量纲分析的基本理论及其应用

量纲分析是研究物理问题的重要方法之一本文在研究量纲分析的基本理论Ⅱ定理的基础上,提出了量纲分析矢量空间的待定系数法,并举了一些实例,使量纲分析的应用和推广深入了一步．     

基于Mathematica的量纲分析及其应用

将量纲分析中的Π定理用线性空间表示,建立一种量纲分析的系统方法,并利用科学计算软件Mathematica 9提供的新功能,使量纲分析变得方便易行.     

黑体辐射公式的量纲分析

量纲分析是研究物理问题的重要方法之一.本文对量纲分析的解题步骤做了梳理归纳,并对于黑体辐射公式进行了量纲分析.     

基于量纲分析的建模研究

在量纲分析理论的基础上,结合工程实际问题研究了量纲分析建模的基本思路和方法.     

玻尔氢原子公式的量纲分析

对量纲分析的解题步骤做了梳理归纳,并应用于玻尔氢原子公式。     

球形破片侵彻多层板弹道极限的量纲分析

为了研究Q235钢多层板的抗侵彻性能,进行了直径为9.45 mm的钨合金球形破片侵彻7.2 mm和(3.6+3.6)mm厚Q235钢双层板试验,获得了相应的弹道极限。在此基础上,建立数值仿真模型,研究了钨合金球侵彻接触式等厚3层、4层、5层、6层板的弹道极限。通过量纲分析方法,分析了分层数对靶板弹道极限的影响。结果表明:对于球形破片,总厚度为7.2 mm的等厚双层板的抗侵彻性能高于单层板;当分层数大于2时,接触式多层等厚靶板的弹道极限随着层数的增加而减小,即分层数越多,靶板的抗侵彻性能越低,通过量纲分析方法得到了靶板分层数与破片弹道极限的关系。研究结果可为未来装甲防护设计提供一定的参考。     

线性代数方程组的行处理法

从几何角度对非奇异线性代数方程组行处理法的收敛性给出证明和收敛速度估计式，介绍其三维投影加速技术并提出对角面投影加速技术，讨论行处理法的迭代止判断。     

线性代数方程组的通用性迭代解法

分析行处理法用于求解线性代数方程组的通用性，以及给出据行处理法收敛状态判断线性代数方程组解的性态的方法。     

Differential algebraic method for arbitrary-order chromatic aberration analysis of electrostatic lenses

In this paper, differential algebra is applied to calculate arbitrary high-order chromatic aberrations of electrostatic electron lenses. Expressions of differential algebraic form of high-order combined chromatic aberration coefficients are obtained and arbitrary-order chromatic aberrations can be calculated numerically. As an example, a typical Schiske's electrostatic lens has been studied. All the first- to third-order chromatic aberration coefficients of the lens have been calculated, and the pattern of the first-order chromatic aberration has been given as well.     

Nonabelian KP hierarchy with Moyal algebraic coefficients

A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new hierarchy can be interpreted as large-N limit of multi-component (gl (N) symmetric) KP hierarchies. Actually, two different hierarchies are constructed. The first hierarchy consists of commuting flows and may be thought of as a straightforward extension of the ordinary and multi-component KP hierarchies. The second one is a hierarchy of noncommuting flows, and related to Moyal algebraic deformations of selfdual gravity. Both hierarchies turn out to possess quasi-classical limit, replacing Moyal algebraic structures by Poisson algebraic structures. The language of W-infinity algebras provides a unified point of view to these results.     

Aberration analysis of electron mirrors by a differential algebraic method

A differential algebraic (DA) method has been developed for the aberration analysis of electron mirrors. Since large ray slopes occur near the turning points in mirrors, the axial position is no longer suitable as the independent variable and the electron trajectory equation used in conventional lens theory is no longer feasible. A DA solution of the electron motion equation, wherein a single DA ray trace is performed on a non-standard extension of real number space called _nD_v, enables the aberrations of a mirror system to be obtained, in principle up to arbitrary order n, and with very high accuracy, due to the remarkable algebraic properties of _nD_v. With the DA method, the enormous effort to derive explicit formulae for the aberration coefficients of electron mirrors is avoided. A software package MIRROR_DA has been developed for the aberration analysis of electron mirrors, based on the DA method. Two examples of electron mirrors are presented. For the first example, for which the electrostatic and magnetic fields are represented by analytical models, the results computed with MIRROR_DA were shown to be in good agreement with those extracted by direct ray tracing, with relative deviations of less than 0.065% for all the primary aberration coefficients. The second example consists of a real magnetic lens and electrostatic mirror, with numerically computed fields, and from the results of MIRROR_DA, the spherical aberration coefficient C_s3 is almost cancelled out because of the correction effect of the mirror. The MIRROR_DA software is a novel, effective and precise tool for the aberration analysis of electron mirrors, capable of handling realistic and complicated systems of electron lenses and electron mirrors.     

Creation-field theory from dimensional analysis

A Lagrangian is obtained which is invariant under space-time dependent changes in the units of mass, length and time. It contains two scalar fields, one of which is effectively the Brans-Dicke scalar (varying gravitational constant), while the other can be interpreted as a creation-field. An erratum to this article is available at .     

量纲分析法求解辐射热传导自相似解

通过量纲分析,将辐射流体方程简化为一阶常微分方程组的形式,进而结合数值计算求得热波烧蚀自相似解。流体方程涉及的内能、状态方程表达式采用依赖于温度、密度两个参量的形式,且参数可调,适用性较广。源边界条件可为恒温、恒流、恒压、常密等情况。以恒温源为例,给出了X射线加热Au壁时烧蚀质量与烧蚀压的定标关系,与文献结果及MULTI辐射流体程序计算结果吻合较好。     

Wigner distributions for finite dimensional quantum systems: An algebraic approach

We discuss questions pertaining to the definition of ‘momentum’, ‘momentum space’, ‘phase space’ and ‘Wigner distributions’; for finite dimensional quantum systems. For such systems, where traditional concepts of ‘momenta’ established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail     

用李代数方法解析研究线性三原子分子振动的动力学纠缠

采用李代数方法研究了线性三原子分子非线性伸缩振动的动力学纠缠,给出了描述纠缠行为的线性熵和冯诺伊曼熵的解析表达式,并分别讨论了初态为Fock态和相干态下的HCN和DCN分子伸缩振动纠缠的动力学性质.