Scattering Problem for a Classical Particle with Spin in a Coulomb Field

We investigate the scattering problem for a relativistic electron with spin in a Coulomb field in the framework of pseudoclassical mechanics. We obtain an analytic expression for the scattering angle and limiting estimates for the scattering parameters for the spinless and nonrelativistic cases. For small angles, the pseudoclassical model under consideration leads to the well-known quantum-mechanical Mott formula.     

如何在材料力学实验中提高学生的学习兴趣

文章分析了材料力学实验的现状和目前存在的问题,针对性地进行了实验教学改革的探索,并应用于实验教学当中,取得了良好的教学效果。     

论统计方法在财务会计中的应用

阐述了财务会计与统计的内在联系及协调统一,分析了统计方法在财务会计领域的运用。     

Fatigue Loading and Life Prediction in Three Fretting Fatigue Fixtures

Three fixtures for conducting laboratory fretting fatigue tests are described and their respective testing methods and the results of the analysis are compared. Each of these fixtures has been used to investigate the effects of various parameters of interest in fretting fatigue. These fixtures include a unique apparatus in which all load applied to the specimen is transferred to the fretting pads, an apparatus similar to many found in the literature where partial load transfer occurs across the pads, and a simplified dovetail fixture in which the clamping load, P, and the shear load, Q, are varied in phase. Select test conditions from prior experiments performed on identical material and resulting in similar lives ranging from one to ten million cycles from these fixtures are identified. The various testing conditions were used to compute the unique stress field for each case. The resulting contact stresses were used to calculate crack initiation based criteria, and to calculate stress intensity factors. The three fixtures were shown to be able to accommodate a range of loads, fretting pad contours, and specimen geometries that produced a variety of stress fields. A crack-initiation-based criterion was shown to predict the failure lives of thinner specimens accurately. The stress intensity factor calculations showed the possibility of a crack arresting for a stress field that decays rapidly and the possibility of a local minimum for K as a function of depth. The fixtures are shown to be complementary in generating data for development of robust fretting fatigue models that use these criteria.     

结构力学计算机辅助教学模式的应用研究

针对结构力学这门课程,从教学改革的需要出发,分析了计算机辅助教学的必要性,介绍了CAI课件的研制与课堂应用效果。     

Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Path Integrals in Noncommutative Quantum Mechanics

We consider an extension of the Feynman path integral to the quantum mechanics of noncommuting spatial coordinates and formulate the corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians). The basis of our approach is that a quantum mechanical system with a noncommutative configuration space can be regarded as another effective system with commuting spatial coordinates. Because the path integral for quadratic Lagrangians is exactly solvable and a general formula for the probability amplitude exists, we restrict our research to this class of Lagrangians. We find a general relation between quadratic Lagrangians in their commutative and noncommutative regimes and present the corresponding noncommutative path integral. This method is illustrated with two quantum mechanical systems in the noncommutative plane: a particle in a constant field and a harmonic oscillator.     

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.