血液流动与血管壁运动

本文讨论了哺乳动物循环系统的血液流动与血管壁运动之间的相互作用问题.在假定流动处于稳定的振荡流动情况下,导得了一组血液流动速度分布公式,压力分布公式以及约束应力公式,管壁位移公式.把Kuchar的公式从定常流动情况推广到非定常的振荡流动情况.文中还讨论了动脉血管壁的弹性效应问题.     

圆锥形血管中的振荡发展流动

本文在小锥度角的假设下,研究了圆锥形血管的非定常振荡的发展流动问题.导得了相应的速度分布公式.分析表明,所有收缩的圆锥形血管的流动都是发展流动,而且锥度角对发展流动的影响随着锥度角的增大而增大.     

等腰三角形管道进口段流动阻力研究

本文首先利用Л.В.Канторович变分方法求出了等腰三角形管道不可压缩流体层流完全发展段流动速度的变分解,并且给出了压力损失的理论计算值与实验值.继而,本文推求出适用于各种顶角的等腰三角形管道进口段流动的速度分布模型和附加压力损失系统以及进口段长度计算方法.并对两种顶角(2α=45.1°,60°)的等腰三角形管道进口段流动进行了具体计算和实验.本文的理论分析与其他作者的理论分析比较表明,本文的分析结果具有很高的精度和广泛的实用性,并与作者的实验结果吻合较好.     

高速流动激光器的稳定振荡条件、模式结构与输出功率特性

本文直接由辐射场方程与边界条件导出了高速流动激光器的稳定振荡条件,指出了文献[1]所假定的稳定振荡条件仅在一定条件下近似成立,用本文得到的稳定振荡条件与文献[2]的饱和增益公式导出了GDL输出功率表达式,指出了输出功率与GDL各种参量之间的关系,用几何光学近似导出了光腔模式的解析表达式,指出了充有流动激活介质的Fabry-Perot腔的模式结构与特征.文中对Gerry的典型实验进行了计算.     

锥面间流体流动考虑流动惯性的近似解

本文采用锥坐标下的Navier-Stokes方程式,利用迭代近似解法,求出了考虑流动惯性时锥面间流体流动的速度分布、压力分布以及流量的解析式;并对轴对称过流流动的外向流和内向流进行了比较.     

湍流边界层外区大尺度相干结构的理论模型及与实验的比较

本文基于流动稳定性理论,提出了一种解释湍流边界层外区大尺度相干结构产生机理的理论模型.将计算所得流线、等涡线分布及利用相干结构理论模型计算湍流边界层中平均温度分布的结果与实验比较,结果是比较满意的.     

论流动稳定性中的弱非线性理论

弱非线性理论提出已有30多年,被广泛用于流动稳定性及其他领域的问题.但能与实验比较并证实其有效性的理论计算结果很少.本文研究了其原因,发现主要是平均流修正的计算方法有问题,导致它的结果与数值模拟的结果吻合得不好.提出了正确的算法,结果相当满意.     

经过修正的层流流动的流动稳定性问题(Ⅲ)——经过修正的平行剪切流的非线性稳定性研究

本文根据文[1]给出的经过修正的层流流动的流动稳定性理论及平行剪切流中平均速度的一类修正剖面,研究了平行剪切流的非线性稳定性性质,并在本文的假设下,把背景湍流噪声的干扰引入了流动稳定性计算,对于平面Poiseuille流动和圆管Poiseuille流动,得到了与实验趋势相一致的结果.     

解任意形状扁轴对称体Stokes流动的连续奇点分布法

本文以Sampson球形无穷级数作为基本奇点,采用分段等强度和分段二次抛物分布两种体内连续分布法解任意形状扁轴对称体的Stokes流动.通过扁球的无界绕流问题,对这两种方法的收敛性,精度和适用范围做了检验和比较.结果表明,在一定的范围内,无论是阻力系数或压力分布,它们的计算结果都和精确解符合得很好,而且,随着分布函数逼近程度的提高,其收敛性得到改善,适用范围也随之扩大.作为一般算例,分别用这两种方法解决了卡西尼扁卵形体的绕流问题,得到了一致的结果.最后,用分段二次连续分布法计算了具有一定生理意义的红细胞体的Stokes流动,首次得到了它的阻力系数和表面压力分布.     

环空管内粘弹性流体不定常旋转流的解及流动特性分析

本文用Hankel积分变换法分别求得二阶流体和Maxwell流体在环管内不定常旋转流运动方程的解析解,据此可以分析环管内旋转速度和切应力的分布与变化特征;流体物性参数、管道环隙大小等参量在解析公式中有明确反映,便于定性分析和讨论,本解可以为钻探工程和高分子加工工艺的设计提供理论依据,另外还可用来分析双筒粘度计的流动状态和应力特征,拟合曲线,确定材料的粘弹性参数,在对这种流体进行特性分析时,我们发现,Maxwell流体的旋转流动在起动初期表现为方波振荡,振动的幅度和周期随Ha(物质常数)的增大而增大,此种现象还是首次发现,可能对实际应用有一定的意义。     

Inertia Effects in Squeeze Flows of Viscoplastic Fluids

A squeeze flow of a viscoplastic fluid through a narrow clearance between two coaxial surfaces of revolution is considered. The problem is described by boundary-layer equations. With the use of the method of integral approaches, formulas for the pressure distribution are obtained. Generally, the flow of viscoplastic fluids given by the nonlinear Shulman model is considered. The flows of viscoplastic fluids given by the Herschel, Bulkley, Bingham, Ostwald-de Waele, and Newton models are discussed in detail. Numerical examples of pressure distributions in the clearance between parallel disks are presented.     

双约束孤立子流的可积形变

提出了基于Lax矩阵的构造双约束孤立子流的可积形变的新方法.作为应用,导出了双约束KdV流和双约束mKdV流的可积形变,并给出了这些形变的Lax表示、r-矩阵和守恒积分.     

Counting Integer Flows in Networks

This paper discusses analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory, representation theory, and statistics. Our methods are based on the study of rational functions with poles on arrangements of hyperplanes; they surpass traditional exhaustive enumeration and can even yield formulas when the input data contains some parameters. We also discuss the calculation of chambers in detail because it is a necessary subroutine.     

带激波的一维非定常两相流动的数值模拟

本文将处理带激波的单相气体非定常流动问题的两种高分辨数值方法(随机取样法和二阶GRP有限差分法)推广应用于气固悬浮体(亦称含灰气体)两相情况,计算了含灰气体激波管中两相激波特性、波后流场结构及气固两相流动参数随时间的变化.数值结果表明:这两种方法均能给出带有尖锐间断阵面的两相激波松弛结构.二阶GRP方法在计算精度和机时耗用等方面优于随机取样法.     

Long Eddies in Sheared Flows

The characteristic feature of the wide variety of hydraulic shear flows analyzed in this study is that they all contain a critical level where some of the fluid is turned relative to the ambient flow. One example is the flow produced in a thin layer of fluid, contained between lateral boundaries, during the passage of a long eddy. The boundaries of the layer may be rigid, or flexible, or free; the fluid may be either compressible or incompressible. A further example is the flow produced when a shear layer separates from a rigid boundary producing a region of recirculating flow. The equations used in this study are those governing inviscid hydraulic shear flows. They are similar in form to the classical boundary layer equations with the viscous term omitted. The main result of the study is to show that when the hydraulic flow is steady and contained between lateral boundaries, the variation of vorticity ω(ψ) cannot be prescribed at any streamline which crosses the critical level. This variation is, in fact, determined by (1) the vorticity distribution at all streamlines which do not cross the critical level, by (2) the auxiliary conditions which must be satisfied at the boundaries of the fluid layer, and by (3) the dimensions of the region containing the turned flow. If at some instant the vorticity distribution is specified arbitrarily at all streamlines, generally the subsequent flow will be unsteady. In order to emphasize this point, a class of exact solutions describing unsteady hydraulic flows are derived. These are used to describe the flow produced by the passage of a long eddy which distorts as it is convected with the ambient flow. They are also used to describe the unsteady flow that is produced when a shear layer separates from a boundary. Examples are given both of flows in which the shear layer reattaches after separation and of flows in which the shear layer does not reattach. When the shear layer vorticity distribution has the form ωαyⁿ, where y is a distance measure across the layer, the steady flows are of Falkner-Skan type inside, and adjacent to, the separation region. The unsteady flows described in this paper are natural generalizations of these Falkner-Skan flows. One important result of the analysis is to show that if the unsteady flow inside the separation region is strongly sheared, then the boundary of the separation region moves upstream towards the point of separation, forming large transverse currents. Generally, the assumption of hydraulic flow becomes invalid in a finite time. On the other hand, if the flow inside the separation region is weakly sheared, this region is swept downstream and the flow becomes self-similar.     

Flow does not Model Flows up to Weak Dihomotopy

We prove that the category of flows cannot be the underlying category of a model category whose corresponding homotopy types are the flows up to weak dihomotopy. Some hints are given to overcome this problem. In particular, a new approach of dihomotopy involving simplicial presheaves over an appropriate small category is proposed. This small category is obtained by taking a full subcategory of a locally presentable version of the category of flows. Mathematics Subject Classifications (2000) 55P99, 68Q85, 18A32, 55U35.     

流体层流运动稳定性中的Ляпунов方法

本文是[1]的继续.在本文中,利用[1]的结果我们证明了,对于流体的层流运动稳定性而言,在线性化问题中,按特征值定义与按扰动能量定义二者是完全等价的,从外,借助于Ляпунов方法,我们又证明了,如果线性化问题是渐近稳定的,当考虑非线性影响时,只要扰动能量足够小,则仍然是渐近稳定的.     

The Effect of Mean Flows on Enhanced Diffusivity in Transport by Incompressible Periodic Velocity Fields

Avellaneda and one of the authors ([1], [3]) have recently established that an upper bound for the enhanced diffusivity in the large scale, long time advection-diffusion with periodic steady incompressible velocity fields has the form where Pe is the Peclet number and is the reciprocal of the Prandtl number. In this paper, flow fields with maximal and minimal enhanced diffusion are studied. Maximal enhanced diffusion requires that in some directions the enhanced diffusion tensor also has the lower bound . For minimal enhanced diffusion, the effect of the velocity field is to boost the enhanced diffusivity by a negligible amount that is bounded by a fixed constant times the bare diffusivity regardless of Peclet number. Stieltjes measure formulas are used to develop a simple, necessary, and sufficient condition for maximal enhanced diffusion and also to characterize minimal enhanced diffusion. It is established here that constant mean flows can have a dramatic effect on maximal and minimal enhanced diffusion. In particular, for flows in two space dimensions, an explicit criterion is developed that guarantees the surprising fact that mean flows with rational ratios typically generate maximal enhanced diffusion through interaction with an arbitrary steady periodic incompressible flow with zero mean. In contrast, a simple criterion for flows without stagnation points is developed here that guarantees that the effect of mean flows with irrational ratios on advection-diffusion in two dimensions creates minimal enhanced diffusion. The theory for the phenomena mentioned above is elementary yet mathematically rigorous. Examples are emphasized throughout this work including a discussion of enhanced diffusivity for a class of flows recently introduced by Childress and Soward [8]. The theory developed here is also supplemented by a series of numerical experiments that both verify the theoretical predictions and display interesting crossover phenomena at rather large but finite Peclet numbers.     

Comparison of Random Cash Flows

In this paper we provide stochastic-dominance conditions forrandom cumulated cash flows, when various criteria of choiceare assumed. Three (progressively finer) criteria are considered.The first one assumes only the expected utility principle. Thesecond one involves discounting and preference scaling. Thethird one involves discounting and preference scaling, too,but in reverse order. Our results are finally compared withother known results for the case of nonrandom cash flows.