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.     

巧用齐次化与非齐次化的思想解不等式竞赛题

解析式是中学数学的重要内容之一,也是研究函数、方程、不等式的基础,数学的其它各分支学科均离不开解析式的恒等变换.因此,熟练地掌握一些解析式的变形规律是学好代数及相关学科的前提.本文主要讨论如何利用齐次化与非齐次化的思想,解决一些竞赛中的不等式问题.定义1设xi≥0(i     

谐和与随机噪声联合作用下Van der Pol-Duffing振子的参数主共振

研究了Van der Pol-Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题。     

用Riccati变换求解同调谐振子

利用Riccati变换求解同谐谐振子的定态薛定谔方程,求得了能谱及态函数 关键词： 同调谐振子 本征值谱 Riccati变换法     

赤道不是轨道弧的n次多项式向量场的Poincaré紧化场之拓扑结构

本文证明了赤道不是轨道弧的n次多项式向量场的Poincare紧化场之拓扑结构包含赤道是轨道弧的n-1次多项式向量场的Poincare紧化场之拓扑结构;当n=2时,这种包含关系是相等的,且其Poincare紧化场有五种不同的拓扑结构;当n=2k+1(k=1,2…)时,这种包含关系是真子集。     

(111)择优取向的Pb(Zr0.52Ti0.48)O3铁电薄膜的制备及研究

选用不同浓度的Pb(Zr_0.52Ti_0.48)O₃溶胶，用Sol-gel法在Pt/Ti/SiO₂/Si基片上沉积一层厚度不同的Pb(Zr_0.52Ti_0.48)O₃ (PZT52)过渡层，经400℃烘烤、550℃退火等程序后，再用Sol-gel法在PZT52过渡层上沉积Pb(Zr_0.52Ti_0.48)O _{关键词： PZT铁电薄膜 择优取向 过渡层 剩余极化强度}     

A comparative study of the structure and crystallization of bulk metallic amorphous rod Pr60Ni30Al10 and melt-spun metallic amorphous ribbon Al87Ni10Pr3

Pr-based bulk metallic amorphous （BMA） rods （Pr60Ni30Al10） and Al-based amorphous ribbons （Al87Ni10Pr3） have been prepared by using copper mould casting and single roller melt-spun techniques, respectively. Thermal parameters deduced from differential scanning calorimeter （DSC） indicate that the glass-forming ability （GFA） of Pr60Ni30Al10 BMA rod is far higher than that of Al87Ni10Pr3 ribbon. A comparative study about the differences in structure between the two kinds of glass-forming alloys, superheated viscosity and crystallization are also made. Compared with the amorphous alloy Al87Ni10Pr3, the BMA alloy Pr60Ni30Al10 shows high thermal stability and large viscosity, small diffusivity at the same superheated temperatures. The results of x-Ray diffraction （XRD） and transmission electron microscope （TEM） show the pronounced difference in structure between the two amorphous alloys. Together with crystallization results, the main structure compositions of the amorphous samples are confirmed. It seems that the higher the GFA, the more topological type clusters in the Pr-Ni-Al amorphous alloys, the GFAs of the present glass-forming alloys are closely related to their structures.     

行波型热声发动机的分布参数法热力分析

在现有热声网络模型的基础上 ,对行波型热声发动机采用分布参数法进行了详细地分析 ,得到了较为完整的分布参数法网络模型 ,并给出了该模型的定性关系式 ,所得结果与采用集总参数法的结果有很大差异。分析表明 ,分布参数法更适合于一般的系统情况 ,集总参数法仅仅在一定条件下才适用。文中对一个实际系统应用分布参数法进行了分析 ,得到一些结论 ,对于我们设计行波型热声发动机有非常重要的理论指导意义