一种简洁统一的多普勒效应探究

陈光平等给出了多普勒效应的一种统一形式,但当波速低于光速时,其涉及第三方参考系——介质系的观测,故而使用起来颇为不便.本文探讨了一种多普勒效应的简洁统一形式并给出证明,同时给出了这种简洁统一形式在光速和远小于光速时的情况.这种简洁统一形式不仅不会涉及介质系,而且具有对称的物理美.并且,通过对公式本身的作图分析,得知多普勒效应中的相对论效应是随着速度的增加而逐渐显现的,并不是与经典多普勒效应的简单叠加.     

狭义相对论教学中的几个问题

本文讨论了相对论教学中几个方面的问题,包括常见例子的问题,洛伦兹变换的方便形式,同时相对性例子在另一参考系的讨论,长度测量在另一参考系看到的现象,时间延缓及运动参考系各点时间不同和光的多普勒效应的简单推导.通过不同过程在不同参考系中的讨论,掌握在运动系讨论问题的方法,以及同一过程在不同惯性系内的不同表现,而所有现象的测量结论在洛伦兹变换下保持不变.     

展示相对性原理和电磁场相对性的一个佳例

以条形磁铁与导体圆环相对运动为例,依据导体圆环产生感应电流这一事实,首先讨论了条形磁铁参考系和导体圆环参考系下电场和磁场的不同.并在条形磁铁参考系下,从产生动生电动势的物理本质洛伦兹力出发,导出了法拉第电磁感应定律.然后,在导体圆环参考系下,由相对性原理直接给出了感生电场性质的数学表述,并深入讨论了电场和磁场的联系.最后,给出了爱因斯坦和费曼对该问题的不同思考并进行了简单分析.     

经典物理理论中电磁波的传播规律

为了处理波传播的相关问题,引用了麦克斯韦经典理论中波的传播规律.基于麦克斯韦方程组和伽利略变换,利用微分方程来计算不同参考系下同-电磁波的传播.由于介质的运动对波动有重要的影响,所以在多普勒效应中介质的运动也被考虑进来.同时,根据该经典物理理论中的波的传播规律从不同的角度来解释迈克尔逊-莫雷实验的结果.经典物理理论中电...     

一般多普勒效应的综合统一分析

在物理学教材中分别给出了声波和光波的多普勒效应公式，但两者表达式不同.一些文献分析了两者间的联系，但没有真正地将两者统一起来；另一些文献虽作了统一分析，但均在特殊洛伦兹变换下讨论问题，所得结果又不具有一般性.本文在不区分声波与光波的情况下，基于波动传播的共同本质，综合运用多种方法导出一般多普勒效应的表达式，系统地论证两者的统一性.通过分析得到了一般多普勒效应的3个等价表达式，而教材中声波与光波的多普勒效应公式乃是其不同情况下的特例.     

巧用加速度合成解一道竞赛题

研究物体的运动需要建立参考系.牛顿运动定律在其中有效的参考系叫做惯性参考系.如果已知S是一个惯性参考系,则任何对于S做匀速直线运动的参考系S′都是性参考系.判定一个给定的参考系是不是惯性参考系,取决于人们能以多大的精度去观测出这个参考系的微小的加速度效应.     

相对论感应电动势及其在参考系变换下的计算

本文考察相对论情况下动生、感生电动势之间的相对性.分析不同参考系总感应电动势数值改变的原因.给出参考系变换下计算总感应电动势的普遍公式.计算了无线长直导线电流外运动矩形及圆形线圈的感应电动势.最后指出运动观者测出的总感应电动势等于静止观者不同时刻在导体不同位置测量电动势的总和.     

匀速和变速运动时声波多普勒效应公式的推导

给出了波源和观察者在匀速和变速运动情况下声波多普勒效应公式的详细推导过程. 结果显示,无论 观察者和波源做匀速运动,还是做变速运动,对应的多普勒效应公式都是相同的     

再谈用闵氏几何解析“双生子佯谬”

利用二维闵氏时空图解析双生子效应.明确闵氏几何线元长度与质点的固有时成正比,利用时空图中比较世界线长短的方法直观地在不同参考系中对双生子效应进行了定量的分析.另外,对"三生子佯谬"进行了定性半定量分析.     

激光场的线宽对双光子电磁感应光透明及共振吸收增强的影响

讨论了四能级系统中激光场的线宽及多普勒效应对双光子电磁感应光透明及共振吸收增强的影响，并给出了该系统中消除多普勒效应的最佳实验方案.     

Studies of beam propagation characteristics on apertured fractional Fourier transforming systems

Based on the principle that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, propagation characteristics of a Gaussian beam or a plane wave passing through apertured fractional Fourier transforming systems are analyzed and corresponding analytical formulae are obtained. Analytical formulae in different fractional orders are numerically simulated and compared with the diffraction integral formulae, the applicable range and exactness of analytical formulae are confirmed.It is shown that the calculating speed of using the obtained approximate analytical formulae, is several hundred times faster than that of using diffraction integral directly. Meanwhile, by using analytical formulae the effect of different aperture sizes on Gaussian beam propagation characteristics is numerically simulated, it is shown that the diffraction effect can be neglected when the aperture size is 5 times larger than the beam waist size.     

有限点方法研究

在二维散乱离散点集上研究一类无网格方法——有限点方法(Finite Point Method,简称FPM),建立方法的基础.采用方向微商和方向差商讨论有限点方法,建立各阶各方向微商间的关系式.利用这些关系式,根据被逼近点的邻点数目差异,分别建立数值方向微商的五点公式及少点(两点、三点、四点)公式;研究五点公式的可解性条件与可允许邻点集;获得典型微分算子的数值方向微商公式等.理论分析和数值试验表明,随着邻点数目的增加,相应数值公式的逼近精度随之提高.这类近似公式不仅为在散乱离散点集上构造各类偏微分方程的格式奠定了基础,同时,也可应用于偏微分方程非结构网格计算方法,提高方法的精度.     

环形电场与非均匀磁场重叠场中能量分散形式的二级离子轨迹及其转换公式

本文用变分方法计算了环形电场与非均匀磁场重叠场的二级离子轨迹,以能量分散形式加以表述。讨论了在能量、速度、动量三种分散形式间的系数转换公式。给出了相应的转换矩阵。以上结果,便于在离子光学理论研究和质谱仪器的实际设计中应用。 关键词：     

Recursion-transform method and potential formulae of the m × n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform(RT) method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.     

基于中国颜色体系的色差公式分析

CIE均匀颜色空间及利用色差公式对色差进行计算对彩色复制品的评价具有很关键的作用。利用中国颜色体系在视觉上为等色差系统以及色调、彩度和明度可以单独改变的特性,分别从色调、彩度、明度三方面对CIEL*a*b*、CMC(l:c)、CIE94、CIEDE2000色差公式进行了比较分析。结果表明:用各色差公式计算出的平均色差值是不同的,它们的均匀性也不同。需要针对不同的明度、彩度、色调选择使用不同的色差公式。     

Quantum theory of sticking: equivalence of various approaches and application to a simple model

The basic formulae of four different quantum mechanical approaches to the calculation of the sticking coefficient of an atom on a cold solid are re-examined in order to discuss the connections between them. All approaches pursued exactly give the same result, and this is exhibited for a one-dimensional model which is exactly solvable to provide closed-form formulae for the sticking coefficient. Numerical results, which reproduce the qualitative behaviour of atomic sticking, are presented for different assumed densities of substrate excitations responsible for the energy loss, including the physically important cases of low-energy single phonons, and low-energy electron-hole pairs in a metal.     

Calculation of the eigenvalues of pure quadrupole interaction in Mössbauer effect studies

Summary Two approximate formulae to calculate the eigenvalues of pure quadrupole interaction in M?ssbauer effect studies have been proposed and the eigenvalue coefficients in the formulae have been given for various excited states and ground states of the nucleus with different spin. All the eigenvalues of pure quadrupole interaction between both excited state and ground state of nucleus with spinI=3/2÷9/2 and the electric-field gradient with different asymmetry parameter (η=0÷1.0) have been calculated by these formulae. The results show that the accuracies in all the calculations are more satisfactory or same in comparison with those obtained by the formula of Shenoy and Dunlap, especially when the asymmetry parameter of electric-field gradient is larger than 0.8 for the nucleus with spinI=5/2.     

高斯光束在受限空间滤波器中传输的快速分析

根据矩形函数可以展开为有限复高斯函数之和的方法,从柯林斯衍射积分公式出发,对高斯光束通过受限空间滤波器传输特性进行分析,得到了相应的近似解析式。利用Matlab对其解析式进行数值模拟,得出一组直观的结果。通过比较这些结果可以看出透镜的有限尺寸对光束传输的影响,以及空间滤波器的滤波小孔在传输中具有明显作用。     

Calculation of the light intensity distribution reflected by a spherical cube corner retroreflector array

Because the light intensity distribution (LID) reflected by a spherical cube corner retroreflector array (SCCRA) is of great significance for the detection of the remote laser ranging to receive laser pulse echo precisely and to accomplish the function outstandingly, it is vital to find a method to calculate the LID reflected by SCCRAs with different structural parameters for the SCCRA design. Besides, considering that the reflected light goes through a complex optical system (COS) described by ABCD matrix before it reaches the detector, the method to calculate the LID should be suitable for the COS. This article derives formulae to calculate LID reflected by a SCCRA based on the lens-system diffraction formula of S.A. Collins. In the process of deriving, coordinate transformation matrixes and vector formulations are applied and the dihedral offsets are taken into account. Because the structural parameters of the SCCRA and the expression of the ABCD matrix of the COS are not limited in the deriving process, these formulae are suitable for calculation of the LID reflected by different SCCRA and going through different COS. In addition, computer simulations are applied to explain clearly how to get the LID of a SCCRA by the formulae derived in this paper.