相切双导体球的电容公式研究

鉴于相切双导体球的电容公式是由级数表示的,为了研究其简洁的表达结果,再次运用镜像法研究了相切双导体球电容的通用公式,创造性地应用“平衡缩放”方法得到了一个比较简洁的近似公式,根据应用MATLAB软件对近似公式与精确公式的3种误差比较,证明了该近似公式具有非常高的精确性,完全可作为常用公式使用,该近似公式具有很好的实用性...     

对《一个单摆周期近似公式》一文的讨论

采用级数展开的方法,对<一个单摆周期近似公式>一文中所给出的近似单摆周期公式提供了理论依据,并且还可以得到精度更高的近似公式;同时,通过与其他近似公式的对比,说明该近似公式的精度可提高1～2个数量级.     

用线性插值法求单摆运动周期的近似解

利用线性插值的方法,提出了一个任意摆角条件下的单摆运动周期的近似公式.并利用Mathematica软件将该公式与精确解进行了比较,还与其他近似公式进行了对比.结果表明,该公式的近似程度相当好.     

关于对称尖刃式簧片固有频率的理论和实验研究

本文研究簧片哨里簧片的固有频率.根据Leitner和Hiedemann的簧片基频计算方法,推出了簧片二次频的公式.提出簧片基频在液体介质中的近似公式.在水中获得的实验结果与近似公式相符合.     

基于Mathematica求解任意摆角下的单摆周期近似公式

本文借助于Mathematica软件,利用曲线拟合的方法,通过对相关文献中无阻尼单摆周期公式中精确度最高的近似公式进行修正,得出了一个近似解析函数形式,并对其进行了分析和讨论.     

梯形截面介质光波导的模吸收损耗

本文运用微分法由梯形截面介质光波导的近似模方程导出了模吸收损耗系数的公式.并结合计算实例进行了误差分析.     

用平均值方法导出三种统计分布律

在统计物理学中,运用最可几方法可以导出经典的麦-玻分布律,也可以导出两种量子统计分布律,即费-狄分布律和玻-爱分布律.在推导过程中,应用了斯特令近似公式,但是,应用这个近似公式的条件不是在任何情况下都能得到满足,例如在推导费-狄分布律时,求得系统的费-狄分布的热力学几率为 式中ni为处于第i个能级εi上的粒子数,gi为能级εi上的量子态数.但是,对于费米子系统,可以出现gi=ni的情况,此外,gi>>1,ni>>1这个条件也不是在所有情况下都成立的.因此,在阶乘的展开式中,应用斯特令近似公式是有缺陷的,由此可见,用最可几方法推导分布律不够严格.…     

变形对称双阱势

利用变形双曲函数,将对称双阱势推广为变形对称双阱势模型.证明了该势模型是五参量指数型势模型的特例.运用超对称WKB近似和五参量指数型势模型的能谱公式,获得了变形对称双阱势模型的能谱公式.     

半无限高方势阱能级的近似公式

在无量纲化的基础上,通过引入角参数的方法推出了一个新的一维半无限高方势阱的能级关系.由此进一步得到了能级的近似公式,并进行了误差分析.经过与数值结果的对比,本文得到的近似公式具有较高的精确度和较一般的适用性.     

高斯分布扩散光波导折射率分布的多项式近似

本文用适当的多项式函数近似高斯折射率分布函数,利用Ikuno的结果,导出了扩散平面光波导导模有效折射率的更精确近似解公式.这个公式不仅简单便于计算,而且由它求得的导模有效折射率更接近光线方法的数值结果,其精度不仅优于无微扰的适当双曲正割分布近似,也优于微扰的适当双曲正割分布近似.同时也改善了较高阶导模的数据精度.     

渐变折射率波导传播特性微扰计算的代数递推公式

应用量子力学的超位力定理（HVT）和赫尔曼－费恩曼（Hellmann-Feynman）定理（HFT），导出了用微扰法计算渐变折射率平面波导传播常数各级近似值的代数递推公式，并给出了由传播常数近似值计算模场近似表达式的代数式。计算了几个典型实例，此法的特点是便于直接计算任意级近似的传播常数及模场分布，且可推广到二维波导的计算。     

A new approximate analytical approach for dispersion relation of the nonlinear Klein-Gordon equation

A novel approach is presented for obtaining approximate analytical expressions for the dispersion relation of periodic wavetrains in the nonlinear Klein-Gordon equation with even potential function. By coupling linearization of the governing equation with the method of harmonic balance, we establish two general analytical approximate formulas for the dispersion relation, which depends on the amplitude of the periodic wavetrain. These formulas are valid for small as well as large amplitude of the wavetrain. They are also applicable to the large amplitude regime, which the conventional perturbation method fails to provide any solution, of the nonlinear system under study. Three examples are demonstrated to illustrate the excellent approximate solutions of the proposed formulas with respect to the exact solutions of the dispersion relation. (c) 2001 American Institute of Physics.     

用局部常化三倍角公式研究单摆周期

应用局部常化方法对三倍角公式进行局部常化处理,对一类非线性动力学方程进行了一种简洁的近似修正,得到精确度较高的大摆角单摆运动周期的两个新结论,同时用此结论推导出一个简洁的推论,并且用3种方法进行了具体比较.     

A semiempirical theory of a one-layer cellular sound-absorbing lining with a perforated face panel

On the basis of the known approximate theories and the recent experimental data, a semiempirical theory of a resonance-type one-layer cellular sound-absorbing lining is developed. Approximate formulas are obtained for calculating the effective normal impedance with allowance for the geometric parameters of the sound-absorbing lining, the high sound-pressure levels, the presence of an entraining flow, and the nonlinear interaction of sound components of different frequencies within a given one-third-octave spectrum of noise. The results of numerical calculations by approximate formulas are compared with experiments and with the experimental and theoretical data reported by other authors. The proposed theory is found to agree well with experimental data.     

基于MATLAB的单摆周期近似解的比较

利用MATLAB计算软件,得出了无阻尼情况下单摆运动周期的精确解,并通过图示及最小二乘原理,对文献报道的十几个单摆周期的近似解与精确解进行了比较.     

Analytical formulas for a circular or non-circular flat-topped beam propagating through an apertured paraxial optical system

Propagation of a flat-topped beam of circular or non-circular (rectangular or elliptical) symmetry through an apertured optical system is investigated. By expanding the hard aperture function as a finite sum of complex Gaussian functions, some approximate analytical propagation formulas are derived for a flat-topped beam of circular or non-circular (rectangular or elliptical) symmetry propagating through an apertured paraxial general astigmatic (GA) optical system or an apertured paraxial misaligned stigmatic (ST) optical system. The derived formulas are very fast to compute. The results obtained by using the approximate analytical expressions are in a good agreement with those obtained by direct numerical integration. The present analytical formulas provide a convenient and effective way for studying the propagation and transformation of a circular or non-circular flat-topped beam through an apertured general optical system.     

The electromagnetic fields of a vertical and a horizontal electric dipole located above a single-layer half-space

In the article we consider the secondary electromagnetic fields of elementary electric sources above a single-layer half-space. The results of calculations from approximate formulas obtained in the article are compared with the strict solution. The calculations by the strict formulas were carried out on a computer.     

Determining reflections for beam propagation algorithms

Reflections occur whenever different waveguide sections are concatenated. In this paper, we will give approximate formulas for determining the reflection coefficient. Starting with generalized transmission line equations we will derive general formulas where suitable approximations are introduced. These approximations allow the determination of the reflections with low numerical effort. The expressions were implemented in an FD-BPM algorithm to determine the field distribution in waveguide devices. For an application in CAD systems the reflection coefficient of the fundamental mode was computed with the approximate formulas. Numerical results were obtained for various concatenations of different waveguide sections. A comparison with the method of lines, a semi-analytic algorithm, shows a good agreement.     

自行车系统的计算机模拟

自行车系统是一个具有非完整约束的复杂系统,可以根据最小作用量原理通过欧拉-拉格朗日方程求解,利用差分代替微分及一系列修正截断误差的方法计算近似值.利用MATLAB,只要给定任意质点系的拉格朗日函数以及约束系数,即可求出系统的近似解,并通过这个方法为分析自行车的运动与稳定性提供一种新的思路.     

Bremsstrahlung of ultrarelativistic deuterons in the field of the nucleus

We consider the differential cross section for bremsstrahlung of ultrarelativistic deuterons subject to diffraction scattering by nuclei. By comparison of the approximate formulas obtained here with exact numerical calculations, the region of applicability of the approximate formulas is discussed.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 2, pp. 16–19, February, 1987.