characterization of correlations can be applied to quantum mechanics. Explicit calculations on simple examples outline that a same quantum state can show only classical correlations or only entanglement depending on its statistical content; situations may also arise in which the two kinds of correlations compensate each other.     

Altering the Remote Past

An abstract treatment of Bell inequalities in proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that a property of a system can be changed by the timing of a distant measurement, which could take place in the future.     

The Reality in Bohmian Quantum Mechanics or Can You Kill with an Empty Wave Bullet?

Several situations, in which an empty wave causes an observable effect, are reviewed. They include an experiment showing surrealistic trajectories proposed by Englert et al. and protective measurement of the density of the quantum state. Conditions for observable effects due to empty waves are derived. The possibility (in spite of the existence of these examples) of minimalistic interpretation of Bohmian quantum mechanics in which only Bohmian positions supervene on our experience is discussed.     

Design of interdigital transducers for crack detection in plates

Interdigital transducers (IDT) for non-destructive evaluation (NDE) of cracks in plates are designed based on an analytical model established previously. Key considerations include mode selectivity, excitation strength, collimation of wave and cost. The advantage of mode selectivity of IDT over PZT patch is presented both analytically and experimentally. Effects of parameters, namely finger spacing, width, length, number of fingers, and the size of IDT, on the excitation strength and mode selectivity are considered. This led to the design of a mobile double-sided IDT as an efficient device where excitation strength is strong and focused. The device was fabricated in-house using commercially available piezoelectric ceramics and used to develop a procedure for accurate identification of the direction and extent of cracks in plates. Three aluminum plates, one with a linear deep crack, another with a piecewise linear shallower crack and the third with a curved crack, were used to illustrate the accuracy and efficiency of both the proposed device and procedure for effective NDE.     

On the general expression of Fredholm Integral Equations Method in elasticity

In this paper, the concept of covering domain is introduced to develop a general expression for the Fredholm Integral Equations Method, by which elasticity problems of arbitrarily shaped bodies loaded by external forces can be solved. Some special expressions are given for a body with non-zero remote stresses, or subjected to some concentrated forces on its boundary. The relationship between the loading forces and solutions are also discussed. Some analytical solutions can be obtained for simple cases. When numerical computations are needed for the solution, the method proves to have high precision and fast convergency.