Dynamic non-linear response of beams subjected to impact loads

A non-linear theory is presented for plane deformation of beams which allows for longitudinal stretching as well as for cross-sectional stretching and shearing. The exact strain measures for this theory are also deduced. The longitudinal and flexural motions are coupled in the theory. If the cross section is constrained from stretching, the resulting theory may be classified as a non-linear Timoshenko beam theory. The equations of the latter theory are used to study the motion of beams under impact loads.     

Some New Developments in the Theory of Path Integrals,with Applications to Quantum Theory

A survey of recent developments concerning rigorously defined infinite dimensional integrals, mainly of the type of “Feynman path integrals,” is given. Both the theory and its applications, especially in quantum theory, are presented. As for the theory, general results are discussed including the case of polynomially growing phase functions, which are handled by exploiting the connection with probabilistic functional integrals. Also applications to continuous measurement theory and the stochastic Schrödinger equation are given. Other applications of probabilistic methods in non relativistic quantum theory and in quantum field theory, and their relations with statistical mechanics, are discussed.     

Generalized measure theory

It is argued that a reformulation of classical measure theory is necessary if the theory is to accurately describe measurements of physical phenomena. The postulates of a generalized measure theory are given and the fundamentals of this theory are developed, and the reader is introduced to some open questions and possible applications. Specifically, generalized measure spaces and integration theory are considered, the partial order structure is studied, and applications to hidden variables and the logic of quantum mechanics are given.     

Introduction to string theory and conformal field theory

A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.     

雷暴云带电的理论研究

本文对雷暴云的起电机制进行了研究，提出了雷暴云起电的对流碰撞理论，建立了雷暴云带的简化模型。由该模型给出了雷暴云中电荷的分布函数以及雷暴云轴线上电场强度的计算公式。并对雷暴云闪电过程中电荷的交换情况进行了分析。     

The refined theory of deep rectangular beams based on general solutions of elasticity

The problem of deducing one-dimensional theory from two-dimensional theory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the refined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two examples, it is shown that the new theory provides better results than Levinson’s beam theory when compared with those obtained from the linear theory of elasticity.     

基于非线性光学理论的激光防护材料近况

按照防护原理,可将激光防护材料分为基于线性光学理论的防护材料和基于非线性光学理论的防护材料。综述了基于非线性光学理论的多种激光防护方法及其防护原理,介绍了基于非线性光学理论的多种新型防护材料及其研究进展,比较了四种基于非线性光学理论的激光防护方法的优、缺点,简短地分析了激光防护材料今后发展的基本方向。     

Stability and vibration of isotropic,orthotropic and laminated plates according to a higher-order shear deformation theory

A higher-order shear deformation theory is used to determine the natural frequencies and buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia. Exact solutions of simply supported plates are obtained and the results are compared with the exact solutions of three-dimensional elasticity theory, the first-order shear deformation theory, and the classical plate theory. The present theory predicts the frequencies and buckling loads more accurately when compared to the first-order and classical plate theories.     

On second-quantized open superstring theory

The SO(32) theory, in the limit where it is an open superstring theory, is completely specified in the light-cone gauge as a second-quantized string theory in terms of a “matrix string” model. The theory is defined by the neighborhood of a 1 + 1-dimensional fixed point theory, characterized by an Abelian gauge theory with type IB Green-Schwarz form. Non-orientability and SO(32) gauge symmetry arise naturally, and the theory effectively constructs an orientifold projection of the (weakly coupled) matrix type IIB theory (also discussed herein). The fixed point theory is a conformal field theory with boundary, defining the free string theory. Interactions involving the interior of open and closed strings are governed by a twist operator in the bulk, while string endpoints are created and destroyed by a boundary twist operator.     

Thermodynamic-like transformations in information theory

This article explores the application of thermodynamic and statistical thermodynamic formalism to information theory problems. In particular, the applicability of the transformation theory of thermodynamics is investigated. After a brief tutorial discussion of thermodynamic and statistical thermodynamic methods and concepts, their information theory analogues are developed. Besides information theory entropy, the information theory counterparts of temperature, chemical potential, Helmholtz free energy, etc., are developed and related to conventional information theory concepts such as channel capacity, matching of source and channel, etc. Information theory theorems are proved via the statistical thermodynamic analogue method; and, finally, several problems are formulated and solved using thermodynamic-like transformations. This article is aimed chiefly at bridging the interface between the two disciplines, and is intended to be provocative. Therefore, no attempt has been made to have it be all inclusive.     

The physics of swarms and some basic questions of kinetic theory

This report provides an introduction to the physics of swarms to those interested in kinetic theory. After a brief historical sketch the principles of experiments and their phenomenological analysis are discussed. The relation of this analysis to kinetic theory and the potential of the experiments for studying the nature of hydrodynamic regime and the nonhydrodynamic effects is pointed out. Recent advances in the kinetic theory of swarms in free space are surveyed. They include results such as the generalised Einstein relations and others from the momentum transfer theory, which point to some interesting properties of the many averages that occur in kinetic theory and their relation to thermodynamics, as well as the more technical advances in analysing the structure of the collision operator and solutions of kinetic equations which have lead to very precise calculations of the transport coefficients. The use of theory and experiment in precise determination of cross-sections, potentials and reaction rates is illustrated. Observations showing the effects of finite enclosures are summarised and a theory of swarms in a finite enclosure is outlined. The implications of the subject for kinetic theory are discussed.     

半导体超晶格属性的高分辨率X射线衍射研究

详细阐述了低维半导体材料的X射线衍射的动力学理论和运动学理论从高木陶平(T-T)方程出发,基于波动光学原理,推导出任意结构的多层膜的X射线衍射振幅的递推关系式并编写X射线衍射的程序,分别用动力学和运动学衍射理论模型模拟了20层GaAlAs/GaAs超晶格的X射线衍射结果,得到超晶格样品的结构参量.     

Equations of motion in unified five-dimensional geometrized theory

The equations of motion in unified five-dimensional theory of gravitation, electromagnetism, and scalar field are considered. It is shown that some of the equations of the theory follow from the rest as equations of motion. In the classical limit of the theory, the equations of motion are found, which coincide with the related equations of general relativity. The similarity of the classical limit of the five-dimensional theory and of the Brans-Dicke theory is noted.     

Application of Lie transform perturbation method for multidimensional non-Hermitian systems

Three-dimensional non-Hermitian systems are investigated using classical perturbation theory based on Lie transformations. Analytic expressions for total energy in terms of action variables are derived. Both real and complex semiclassical eigenvalues are obtained by quantizing the action variables. It was found that semiclassical energy eigenvalues calculated with the classical perturbation theory are in very good agreement with exact energies and for certain non-Hermitian systems second-order classical perturbation theory performed better than the second-order Rayleigh–Schroedinger perturbation theory.     

限流扩散理论的局限性及其改进

对几种典型的限流扩散理论的局限性与含时间吸收项的渐近扩散理论的长处作了分析和数字计算比较。结论是,理论上所导出的限流扩散方程,虽然形式上解决了中子迁移的限流问题,但由于理论推导中所作的假定带有一定的局限性,往往使限流过度;而带有时间吸收项的渐近扩散理论避免了上述的局限性,因而它对中子迁移问题的描述优于限流扩散理论。     

On the axiomatic approach to quasi-classical field theory

We study the connection between quasi-classical field theory and axiomatic statements of the quantum field theory, Schwinger source theory, and the Lehmann-Symanzik-Zimmermann (LSZ) formalism. The classical Schwinger source is connected with the classical field; the LSZ R-function is connected with the quantum field operator. The axioms of the quantum field theory are written in the context of the quasi-classical expansion. In the considered approach, the stationary action principle and canonical commutation relations for field operators are obtained as corollaries and are not postulated as initial statements of the theory.     

长周期光纤光栅傅里叶模式耦合理论

建立了长周期光纤光栅傅里叶模式耦合理论.在分析同向模式耦合时,发现了同向耦合模式的振幅系数间存在傅里叶变换关系.推导了长周期光纤光栅的同向耦合谱和透射谱的通用表达式.该理论是用傅里叶变换分析得出长周期光纤光栅折射率微扰的空域谱,再对该空域谱进行模式同向耦合分析,从而得到长周期光纤光栅光谱特性的通用表达式.根据该理论模拟分析了长周期光纤光栅在不同长度和微扰幅值时的光谱特性,与传统耦合模理论进行了对比分析.结果表明,该长周期光纤光栅傅里叶模式耦合理论具有简单、精确和高效的特点,与实际长周期光纤光栅的透射谱特性一致.应用该理论可分析无过耦合的任意轴向折射率微扰分布的长周期光纤光栅光谱特性.     

Free vibrations of skirt supported pressure vessels — an engineering application of timoshenko beam theory

Timoshenko beam theory is applied to the study of the free vibrations of skirt supported pressure vessels in this paper; such systems are used in the process and power generation industries as well as aboard nuclear powered vessels. It is shown that the analysis is not significantly more complicated than the analysis of skirt-vessel combinations by Euler-Bernoulli beam theory. This latter analysis is provided in an appendix. Two sets of boundary conditions are considered: namely, the cases of (a) a cantilevered system and (b) a fixed-pinned system. The first two natural frequencies of nine typical cases are calculated and compared with the corresponding results obtained from Euler-Bernoulli beam theory. The numerical differences are significant so that if a beam theory is adequate to model the system, it is clear that Timoshenko beam theory is the appropriate one to use. In addition, the first two mode shapes for a particular case are presented for comparison with the corresponding mode shapes predicted by Euler-Bernoulli beam theory. Finally, some comments on the modeling and analysis of specific, real systems are made. It is emphasized that the purpose of the paper is to demonstrate that Timoshenko beam theory is not unduly difficult to apply to problems of engineering interest when a beam theory model is suitable.     

第四讲 量子对策论

量子对策论是量子信息学的新兴分支,是经典对策论与量子信息学两门学科的交叉学科.由 于引入了量子力学中的量子叠加性和纠缠态,量子对策得出了与经典对策迥然不同的结果.     

Bragg光纤光栅傅里叶模式耦合理论

建立了Bragg光纤光栅傅里叶模式耦合理论.在分析光纤光栅的耦合模时,发现了耦合模式的振幅系数间存在傅里叶变换关系.推导了将傅里叶变换和模式耦合融合在一起的Bragg光纤光栅反射谱和透射谱的通用表达式.该理论是用傅里叶变换得到Bragg光纤光栅折射率微扰的空域谱,再对该空域谱进行模式耦合分析计算,从而得到Bragg光纤光栅的光谱特性.根据该理论,仿真分析了Bragg光纤光栅的谱特性,与耦合模理论、直接傅里叶变换法进行了对比分析.结果表明,傅里叶模式耦合理论与传统的耦合模理论及实际Bragg光纤光栅的光谱特性一致,具有简单、清晰、直接、精确和分析效率高的特点,可分析任意轴向折射率微扰分布的Bragg光纤光栅结构.