Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.     

说说我们的家园——地球的命运

国人大概都知道杞人忧天的故事．相传战国时列御寇所撰《列子》一书中的《天瑞》篇载有“杞国有人，忧天地崩坠，身亡所寄，废寝食者”；唐朝大诗人李白《梁甫吟》一诗中也提到这件事：“白日不照吾精诚，杞国无事忧天倾”；清李汝珍所著《镜花缘》第二十七回也有言：“杞人忧天，伯虑愁眠”．说的都是古时候杞国有个人，老爱瞎操心，明明不用担忧的事情，他也是不放心，特别是害怕天会塌下来，弄得自己无处安身．     

CsNiCl3晶体的光谱精细结构、零场分裂参量及Jahn-Teller效应

应用不可约张量理论构造了三角对称晶场中3d²/3d⁸态离子的45阶可完全对角化的微扰哈密顿矩阵，研究了CsNiCl₃晶体的光谱精细结构、晶体结构、零场分裂参量、Jahn-Telller效应以及自旋单重态对Ni²⁺离子基态能级的影响，理论与实验相符合.在此基础上，进一步研究了以前工作中被忽略的自旋-自旋耦合作用和Trees修正对CsNiCl₃晶体的光谱精细结构和零场分裂参量的影响，发现有四种机理会影响零场分裂参量：1)自旋-轨道耦合机理，2)自旋-自旋耦合机理；3)自旋-轨道与自旋-自旋联合耦合机理；4)自旋-轨道与Trees修正联合耦合机理，其中自旋-轨道耦合机理是最主要的，其他三种机理也是不可忽略的. 关键词： 基态能级 精细结构 零场分裂 自旋-自旋耦合     

简谐速度噪声及其与势场之间的频率共振

为了描述复杂的噪声环境，考虑了一种具有频率结构的噪声——简谐速度噪声，包括它的产生、关联函数、功率谱以及作为热噪声时的频率特性所导致的一些行为.结果表明：在频谱空间中简谐速度噪声是一种带通噪声，存在一个峰值频率，且噪声带宽由参量Γ控制.当简谐势中的一个布朗粒子受热简谐速度噪声驱动时，粒子能量极大值出现在两种频率相等的情况下.这表明噪声和势场的频率之间存在动力学共振，决定着粒子能量的大小. 关键词： 简谐噪声 简谐速度噪声 功率谱 频率共振     

掺入Ni元素的LiCoO2晶体光谱结构及电子顺磁共振g因子

在弱场图像下,利用Racah不可约张量算符方法得到了三角对称3d4/3d6电子组态的210阶可完全对角化的微扰哈密顿矩阵、最近邻点电荷模型晶体结构常量公式和电子顺磁共振g因子公式.研究了LiCoO2晶体和掺入Ni的LiCoO2:Ni晶体中Co3+的基态能级、晶体结构和电子顺磁共振g因子.考虑了LiCoO2晶体和LiCoO2:Ni晶体中自旋单重态和三重态对Co3+基态能级的影响,讨论了LiCoO2晶体和在LiCoO2晶体中掺杂Ni后Co3+局域结构常量大小的变化是引起Co3+的基态能级变化的主要原因,理论和实验都证实了这一点.还计算了掺杂前后的电子顺磁共振g因子,计算结果与实验值符合得较好.     

一种时延范德波尔电磁系统中的复杂行为(Ⅱ)——时空混沌图案动态

对于一个由线性无损传输线加非线性边界条件组成的简单无穷维电磁系统，应用行波理论确定了电压反射波的局部映射关系.数值仿真结果表明，当系统参数发生变化时，传输线沿线电压存在着非常丰富的时空非线性现象.通过描绘出空间振幅变化图和时空行为发展图，定性分析了传输线沿线电压的时空混沌图案动态，为研究和理解时空混沌提供了一种良好的可求解模型. 关键词： 图案 时空混沌 无穷维系统 时延范德波尔电磁系统     

科学和艺术

科学与完美是不是一致的？科学家们是否有权使用完美这个词？至少，对于物理学家和数学家来说答案是肯定的“是”．2002年，温伯格（Steven Weinberg）写道：“近代物理学的一些重要方程式是科学知识的永久部分，甚至比它们较早出现的美丽大教堂还要经久不衰．”1960年代，狄拉克（Paul A．M．Dirac）有句名言：“完整的方程式之完美较之它们适合实验结果更为重要．”1965年诺贝尔物理学奖获得者费因曼（Richard P．Feynman）也坚信他提出的一项理论，即使该理论显得与实验数据有矛盾．1957年，他写道：“理论是优雅和完美的，重大事件是短暂的闪光．”     

Using multi-exposure of color fringes to measure the beating motion of a moth

A multi-exposure of color fringes method has been developed to improve the capture speed of a conventional color CCD camera. In the method, four groups of projected fringe patterns encoded with different colors and different directions are stored in one CCD frame. Therefore the capture frequency of the conventional CCD can be improved to 200 Hz. It is available to measure the insect wings with low beating frequency, such as dragonfly, moth, or butterfly, whose beating frequency is about 30–40 Hz. We have used the method to measure the beating motion of a moth successfully.     

Energy loss effect in high energy nuclear Drell-Yan process

The energy loss effect in nuclear matter, which is a nuclear effect apart from the nuclear effect on the parton distribution as in deep-inelastic scattering process, can be measured best by the nuclear dependence of the high energy nuclear Drell-Yan process. By means of the nuclear parton distribution studied only with lepton deep-inelastic scattering experimental data, the measured Drell-Yan production cross sections for 800 GeV proton incident on a variety of nuclear targets are analyzed within the Glauber framework which takes into account the energy loss of the beam proton. It is shown that the theoretical results with considering the energy loss effect are in good agreement with the FNAL E866 data.Arrival of the final proofs: 24 June 2003     

加权二次有理Bézier插值曲线

在本文中,给定一组有序空间数据点列及每个数据点的切矢向量,利用加权二次有理Bézier曲线对数据点作插值曲线,使该曲线具有C1连续性,并且权因子只是对相应顶点曲线附近产生影响,同调整两个相邻的权因子可以调整这两个相邻顶点之间的曲线和它的控制多边形.