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.     

半导体带电粒子探测器的研制及其在空间物理中的应用

阐述了空间辐射环境监测的意义,描述了半导体带电粒子探测器的研制及由其组成的望远镜系统在空间物理中的应用,并给出了用此探测器在卫星上进行地球辐射环境监测、太阳质子事件和地磁暴探测的部分结果.     

A Strongly and Superlinearly Convergent SQP Algorithm for Optimization Problems with Linear Complementarity Constraints

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998), 5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.     

The 4s 24p 3-4s4p 4 transition in AsI-like AgXV

Some terms of the 4s4p ⁴ configuration in RuXII, RhXIII and PdXIV ions can be improved and all the energy values of the configuration in AgXV can be predicted theoretically by means of a configuration-interaction ab initio analysis for the level structure of the 4s4p ⁴ configuration along the AsI sequence of KrIV-AgXV ions. Calculations of the wavelengths and oscillator strenghts are presented for the 4s ²4p ³-4s4p ⁴ transition in AgXV.     

气体团簇离子束两步能量修形法的平坦化效应

本文提出采用气体团簇离子束的两步能量修形法来改善4H-SiC(1000)晶片表面形貌.先用15 keV的高能Ar团簇离子进行整体修形,再用5 keV的低能团簇离子优化表面.结果表明,在相同的团簇离子剂量下,与单一15 keV的高能团簇处理相比,两步法修形后的表面具有更低的均方根粗糙度,两者分别为1.05 nm和0.78 nm.本文还以原子级平坦表面为研究对象,揭示了载能团簇引起的半球形离子损伤(弧坑)与团簇能量的关系,及两步能量修形法在弧坑修复中的优势.在原子力显微镜表征的基础上,引入了二维功率谱密度函数,以直观全面地给出材料的表面形貌特征及其随波长(频率)的分布.结果表明,经任何能量的团簇离子轰击的表面,在0.05—0.20μm波长范围内,团簇轰击都能有效地降低粗糙度,而在0.02—0.05μm范围内,则出现了粗化效应,这是由于形成了半球形离子损伤,但第二步更低能量的团簇离子处理可以削弱这种粗化效应.     

银负载量对网状TiO_2柔性薄膜电极储锂性能的影响

采用水热法结合银镜反应制备出一系列不同Ag负载量(2.2%、4.0%、6.4%,w/w)改性的3D纳米网状结构Ag@Ti O2薄膜电极。利用电感耦合等离子体技术(ICP)、X射线衍射(XRD)、扫描电镜(SEM)、透射电镜(TEM)和X射线能谱(EDX)等表征手段测试所合成材料的形貌及成分,实验结果表明Ag纳米颗粒可以成功沉积在Ti O2纳米线表面。电化学测试数据则表明,4.0%(w/w)负载量的Ag@Ti O2相比于未改性和其他负载量的Ti O2纳米线具有更好的倍率性能和更稳定的可逆容量。在50,100,200,400,800和1 200 m A·g~(-1)的电流密度条件下,该改性电极的放电容量可分别达到261.4,253.7,239.5,216.5,193.1和185.1 m Ah·g~(-1),在200 m A·g~(-1)下循环80次后容量保持率仍能达到99.8%。     

三层流体界面内波的二阶Stokes解

以小振幅波理论为基础，利用摄动方法研究了三层密度成层状态下的界面内波，求得了三层成层状态下各层速度势的二阶渐近解及界面内波波面位移的二阶Stokes解.结果表明：一阶解为正弦波解，与传统线性理论的结果相一致；二阶解描述了界面波的二阶非线性修正及两界面波之间的非线性相互作用；一阶解及二阶解都依赖于各层流体的厚度及密度.Umeyama导出的理论结果为本文的特殊情形. 关键词： 三层密度成层流体 内波 二阶Stokes解 小振幅波理论     

组合KdV方程的显式精确解

借助计算机代数系统Mathematica，利用双曲函数法找到了组合KdV方程(Combined KdV Equation)的精确孤立波解，包括钟型孤立波解和扭结型孤立波解.在此基础上又对双曲函数法的思想进行了推广，从而获得了其更多的显式精确解，包括间断型激波解和指数函数型解.这种方法也适用于求解其他非线性发展方程(组). 关键词： 组合KdV方程 双曲函数法 孤立波解 精确解     

三层流体系统非线性界面内波传播理论的研究

基于波陡很小的假设, 利用摄动法, 讨论了任意深度的二维不可压缩、无黏性、无旋的三层流体系统. 在刚性上边界、平底不可渗透条件下, 给出了界面内波传播的统一理论以及描述其波剖面的近似非线性演化方程(NEEs). 最后讨论了几种特殊情形下的近似NEEs.结果表明文献导出的理论结果为本文的特殊情形.     

Effects of Buoyancy on Langmuir Circulation

Based on the Navier-Stokes equation, an equation describing the Langmuir circulation is derived by a perturbation method when the influences of Coriolis force and buoyancy force are both considered. The approach used in the analysis is similar to the works carried out by Craik and Leibovieh [3. Fluid Mech. 73 （1976）401], Leibovieh [3. Fluid Mech. 79 （1977） 715] and Huang [3. Fluid Mech. 91 （1979） 191]. Potential applications of the equation proposed are discussed in the area of Antarctic circumpolar current.