用环形横向剪切干涉法精密测定透镜的折射率和色散

本文采用环形横向剪切干涉法和折射计相结合来测定透镜或胶合透镜的拆射率和色散.讨论了该方法的测量精度及提高灵敏度等有关问题.     

激光干涉技术在磨边定心中的应用

本文提出一种利用激光干涉技术测定磨边透镜中心偏差的方法。根据等厚干涉的基本原理，用平行的激光束投射到磨边工件表面，可以得到两个干涉同心圆，这两个像分别反映了工件前后表面的球心点位置。适度调节这两个像即可达到透镜允许的中心偏差精度     

洛埃镜测杨氏模量

本文介绍用洛埃境干涉法测量钢丝的伸长量ΔＬ，从而测定材料的杨氏模量。此法提高了测量精度，相对误差可降到３％左右。     

迈克尔逊干涉仪实验中的三个问题

本文对在大学物理实验迈克尔逊干涉仪调节和使用题目中被教师忽略却常被学生提出的三个问题进行了细致分析和讨论，并给出了解决建议。     

一种改进的载波电子散斑干涉处理方法

提出了一种新的载波电子散斑干涉的处理方法,该方法将载波所形成的直条纹和包含物体变形信息的弯曲条纹在频域直接比较, 避免了传统载波干涉方法中的载波频率计算和由此带来的误差. 因此在准确程度和方便性方面都有明显改进. 本文在给出理论分析的同时进行了实验验证.     

多缝干涉的次极大

为了加深学生对多缝干涉次极大的认识和理解，本文介绍了一种深入浅出的教学方法，以供参考。     

光拍频和干涉现象

本文对比了光拍频和光干涉两种现象，强调了它们的同一性。前者是强度随时间相位［（ω１－ω２）ｔ］而变的一种运动形式。后者则是强度随空间相位（光程差引起）而变的．本文并指出，在干涉现象中，全面地辩证地把握两种相位形式，对解决一些科学实际问题是有益的．     

表面粗糙度测量的磁光位相调制和锁相干涉

提出了一种表面粗糙度测量的新方法，该方法采用了微分偏振干涉的原理，利用由法拉第磁光调制器所组成的调制系统对偏振干涉光路的位相进行调制，利用锁相干涉原理对位相进行探测，该方法可实现无参考面快速非接触测量，在普通实验条件下，也可保持良好的稳定恶性循环 ，实验装置即可给出表面的轮廓又可给出其它统计数据，其横向分辨率为１．２μｍ纵向为２ｎｍ。     

等厚干涉法测量盐度

根据等厚干涉的原理,本文提出了一种通过测量水质的折射率来测定盐度的光学方法。测量误差低于3％。     

云纹干涉法面内位移测量的光栅补偿方法研究

运用光的干涉与衍射理论，导出了对称入射光路云纹干涉法面内位移计量的基本公式。针对云纹干涉法在实际应用中易引入刚体位移对真实面内位移干扰这一棘手问题，设计了定量补偿面内位移和变形的非对称光栅补偿光路系统。由于采用高灵敏度基准光栅调节的方法，比螺旋测微器等纯机械方法具有众多优越性。本文分析了该补偿方法对面内正应变条纹梯度和面内剪应变条纹梯度的补偿原理和具体实施过程。本方法大大提高了云纹干涉法面内位移计量和补偿的可靠性。     

An irrational trial equation method and its applications

An irrational trial equation method was proposed to solve nonlinear differential equations. By this method, a number of exact travelling wave solutions to the Burgers-KdV equation and the dissipative double sine-Gordon equation were obtained. A more general irrational trial equation method was discussed, and many exact solutions to the Fujimoto-Watanabe equation were given.     

概率波和非概率波

对于把克莱因-戈尔登方程当作是玻色子的方程的看法提出异议,认为它是所有微观粒子均要满足的方程,但它却不能成为任何一类粒子的波动方程.提出了克-戈方程中包含着概率和非概率两类波的概念,认为概率波还要遵从一个对时和空都是一阶导数的方程,这才是粒子的波动方程.不同种类粒子性质的不同则体现在他们概率波类型的不同上.     

构造非线性发展方程精确解的一种方法

在双曲正切函数法、齐次平衡法、辅助方程法的基础上引入非线性发展方程的一个新形式解和新辅助方程，并利用符号计算系统Mathematica构造了Benjamin-Bona-Mahoney(BBM)方程和修正的 BBM方程的新精确孤立波解.这种方法在寻找其他非线性发展方程的新精确解方面具有普遍意义. 关键词： 新辅助方程 形式解 非线性发展方程 精确孤立波解     

不同势函数状态方程湿空气性质的模拟研究

本文从L-J维里状态方程、L-J径向状态方程,TIP4P维里状态方程以及TIP4P径向状态方程四种模型出发,利用分子动力学模拟技术,进行了湿空气性质的研究.对不同状态方程的模拟结果的稳定性进行了探讨,发现径向状态方程的稳定性要好于维里状态方程,最后采用径向分布方程及TIP4P模型,模拟了湿空气的性质,结果表明湿空气在低温、高压和高含湿量下,其性质不再接近于理想气体的性质.     

Solving Kadomtsev—Petviashvili Equation via a New Decomposition and Darboux Transformation

Recently,a new decomposition of the (2 1)-dimensional Kadomtsev-Petviashvili(KP) equation to a (1 1)-dimensional Broer-Kaup (BK) equation and a (1 1)-dimensional high-order BK equation was presented by Lou and Hu.In our paper,a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems.As application,new explicit soliton-like solutions with five arbitrary parameters for the BK equation,high-order BK equation and KP equation are obtained.     

超细长弹性杆动力学的Gauss原理

研究基于Gauss 变分的超细长弹性杆动力学建模的分析力学方法.分别在弧坐标和时间的广义加速度空间定义虚位移,给出了非完整约束加在虚位移上的限制方程;建立了弹性杆动力学的Gauss原理,由此导出Kirchhoff方程、Lagrange方程、Nielsen方程以及Appell方程;对于受有非完整约束的弹性杆,导出了带乘子的Lagrange方程;建立了弹性杆截面动力学的Gauss最小拘束原理并说明其物理意义. 关键词： 超细长弹性杆动力学 分析力学 Gauss变分 最小拘束原理     

非均匀反射全息图的理论分析

本文对非均匀反射全息图进行了理论分析.在考虑记录介质吸收的情况下,通过适当的变换,将耦合波理论中由两个线性微分方程构成的微分方程组——耦合波方程,化为一个变系数非线性微分方程——黎卡提方程.并对方程的性质进行了分析.通过数值解,发现了一些新的很有意义的现象.     

Generalized equation for describing the magnetization in spoiled gradient-echo imaging

The purpose of this study was to demonstrate a generalized equation for describing the magnetization in spoiled gradient-echo (SPGR) imaging in which the in-pulse relaxation and magnetization transfer (MT) effects are taken into account. First, the time-dependent Bloch equations for the two-pool exchange model with MT effect were reduced to an inhomogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation. Second, the equations describing the magnetization before and after the radiofrequency (RF) pulse were derived based on the above solution for the RF-pulse excitation and evolution phases. Finally, a generalized equation describing the steady-state magnetization was derived. The validity of this equation was investigated by comparing with the transverse magnetization obtained by the regular Ernst equation and analytical solution in which the in-pulse transverse relaxation is considered. When the same assumption was made in our method, there were good agreements between them, indicating the validity of our method. The in-pulse transverse and longitudinal relaxations decreased the transverse magnetization compared to the case in which these effects were neglected, whereas MT increased it. In conclusion, we derived a generalized equation for describing the magnetization in SPGR imaging. This equation will provide a suitable basis for understanding the signal intensity in SPGR imaging and/or T₁ measurement using an SPGR sequence in cases in which the effect of in-pulse relaxation and/or MT cannot be neglected.     

激光输出功率随耦合率及放大率的变化规律

建立了涵盖稳定腔和非稳腔的激光有源理论模型和激光开式谐振腔的边界条件。根据定态薛定谔方程与亥姆霍兹方程的等价性,采用量子力学方法求解谐振腔的亥姆霍兹波动方程,得到满足方程、边界条件、矩阵光学、稳定条件的本征解和本征方程。根据本征方程推导出横模数目随耦合率变化的规律,进而推导出激光输出功率随耦合率变化公式,以及激光输出功率随放大率的变化规律。该理论模型能够从稳定腔自然过渡到非稳腔,在小耦合率情况下退化到与传统公式基本一致的形式,又能在大耦合率情形下与实验结果符合得很好。     

Stable first-order particle-frame relativistic hydrodynamics for dissipative systems

We propose a stable first-order relativistic dissipative hydrodynamic equation in the particle frame (Eckart frame) for the first time. The equation to be proposed was in fact previously derived by the authors and a collaborator from the relativistic Boltzmann equation. We demonstrate that the equilibrium state is stable with respect to the time evolution described by our hydrodynamic equation in the particle frame. Our equation may be a proper starting point for constructing second-order causal relativistic hydrodynamics, to replace Eckart's particle-flow theory.