Payne-Whitham型宏观交通流模型波动特性

宏观交通流模型将交通流比拟成流体流,通过整体变量如交通流量、平均车速以及交通密度来研究其整体性质,得到了越来越多的肯定.文章采用波前展开的方法,研究Payne-Whitham型宏观交通流模型描述扰动沿交通流波动的特性,同时给出了相应的稳定性条件.最后利用Padé逼近法进行数值仿真,得到的结果与理论分析相一致.     

Stokes flow in a junction of two-dimensional orthogonal channels

The purpose of this study is to calculate Stokes flow structures in relation to flow rate distribution in a junction of four orthogonal channels. Particular attention was paid to the existence of recirculation flow inside the channels for low Reynolds numbers. The presence of this recirculation flow may be observed, but only when the flow rate is relatively low in at least one of the branches.     

Stokes flow in a junction of two-dimensional orthogonal channels

The purpose of this study is to calculate Stokes flow structures in relation to flow rate distribution in a junction of four orthogonal channels. Particular attention was paid to the existence of recirculation flow inside the channels for low Reynolds numbers. The presence of this recirculation flow may be observed, but only when the flow rate is relatively low in at least one of the branches.     

Finite-volume modelling of system with compressible flow propelled and actuated body motion

A finite-volume model for the gas flow in a compressible flow driven system with two moving components is developed and applied. In this system, high pressure and temperature compressible flow propels one body along a main flow channel. When this body passes an opening in the main flow channel, some of the high pressure gas bleeds off, entering a secondary, telescoping, flow channel that empties into a plenum. The bleed-off flow causes the pressure in the plenum to increase, actuating the motion of a secondary (actuated) body that forms a bounding surface of the plenum, causing the plenum to expand and the secondary channel to lengthen.     

The Modulation Equations for the Asymptotic Suction Velocity Profile and the Ekman Boundary Layer

In this article two types of flows are considered, the asymptotic suction velocity profile, which is a nearly parallel flow, and the Ekman boundary layer, which is a nonparallel flow. The modified Orr-Sommerfeld equation for the asymptotic suction velocity profile, which is the linearized stability equation for this flow, is analyzed and it is shown to have finitely many eigenvalues. In addition, the Ekman boundary layer is considered and the modulation equation for this nonparallel flow is derived for the first time.     

Hyperbolic mean curvature flow

In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations is strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with dimension larger than 4. We derive nonlinear wave equations satisfied by some geometric quantities related to the hyperbolic mean curvature flow. Moreover, we also discuss the relation between the equations for hyperbolic mean curvature flow and the equations for extremal surfaces in the Minkowski space-time.     

Investigation of sediment transport at the interface of a porous and a free flow domain

Sediment transport involves fluid flow in two different regions. In the free flow domain, the flow is governed by the viscous Newtonian fluid; sediment only occurs as suspended particles. In the porous domain however, the flow is governed by the pore geometry of the porous skeleton consisting of sedimented grains. In nature, the interface between these two domains is not a no-slip boundary for the free flow. In this study, we quantify how sediment transport is affected by the interaction of the two different flows. We do this by comparing fluid flow in no-slip bounded flow channels to fluid flow in channels containing both a free and a porous domain. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

血液自然分布单位全面血液关系流的实现与维护

在全面关系流管理理论的基础上,研究人体血液自然分布单位组织全面血液关系流的实现与维护.实现关系流应该从关系流的性质、时间约束、血液自然分布单位的状态与行为,以及可行性等方面综合考虑.当全面关系流建立起来后,人体组织就基于血液关系流建立起自然法则,当血液关系流不再适用时,相关的血液自然分布单位需进行关系流的再设计,以适应新的组织行为.     

Minimum Maximal Flow Problem: An Optimization over the Efficient Set

The network flow theory and algorithms have been developed on the assumption that each arc flow is controllable and we freely raise and reduce it. We however consider in this paper the situation where we are not able or allowed to reduce the given arc flow. Then we may end up with a maximal flow depending on the initial flow as well as the way of augmentation. Therefore the minimum of the flow values that are attained by maximal flows will play an important role to see how inefficiently the network can be utilized. We formulate this problem as an optimization over the efficient set of a multicriteria program, propose an algorithm, prove its finite convergence, and report on some computational experiments.     

The Ricci flow in a class of solvmanifolds

In this paper, we study the Ricci flow of solvmanifolds whose Lie algebra has an abelian ideal of codimension one, by using the bracket flow. We prove that solutions to the Ricci flow are immortal, the ω-limit of bracket flow solutions is a single point, and that for any sequence of times there exists a subsequence in which the Ricci flow converges, in the pointed topology, to a manifold which is locally isometric to a flat manifold. We give a functional which is non-increasing along a normalized bracket flow that will allow us to prove that given a sequence of times, one can extract a subsequence converging to an algebraic soliton, and to determine which of these limits are flat. Finally, we use these results to prove that if a Lie group in this class admits a Riemannian metric of negative sectional curvature, then the curvature of any Ricci flow solution will become negative in finite time.     

On Symmetric Boundary Conditions in the Context of Viscoelastic Fluid Flows

In order to reduce the numerical cost of three dimensional flow problems with geometrical symmetry, the use of symmetric boundary conditions is standard. For Newtonian fluid flow problems this approximation is usually appropriate, particularly when the Reynolds number is small. In the case of viscoelastic fluid flow simulations with stabilization techniques, such as the so-called DEVSS and/or Log-Conformation tensor methods, at high Deborah number flows this implementation is not straightforward, as in the Newtonian case. It is well known that viscoelastic models (e.g. Maxwellian models), show (purely) elastic flow instabilities when the Deborah number is increased above a critical value, even under creeping flow conditions. In this work we present numerical simulations with different stabilization techniques and different differential viscoelastic models at high Deborah number flows. As a test-case, we compare the flow in a full two-dimensional cross-slot geometry to show the asymmetrical behavior of the viscoelastic fluid flow. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two-dimensional numerical simulation of a wave with a current past a circular cylinder. Part 1: Inline flow

This study considered a 2D numerical simulation with LES modeling of a sinusoidal oscillatory flow inline with an imposed uniform flow using primitive variables. The study is performed by a customized code particularly built for this simulation. This code allows an easy implementation to a customized combination of different boundary conditions and discretization schemes. The code is verified against well-recognized studies of a similar type to validate the calculated results. It is found that the drag and inertia coefficients of the wavy flow are reduced with the increased strength of the imposed uniform flow. A strong chaotic behavior was observed in the flow field structures. This behavior has a significant unpredictable influence on the resulting inline and transverse forces through the flow field pattern within the vicinity of the cylinder surface. This influence sometimes causes the exerted forces to increase when compared to the purely wavy flow. Based on this study, it is highly recommended not to uncouple wavy flows from uniform flows to simultaneously capture the combined interactions of such flow scenarios.     

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.     

Discrete storage processes and their Poisson flow and fluid flow approximations

Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149.     

Gauss maps of the Ricci-mean curvature flow

In this paper, we investigate the Gauss maps of a Ricci-mean curvature flow. A Ricci-mean curvature flow is a coupled equation of a mean curvature flow and a Ricci flow on the ambient manifold. Ruh and Vilms (Trans Am Math Soc 149: 569–573, 1970) proved that the Gauss map of a minimal submanifold in a Euclidean space is a harmonic map, and Wang (Math Res Lett 10(2–3):287–299, 2003) extended this result to a mean curvature flow in a Euclidean space by proving its Gauss maps satisfy the harmonic map heat flow equation. In this paper, we deduce the evolution equation for the Gauss maps of a Ricci-mean curvature flow, and as a direct corollary we prove that the Gauss maps of a Ricci-mean curvature flow satisfy the vertically harmonic map heat flow equation when the codimension of submanifolds is 1.     

An algorithm to solve the proportional network flow problem

The proportional network flow problem is a generalization of the equal flow problem on a generalized network in which the flow on arcs in given sets must all be proportional. This problem appears in several natural contexts, including processing networks and manufacturing networks. This paper describes a transformation on the underlying network that reduces the problem to the equal flow problem; this transformation is used to show that algorithms that solve the equal flow problem can be directly applied to the proportional network flow problem as well, with no increase in asymptotic running time. Additionally, computational results are presented for the proportional network flow problem demonstrating equivalent performance to the same algorithm for the equal flow problem.     

经过修正的层次流流动的流动稳定性问题(Ⅱ)——经过修正的平行剪切流的线性稳定性研究

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线性稳定性性质,对于平面Couette流动和圆管Poiseuill流动,首次得到了二维扰动和轴对称扰动也能造成失稳的结果,并给出了这两种流动在某种定义下的中性曲线.     

A geometric introduction to the two-loop renormalization group flow

The Ricci flow has been of fundamental importance in mathematics, most famously through its use as a tool for proving the Poincaré conjecture and Thurston’s geometrization conjecture. It has a parallel life in physics, arising as the first-order approximation of the renormalization group flow for the nonlinear sigma model of quantum field theory. There recently has been interest in the second-order approximation of this flow, called the RG-2 flow, which mathematically appears as a natural nonlinear deformation of the Ricci flow. A curvature flow arising from quantum field theory seems to us to capture the spirit of Yvonne Choquet-Bruhat’s extensive work in mathematical physics, and so in this commemorative article we give a geometric introduction to the RG-2 flow. A number of new results are presented as part of this narrative: short-time existence and uniqueness results in all dimensions if the sectional curvatures K _ij satisfy certain inequalities; the calculation of fixed points for n =  3 dimensions; a reformulation of constant curvature solutions in terms of the Lambert W function; a classification of the solutions that evolve only by homothety; an analogue for RG flow of the 2-dimensional Ricci flow solution known to mathematicians as the cigar soliton, and discussed in the physics literature as Witten’s black hole. We conclude with a list of open problems whose resolutions would substantially increase our understanding of the RG-2 flow both physically and mathematically.     

非牛顿流体偏心环空螺旋流的解析解

石油和化工中许多问题需要求解非牛顿流体偏心环空螺旋流。本文全面地研究了幂律流体和宾汉流体在偏心环空中层流螺旋流的流动规律与流动状态的判别。在理论上,根据流体力学原理,运用数学方法,在作者同心环空螺旋流的理论基础上,通过对偏心环空螺旋流流场的无限细分法,给出了该流场的视粘度分布、速度分布、流量和压降方程,进而建立了判别流态的稳定性参数。