边界类光的常r阶F-平均曲率类空超曲面

设■是以(n-1)-维圆球面为类光边界的紧致类空Wullf形,对应的F(t(v))是Hⁿ上的满足某凸条件的旋转不变函数.本文利用度量扰动和积分公式的方法,证得Lⁿ⁺¹中与■相切于边界且有常r阶F-平均曲率(2≤r≤n)的类空超曲面必为W₍F(t)).     

树上p-Laplacian算子的第一混合特征值

本文研究了树上以唯一根为Dirichlet边界的离散加权p-Laplacian算子的第一特征值问题,该特征值亦为一类加权Hardy不等式的最优常数.通过研究此特征值对应的特征函数的性质,给出具有混合边界的特征值的三种变分公式,该结果可以看做经典变分公式的重要补充.作为应用,给出了此特征值的上、下界的基本估计,并给用两个例子例证相关结果.     

三维快速多极边界元法分析地埋管群传热问题北大核心CSCD

基于三节点三角形线性单元,为克服单元跨叶子积分难题,将三维位势问题快速多极边界元法与几乎奇异积分的半解析算法相结合,实现了三维边界元法中几乎奇异积分的准确计算,该方法适用于U型地埋管薄体结构的换热分析.在制冷、制热两种工况下研究了U型地埋管壁厚对换热量的影响,并进一步分析了管群间的热相互作用.计算结果显示,当管壁导热系数一定时,管壁越厚,对管内流体和土壤之间的换热影响越大.当钻孔间距一定时,管群中埋管数量越多,热干扰现象越强烈,提高管群换热量的主要措施是降低管群间热干扰.因准确计算了几乎奇异积分,三维快速多极边界元法可以有效计算薄体和厚体耦合的三维热传导问题.该文方法和分析结果可为地埋管换热器系统的工程应用提供参考.     

栅极和阴极的相对高度对电子传输比的影响

用边界元法(BEM)和Monte Carlo方法,对一种基于碳纳米管场发射大面积彩色平面型显示器的电子传输比进行了理论分析,通过模拟跟踪发射电子轨迹,证实改变阴极和栅极的相对高度,可以较大幅度地提高电子传输比阳极上电子的分布证实,我们设计的显示器结构能够满足高分辨率、高亮度的显示的要求,而且驱动电压低,工艺简单。     

小攻角下三维细长体定常空化形态研究

基于边界元方法, 使空泡表面和细长体表面分别满足Dirichlet 边界条件和Neumann边界条件, 数值迭代获得小攻角下三维细长体的定常空化形态. 采用线性三角形单元, 将控制点布置在网格节点上, 应用局部正交坐标系并采用迭代方法获得空泡表面的速度势, 进而通过边界积分方程确定空泡厚度的分布. 采用拉格朗日插值方法得到空泡末端的厚度, 避免了迭代过程中网格的重新划分. 数值结果与实验值符合良好, 验证了该方法的合理性. 系统研究了空化数、攻角以及锥角对于三维细长体空化形态的影响规律. 数值结果表明: 攻角使得细长体的空化形态呈现不对称性, 出现空泡向背流面“堆积”的现象; 而空化数越小或锥角越大, 空泡形态的不对称性将越严重. 关键词： 边界元方法 三维细长体 局部空化 攻角     

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.     

Series Solution for Unsteady Boundary-Layer Flows Due to Impulsively Stretching Plate

The third-order nonlinear partial differential equation modelling the unsteady boundary-layer flows caused by an impulsively stretching fiat plate is solved by using the Adomian decomposition method （ADM）. The ADM yields analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The series solution using the ADM for the unsteady flows is presented for the first time.     

用多重网格技术求解平面叶栅跨音绕流

1982年以来,Ni、Davis等人发展了一种与多重网格技术相结合的时间相关有限体积积分方法,这是一个快速求定常解的显式推进方法。本文采用这种方法计算平面叶栅跨音绕流,阐明了Ni-Davis格式的基本思想和处理原则,在物面边界近似处理上本文作了适当改进,为适当选取人工粘性项提出了具体平滑公式,又根据数值试验对多重网格技术提出了改进算法。两个跨音叶栅绕流算例表明,数值结果的精度和计算效率是令人满意的,可以满足航空发动机气动设计的需要。在IBM 4341计算机上,求解一个65×17网格上的跨音流场大约需CPU时间15分钟,使用四层网格技术后可节省CPU时间50%到60%。     

Calculation of the Griffith COhesive Energy of the Ni3AlBx Symmetrical Grain Boundary

A Monte Carlo simulation,with the energetics described by the embedded atom method,has been employed to study the physical behaviour of boron atoms during relaxation of the Ni3AlBx grain boundary,It has also been used to calculate not only the peak concentrations of Ni and B and the valley concentration of Al at the grain boundary,but also the dependence of the grain boundary cohesion on the B bulk concentration.During relaxation of impure Ni3Al grain boundaries,we suggest that,as the segregating species,the B atoms either insert into interstices in the grain boundary or substitute Ni atoms.Meanwhile,as the inducing species,they induce Ni atoms to substitute for Al atoms.Calculations show that in the equilibrium,when the B bulk concentration x increases from 0.1 to 0.9 the peak concentration of B increases,the peak concentration of Ni maximizes while the valley concentration of Al minimizes at x=0.5,The calculations also show the best cohesion of the grain boundary at x=0.5。