伴有化学反应的磁流体传热传质混合对流流经吸入/喷出多孔楔形体时的局部非相似解

研究伴有化学反应的流经多孔楔形体的,传热传质磁流体的自由、受迫和混合对流.使用结合打靶法的Runge-Kutta-Gill方法,和直到3阶截断误差的局部非相似法,将偏微分的控制方程简化为9个常微分方程.通过Falkner-Skan变换,将边界层控制方程表示为无量纲形式.由于楔形体壁面的吸入/喷出,以及可变的壁面温度和浮力的影响,使得流场呈局部非相似性.就一些特定的无量纲参变数,给出具有3阶截断误差的数值计算.图形显示可变壁面温度和浓度条件下,伴有化学反应时磁场强度对无量纲速度、温度和浓度分布的影响.     

T型分叉血管的定常/脉动流动和大分子传质

采用计算流体动力学方法,数值求解了T型分叉流动的定常/脉动流场和低密度脂蛋白(LDL)以及血清白蛋白(Albumin)的浓度分布。计算了雷诺数、主管和支管的流量比等参数对流场和大分子传质的影响,计算结果表明,流体动力学因素影响大分子的分布和跨壁渗透,在动脉硬化的发生和发展过程中起着重要的作用。在流动发生分离处,即支管入口外侧壁面剪应力变化最剧烈,这儿LDL和Albumin的壁面浓度变化也是最剧烈,是动脉硬化危险区。     

微通道内电渗压力混合驱动幂律流体流动模拟

为了研究微通道内电渗压力混合驱动幂律流体的流动特性,建立了微通道内电渗压力混合驱动幂律流体的计算模型,其双电层电势、流体的流场分布分别由Poisson-Boltzmann(P-B)方程和Navier-Stokes(N-S)方程描述.讨论了无量纲Debye(德拜)参数K、壁面ζ*电势和幂律指数n对流体流动特性和Poiseuille数的影响.结果表明,当压力梯度与外加电场方向一致(Γ0)时,剪切变稀流体的速度大于剪切变稠流体;压力梯度与外加电场方向相反(Γ0)时,结果相反.Poiseuille数是无量纲Debye常数K、壁面ζ*电势和幂律指数n的增函数.     

非Darcy多孔介质中的非线性对流

利用温度-浓度-密度关系,研究非Darcy多孔介质中的自由对流问题.对于不同的惯性参数、传递参数、Rayleigh数、Lewis数、Soret数和Dufour数,分析了非线性温度参数和浓度参数对非线性对流的影响.浮力对对流起着辅助的附加作用,当惯性作用不计时,切向速度随着非线性温度和浓度的增加而急剧地增加.然而,当惯性效应不为0时,非线性温度和浓度对切向速度的影响是有限的.对两个传递参数、惯性影响参数以及控制非线性温度和浓度的其他参数,取不同的数值时,浓度分布有点儿变化,并在不同的范围内传播.随着非线性温度和浓度的增加,传热/传质在很大的范围内变化,这取决于是Dacry多孔介质,还是非Darcy多孔介质.当所有的影响(惯性的影响、两个传递系数的影响、Soret和Dufour的影响)同时为0/不为0,在非线性温度/浓度参数以及浮力的共同作用下,分析了传热/传质的变化.发现在Darcy多孔介质中,温度和浓度以及它们的交叉扩散,对传热/传质的影响,要比非Darcy多孔介质要大.发现了浮力的负面作用,随着非线性温度系数的增加,传热/传质率是提高的,而随着非线性浓度系数的增加,传热/传质率是下降的.     

传导-辐射和磁流体组合对磁化可渗透平板自然对流影响的数值解法

研究粘性、不可压缩、导电流体,在磁化可渗透竖直平板上作自然对流时,数值地分析辐射和磁流体组合的影响.采用两种方法数值地求解非相似的控制方程:1)对所有吸入参数值ξ,采用有限差分法;2)为小数值和大数值的吸入参数值ξ,分别建立起级数的渐近解.用图形和列表形式,给出Prandtl数Pr,磁Prandtl数Pm,磁力参数S,辐射参数Rd,壁面温度θw的变化,对壁面摩擦因数、热交换率和电流密度的影响.最后分析上述物理参数对速度分布、温度分布和磁场横向分量的影响.     

化学反应对流过半无限垂直多孔板的粘性耗散非定常磁流体流动的影响

分析了化学反应,对流过半无限竖直多孔板的、粘性耗散的、非定常的磁流体流动的影响．利用随时间变化的相似参数,将运动、能量、溶质的控制方程变换为常微分方程,并用有限单元法数值地求解所得到的常微分方程．用图形给出了不同参数对速度、温度和浓度分布的影响,用表格给出了不同物理参数值时,表面摩擦力、Nusselt数和Sherwood数的数值．     

粘性耗散和热源对含尘流体在不稳定伸展面上流动及其传热的影响

研究含尘流体在不稳定伸展面上,作水动力学边界层流动及其热交换问题.研究中计及摩擦生热(粘性耗散)和内部发热或吸热的影响.应用适当的相似变换,将控制流动和热交换的基本方程组,变成一组非线性的常微分方程.利用Runge-Kutta-Fehlberg-45格式对变换后的方程进行数值求解.按发热进程分两种不同情况分析:VWT(变壁面温度)和VHF(变热通量).物理参数,如像磁场参数、流(体)-固(体微粒)的相互作用参数、不稳定参数、Prandtl数、Eckert数、含尘微粒的数量密度以及热源/汇参数,分别绘出这些物理参数变化时的速度和温度分布曲线;同时,列表和讨论了对壁面温度梯度函数和壁面温度函数的影响.     

NA随机变量的递归密度核估计的渐近正态性

设{Xn,n≥1}为同分布的NA样本序列，其未知概率密度函数为f(x),基于样本X1,…,Xn，用递归密度核估计fn(x)=1/n∑j=1 n 1/hj K(x-Xj/hj)对f(x)进行估计。本文研究了在一定条件下，fn(x)的渐近正态性。     

一类Kn-同胚图色等价类的结构特征

用K（s，n）表示完全图Kn的一条边被长为s（s≥2）的路Ps＋1替代后得到的图．对n≥7，且n-2为素数，刻画了色等价类【K（s，n）]中图的结构特征，进一步，证明了任意任意n≥7，且n-2为素数，K（2，n），K（3，n）是色唯一的．     

在柱坐标系下研究由拉伸缸引起的Casson纳米流体流动与传热传质现象

首次利用柱坐标研究速度滑移和对流表面边界条件下,由拉伸缸引起的稳态层流Casson纳米流体流动、传热及传质现象.采用恰当的相似变换将偏微分控制方程转化为高阶非线性耦合常微分方程,并通过打靶法进行数值求解,图示并详细分析了不同物理参数对速度、温度及浓度分布的影响.结果显示,速度受滑移参数的影响较大,温度和浓度分别受Biot数和Lewis数的影响较大;随着Casson参数的增大,速度下降而温度和浓度都增加;温度随着Brown(布朗)运动参数或热泳参数的增加而上升;浓度随着Brown运动参数的增大而减小,随着热泳参数的增大而增大,当热泳参数较大时,浓度出现了"回流"现象.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].