关于湍流理论中的不封闭性的讨论*

有一种观点认为湍流的不封闭性是由于N-S方程的非线性,这是一似是而非的错误说法。因为工程上要求的量并不仅仅限于湍流的平均速度和平均压力,即使方程式是线性的,也无法把工程上要求的这些量逐个求出来。本文论证了湍流的不封闭性来源于目前的湍流理论中缺少了一个与实际情况符合的有关分布函数,并且进一步说明了湍流模式理论的局限性和用N-S方程直接计算机模拟亦是相当困难的原因。     

180°弯曲方管牛顿流体及一种非牛顿流体湍性流动的数值模拟

运用湍流k-ε模式及实测壁面函数分别模拟牛顿流体(清水)及一种非牛顿流体(聚合物稀薄减阻溶液)流经180°弯曲方管的湍性流动,取得与实测速度分布吻合较好的结果.对于湍流模式对存在大涡的复杂流动的适应性,根据计算和试验结果进行了分析和讨论.     

突然扩张方管中三维湍流流动的数值模拟

本文运用SIMPLEC算法计算了突然扩张方管中的三维湍流流动,湍流模型采用k-ε模型。计算结果详细反映了突然扩张方管中三维湍流流场。从本文结果可以看出,由于突然扩张方管几何形状非轴对称,且尺寸有限,边壁对流场的作用是不可忽略的。以往文献中常见的二维突然扩张湍流的数值模拟结果与三维情况有较大差别,在靠近边壁的区域差别很大,因此对于突然扩张方管中湍流流动的数值模拟应用三维模拟。本文计算所得突然扩张截面后主回流区长度与实验结果接近。本文方法可为数值模拟突然扩张方管中湍流流场及各物理参数的分布提供有效工具。     

Navier-Stokes方程的求解和均匀各向同性湍流理论——数值计算和与实验的比较

本文是文献[2]的继续。主要是通过选择适当的初始条件,用数值方法进行求解。并把理论结果与实验作广泛的比较。文中计算了从衰变初期到衰变后期的整个过程的能谱函数、能谱交换函数、湍流能量的衰变、积分尺度、湍流微尺度、二元速度关联以及三元速度关联。所有计算的统计物理量与实验都符合得相当好,只在某些情况下测量间距较大时有些小的偏离。本文也证明了计算得的能谱函数和能谱交换函数,精确地满足谱空间的Karman-Howarth方程。     

大小涡旋分开考虑的模式理论

近年来,k-ε模式普遍流行,但它是一种梯度形式的模式理论。由于湍流涡旋的衰减时间极长,在一般的流动问题中,上游产生的大涡旋或附近产生的大涡旋在到达当地时还远远没有衰减掉,因此会对当地的流动产生很大的影响。根据不可逆热力学理论的基本原理,必须准平衡、准定常和小偏离的情形下,才能使用梯度形式的流和力的关系式。一般说来这对大涡旋是并不满足的,所以k-ε模式的应用有着很大的局限性。本文根据湍流的实际情况,把湍流脉动分成大涡旋和小涡旋两个组成部份,并且把大涡旋部份再分成局部产生的和上游流来或扩散过来的两个组成部份,这样就得到了由三个部份组成的湍流模式理论。     

不可压缩流体的湍流理论

本文从湍流Reynolds平均运动方程和逐阶速度关联的动力学方程出发,引进了准相似性条件和对关联方程中耗散项的假定,利用逐级近似方法发展了湍流理论.作为一级近似的应用例子,我们曾在忽略三阶关联项下,求解了湍流槽流,平面尾流和射流的平均运动方程和二阶关联方程,得到了理论和实验符合的结果. 本文在一级近似的基础上,进一步引进了三阶和四阶关联的方程作为二级近似,并求解了平面湍流尾流.得出的三阶关联的理论计算和现有的实验的比较是令人满意的.理论也给出了四阶关联。它可以用实验来验证.也可以用它求更高阶的关联.     

大雷诺数平稳湍流的Markov过程描述

湍流扩散是湍流理论中的一个重要问题,并对大气污染等问题具有重要的实际意义。自从Taylor的文章起,五十多年来,许多作者运用拉格朗日观点处理平稳湍流中的扩散问题,取得了不少进展.但至今尚未从理论上解决湍流扩散的概率分布问题,只有解决了这一问题,才箅得到湍流扩散的完整的统计描述。 本文对大雷诺数平稳湍流这一情况,解决了概率分布问题。通过物理分析,文中阐明了大雷诺数平稳湍流可用Markov过程描述;论证了Fokker-Planck方程应采用本文的系数,得到了单粒子运动与二粒子相对运动的转移概率函数,从而得到平稳湍流中单粒子运动及二粒子弥散的完整的统计描述。由此作为特例,证明了单粒子扩散规律与二粒子弥散规律均满足正态性,从而证明了Batchelor的正态假设。此外,作为本文结果的推论,从理论上证明了脉动速度服从正态分布这一著名的实验事实。 关于二粒子相对速度与距离的弥散规律,以及Richardson定律的适用范围,本文与林家翘和W.H.Reid以及E.Krasnoff和R.L.Peskin的结果一致。本文公式当βt<<1时的渐近式与Obukhov一致,从而指明了Obukhov所给方程的局限性。     

一类兰切斯特方程的广义变分迭代解

通过构造一组泛函,用变分迭代地方式研究了兰切斯特方程的各次近似解,这种近似解是解析解,还能继续进行各种解析运算.从而可进一步研究对兰切斯特方程进行定性及定量的研究.     

第三方再制造商回收规模效应对闭环供应链利润的影响

消费者异质需求下,在回收率能够满足市场需求时对比分析4种再制造生产模式;并在一方或双方回收率不能满足市场需求时,分析了原制造商和第三方再制造商同时从事再制造的两种模式,探讨了第三方再制造商的回收规模效应对双方的影响.结果表明:当回收率均可以满足需求时,原制造商利润在NRT和NRTS模式下最高,第三方再制造商在不具有回收规模效应时更倾向NT模式,而第三方再制造商在具有回收规模效应时会倾向NRTS模式;当一方或双方回收率不能满足需求时,在一定条件下第三方再制造商的回收规模效应可以同时增加自身和原制造商的利润.     

非线性非完整系统相对于非惯性系动力学的积分理论*

本文建立非线性非完整系统相对于非惯性系动力学的积分理论.首先,由这种相对运动的Routh方程给出系统的第一积分;其次,分别利用系统的循环积分、能量积分降阶运动方程,得到推广的Routh方程和推广的Whittaker方程;再次,建立这类系统运动的正则方程和变分方程,并由第一积分构造系统的积分不变量;然后,给出系统的Poincare-Cartan型积分变量关系和积分不变量.最后,给出一系列推论.     

卫星和飞船跟踪测控问题的数学模型

针对卫星和飞船跟踪测控的建站问题,基于几何关系和蜂巢式覆盖思想,依据不同情形建立了数学模型,求得实现全程测控时所需最少测控站个数．分析了神舟七号测控站的测控范围．并对模型加以验证．     

对西蒙斯模型的改进及其估计量

针对属性特征的敏感性问题的西蒙斯模型提出了改进方法 ,包括随机方法和确定方法 .讨论了其估计量相应的统计性质及两种方法的适用范围 ,结论表明改进方法的统计性质优于西蒙斯模型 .     

Rate Functions for Symmetric Markov Processes via Heat Kernel

By making full use of heat kernel estimates, we establish the integral tests on the zero-one laws of upper and lower bounds for the sample path ranges of symmetric Markov processes. In particular, these results concerning on upper rate bounds are applicable for local and non-local Dirichlet forms, while lower rate bounds are investigated in both subcritical setting and critical setting.     

Characterization of best uniform approximation with restricted ranges of derivatives

This paper gives a general characterization theorem of a best uniform approximation of generalized polynomial having multiple restricted ranges of its derivatives. This theorem is widely applicable. The results on characterization in many standard approximations, such as approximation with Hermite-Birkhoff interpolatory side conditions, multiple comonotone approximation, and approximation by algebraic polynomials having bounded coefficients, etc., are special cases of our results.     

系数与值域双重约束下最佳同时逼近的特征定理的推广

１９８５年，Ｈ．Ｓｔｒａｕｓｓ在广义多项式的系数和值域同时受约束的情况下约出了最佳同时逼近的一个特征定量。本文在弱得多的条件下用不同方法证明了一个适用性更广的特征定理。     

Some Practical Aspects of the Verification and Validation of Simulation Models

This paper reviews the philosophical questions of model validity and describes the need for practical tests of the adequacy and representativeness of computerized simulation models. The distinction between the concepts of the verification and the validation of such general models is made by means of a delineation of test procedures, primarily those of a statistical nature, which are applicable to the determination of a simulation model's adequacy.     

Energy models for planning and policy assessment

The paper reviews energy models which have been applied to planning and policy assessment questions. It describes the history and methods of the early models, which had been developed for industrial purposes in the sixties. It illustrates how the scope of the model development and application changed during the seventies towards more universal applicable models of the total energy system and finally to models encompassing energy-economy interactions. The energy models applied today are mostly very large systems due to the complexity of the problems described. They consist sometimes of an integrated programming system, but in a few cases a set of disconnected models with different techniques are used.A general survey of energy models is given with the purpose to present the broad categories of some of the well-known models in comparative form, discuss their content and application and provide a classification. A selection of three models which are typical representatives for particular categories is reviewed in detail and then follows an outlook for areas of future improvements.     

Discrete May–Leonard Competition Models I

The local dynamics of two discrete-time models applicable to three competing plant species are shown to have properties similar to the May–Leonard (M-L) differential equation model. The dynamics of the two discrete models are shown to be similar. However, they are not dynamically consistent with the continuous M-L model. Unlike the continuous M-L model, the Hopf bifurcations of the discrete M-L models are not degenerate. The continuous M-L model is the limiting case of the discrete models.     

Nonlinear filtering equations for two-parameter semimartingales

Nonlinear filtering equations for two-parameter semimartingales of a Brownian sheet are obtained by an extended reference probability method, also applicable to the known Gaussian linear models.     

Optimal and efficient designs for Gompertz regression models

Gompertz functions have been widely used in characterizing biological growth curves. In this paper we consider D-optimal designs for Gompertz regression models. For homoscedastic Gompertz regression models with two or three parameters, we prove that D-optimal designs are minimally supported. Considering that minimally supported designs might not be applicable in practice, alternative designs are proposed. Using the D-optimal designs as benchmark designs, these alternative designs are found to be efficient in general.