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2009年 第30卷 第4期    刊出日期：2009-04-16

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Articles

Application of differential constraint method to exact solution of second-grade fluid

张道祥 冯素晓 卢志明 刘宇陆

2009, 30(4):  403-412.  doi:10.1007/S10483-009-0401-x

摘要 ( 1963 )   PDF (319KB) ( 1330 )  

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A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.

Vibration and stability of hybrid plate based on elasticity theory

吕和祥 李俊永

2009, 30(4):  413-423.  doi:10.1007/S10483-009-0402-3

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The governing equations of elasticity theory for natural vibration and buckling of anisotropic plate are derived from Hellinger-Reissner's variational principle with nonlinear strain-displacement relations. Simply supported rectangular hybrid plates are studied with a precise integration method. This method, in contrast to the traditional finite difference approximation, gives highly precise numerical results that approach the full computer precision. So the results for natural vibration and stability of hybrid plates presented in the paper can be riewed as approximate analytical solutions.  Furthermore, several types of coupling effects such as coupling between bending and twisting, and coupling between extension and bending, when the layer stacking sequence is asymmetric, are considered by only one set of governing equations.

Kinetic description of bottleneck effects in traffic flow

张鹏 吴冬艳 黄仕进 陶亦舟

2009, 30(4):  425-434.  doi:10.1007/s10483-009-0403-z

摘要 ( 1663 )   PDF (308KB) ( 1089 )  

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This paper deals with the effects of traffic bottlenecks using an extended Lighthill-Whitham-Richards (LWR) model.;The solution structure is  analytically indicated by the study of the Riemann problem characterized by a discontinuous flux. This leads to a typical solution describing a queue upstream of the bottleneck and its width and height, and informs the design of a $\delta$-mapping algorithm. More significantly, it is found that the kinetic model is able to reproduce stop-and-go waves for a triangular fundamental diagram. Some simulation examples, which are in agreement with the analytical solutions, are given to support these conclusions.

Wavelet spectrum analysis on energy transfer of multi-scale structures in wall turbulence

夏振炎 田砚 姜楠

2009, 30(4):  435-443.  doi:10.1007/s10483-009-0404-8

摘要 ( 1875 )   PDF (385KB) ( 1089 )  

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The streamwise velocity components at different vertical heights in wall turbulence were measured. Wavelet transform was used to study the turbulent energy spectra, indicating that the global spectrum results from the weighted average of Fourier spectrum based on wavelet scales. Wavelet  transform with more vanishing moments can express the declining of turbulent spectrum. The local wavelet spectrum shows that the physical phenomena such as deformation or breakup of eddies are related to the vertical position in the boundary layer, and the energy-containing eddies exist in a multi-scale form. Moreover, the size of these eddies increases with the measured points moving out of the wall. In the buffer region, the small scale energy-containing eddies with higher frequency are excited. In the outer region, the maximal energy is concentrated in the low-frequency large-scale eddies, and the frequency domain of energy-containing eddies becomes narrower.

Numerical simulation of laminar jet-forced flow using lattice Boltzmann method

李元 段雅丽 郭彦 刘儒勋

2009, 30(4):  445-453.  doi:10.1007/s10483-009-0405-z

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In the paper, a numerical study on symmetrical and asymmetrical laminar jet-forced flows is carried out by using a lattice Boltzmann method (LBM) with a special boundary treatment. The simulation results are in very good agreement with the available numerical prediction. It is shown that the LBM is a  competitive method for the laminar jet-forced flow in terms of computational efficiency and stability.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

赵改平 陈二云 吴洁 许世雄 M.W.Collins 龙泉

2009, 30(4):  455-462.  doi:10.1007/s10483-009-0406-y

摘要 ( 1946 )   PDF (311KB) ( 1067 )  

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A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model.  The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.

Analytical solution to stagnation-point flow and heat transfer over a stretching sheet based on homotopy analysis

朱婧 郑连存 张欣欣

2009, 30(4):  463-474.  doi:10.1007/s10483-009-0407-2

摘要 ( 1894 )   PDF (348KB) ( 1227 )  

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This paper is concerned with two-dimensional stagnation-point steady flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit.  The governing system of partial differential equations is first transformed  into a system of dimensionless ordinary differential equations. Analytical solutions of the velocity  distribution and dimensionless temperature profiles are obtained for different ratios of free stream velocity and stretching velocity, Prandtl number, Eckert number and dimensionality index in series forms using homotopy analysis method(HAM). It is shown that a boundary layer is formed when the free stream velocity exceeds the stretching velocity, and an inverted boundary layer is formed when the free stream velocity is less than the stretching velocity. Graphs are presented to show the effects of different parameters.

Analysis and  control of a class of uncertain linear periodic discrete-time systems

孙凯 谢广明

2009, 30(4):  475-488.  doi:10.1007/s10483-009-0408-y

摘要 ( 1926 )   PDF (220KB) ( 981 )  

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Feedback control problems for linear periodic systems (LPSs) with interval-type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality (LMI) for the asymptotical stability and state feedback stabilization, respectively, are given. Problems of $\mathcal{L}_2$-gain analysis and control synthesis  are studied. For the $\mathcal{L}_2$-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an $\mathcal{L}_2$-gain smaller than a positive scalar $\gamma$. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an $\mathcal{L}_2$-gain smaller than the positive scalar $\gamma$. All the conditions are necessary and sufficient.

Nonlinear numerical simulation method for galloping of iced conductor

刘小会 严波 张宏雁 周松

2009, 30(4):  489-501.  doi:10.1007/s10483-009-04-09-x

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Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order ofvertical natural frequency of the transmission line is approximately two times of the horizontal one.

Hall effects on hydromagnetic flow on an oscillating porous plate

S.L.Maji A.K.Kanch M.Guria R.N.Jana

2009, 30(4):  503-512.  doi:10.1007/s10483-009-0410-6

摘要 ( 1871 )   PDF (366KB) ( 1334 )  

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In this paper, an analysis is made on the unsteady flow of an incompressible electrically conducting viscous fluid bounded by an infinite porous flat plate. The plate executes harmonic oscillations at a frequency $n$ in its own plane. A uniform magnetic field $H_0$ is imposed perpendicular to the
direction of the flow. It is found that the solution also exists for blowing at the plate. The temperature distribution is also obtained by taking viscous and Joule dissipation into account. The mean wall temperature $\theta_0(0)$ decreases with the increase in the Hall parameter $m$. It is found that no temperature distribution exists for the blowing at the plate.

Existence of traveling wave solutions for a nonlinear dissipative-dispersive  equation

M.B.A.Mansour

2009, 30(4):  513-516.  doi:10.1007/s10483-009-0411-6

摘要 ( 1999 )   PDF (211KB) ( 1338 )  

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In this paper, we consider a dissipative-dispersive nonlinear equation appliable to many physical phenomena. Using the geometric singular perturbation method based on the theory of dynamical systems, we investigate the existence of its traveling wave solutions with the dissipative terms having sufficiently small coefficients. The results show that the traveling waves exist on a two-dimensional slow manifold in a three-dimensional system of ordinary differential equations (ODEs). Then, we use the Melnikov method to establish the existence of a homoclinic orbit in this manifold corresponding to a solitary wave solution of the equation. Furthermore, we present some numerical computations to show the approximations of such wave orbits.

Solutions to general forward-backward doubly stochastic differential equations

朱庆峰 石玉峰 宫献军

2009, 30(4):  517-526.  doi:10.1007/s10483-009-0412-x

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A general type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a method of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.

Positive solutions to (n-1,1) m-point boundary value problems with dependence on the first order derivative

纪玉德 郭彦平 禹长龙

2009, 30(4):  527-536.  doi:10.1007/s10483-009-0413-x

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Using the extension of Krasnoselskii's fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green's function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.