应用数学和力学

2009 Vol. 30, No. 4

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Application of Differential Constraints Method on Solving Exact Solutions of a Second-Grade Fluid

ZHANG Dao-xiang, FENG Su-xiao, LU Zhi-ming, LIU Yu-lu

2009, 30(4): 379-387.

Abstract(2814) PDF(671)

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

Vibration and Stability of Hybrid Plate Based on Elasticity Theory

LÜHe-xiang, LI Jun-yong

2009, 30(4): 388-398.

Abstract(2925) PDF(650)

Abstract:
The governing equations of elasticity theory for natural vibration and buckling of anisotropic plate were derived from Hellinger-Reissner's variational principle with nonlinear strain-displacement relations.Simply supported rectangular hybrid plates were studied by precise integration method.This method,in contrast to the traditional finite difference approximation,gives highly precise numerical results which approach the full computer precision.So the results for natural vibration and stability of hybrid plates presented can be regarded as approximate analytical solutions.Furthermore,the several types of coupling effects,such as coupling between bending and twisting,coupling between extension and bending,etc.when the layer stacking sequence is not symmetric,are considered by only one set of governing equations.

Kinetic Description of Bottleneck Effects in Traffic Flow

ZHANG Peng, WU Dong-yan, S. C. Wong, TAO Yi-zhou

2009, 30(4): 399-408.

Abstract(3002) PDF(1101)

Abstract:
The effects of traffic bottlenecks using an extended LWR model are dealt with.The solution structure was analytically indicated by study of the Riemann problem,which is characterized by a discontinuo us flux.This leads to a typical solution that describes a queueupstream of the bottleneck and its width and height,and informs the design of a D-mapping algorithm.More significantly,it was found that the kinetic model is able to reproduce stop-and-go waves for a triangular fundamental diagram.Some simulation examples were given to support these conclusions,and are shown to be in agreement with the analytical solutions.

Wavelet Spectrum Analysis on Energy Transfer of Multi-Scale Structures in Wall Turbulence

XIA Zhen-yan, TIAN Yan, JIANG Nan

2009, 30(4): 409-416.

Abstract(2748) PDF(596)

Abstract:
The streamwise velocity component at different vertical heights in wall turbulence was measured.Wavelet transform was employed to study the turbulent energy spectra,which indicates that the wavelet global spectrum results from the weighted average of Fourier spectrum based on wavelet scales.The wavelet transform with more vanishing moments can express the declining of turbulent spectrum;the local wavelet spectrum shows that the physical phenomena such as deforming or breakup of eddies have relations with the vertical position in boundary layer,and the energy-containing eddies exist in multi-scale form.Moreover,the size of these eddies is increasing 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 outer region the maximal energy is concentrated on the low frequent large scale eddies and the frequent domain of energy-containing eddies becomes narrower.

Numerical Simulation of Laminar Jet-Forced Flow Using a Lattice Boltzmann Method

LI Yuan, DUAN Ya-li, GUO Yan, LIU Ru-xun

2009, 30(4): 417-424.

Abstract(3026) PDF(677)

Abstract:
A numerical study on symmetrical and asymmetrical laminar jet-forced flows was presented by 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 very competitive method for laminar jet-forced flow in terms of computational efficiency and stability.

Two-Dimensional Discrete Mathematical Model of Tumor-Induced Angiogenesis

ZHAO Gai-ping, CHEN Er-yun, WU Jie, XU Shi-xiong, M. W. Collins, LONG Quan

2009, 30(4): 425-431.

Abstract(3404) PDF(674)

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

Analytic Solution of Stagnation-Point Flow and Heat Transfer Over a Stretching Sheet by Means of Homotopy Analysis Method

ZHU Jing, ZHENG Lian-cun, ZHANG Xin-xin

2009, 30(4): 432-442.

Abstract(3114) PDF(638)

Abstract:
The steady two-dimensional stagnation-point flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit is concerned.The governing system of partial differential equations was first transformed into a system of dimensionless ordinary differential equations.The analytical solutions for the velocity distribution and dimensio nless temperature profiles were obtained for the various values of the ratio of free stream velocity and stretching velocity,Prandtl number,Eckert number and dimensionality index in the series forms with the help of 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 plotted to discuss the effects of different parameters.

Analysis and Control of a Class of Uncertain Linear Periodic Discrete-Time Systems

SUN Kai, XIE Guang-ming

2009, 30(4): 443-456.

Abstract(2570) PDF(726)

Abstract:
Feedback control problems for linear periodic systems (LPSs) with interva-l type parameter uncertainties are studied in the discrete-time domain.First,the stability analysis and stabilization problems were addressed.Conditions based on linear matrices inequality for asymptotical stability and state feedback stabilization respectively were given.Problems of B2-gain analysis and control synthesis problems were studied.For the B2-gain analysis problem,an LMI-based condition was obtained such that the autonomous uncertain LPS is asymptotically stable and has an B2-gain smaller than a positive scalar gamma.For the control synthesis problem,an LM-Ibased condition was derived to build a state feedback controller ensuring the closed-loop system is asymptotically stable and has an B2-gain smaller than a positive scalar gamma.All the conditions are necessary and sufficient.

Nonlinear Numerical Simulation Method for Galloping of Iced Conductor

LIU Xiao-hui, YAN Bo, ZHANG Hong-yan, ZHOU Song

2009, 30(4): 457-468.

Abstract(3476) PDF(726)

Abstract:
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 was developed.In the procedure of numerical simulation,a three-node isoparametric cable element with three translational and one torsional degrees-o-f freedom at each node was employed to discretize the transmission line;and the nonlinear dynamic system equation was solved by the Newmark time integration method and the Newton-Raphson nonlinear iteration strategy.Numerical examples were employed to demonstrate the efficiency of the presented method and the developed finite element program.Furthermore,a new possible galloping mode,which may reflect the saturation phenomenon of nonlinear dynamic system,was discovered on the condition that the lowest order of vertical 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): 469-478.

Abstract(2970) PDF(651)

Abstract:
An analysis was made on the unsteady flow of an incompressible electrically conducting viscous fluid bounded by an infinite porous flat plate.The plate executes harmonic oscillations with frequencyn n in its own plane.A uniform magnetic field 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 on taking viscous and Joule dissipation into account.The mean wall temperature decreases with increase in Hall parameter.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): 479-483.

Abstract(2984) PDF(592)

Abstract:
A dissipative-dispersive nonlinear equation which appears in many physical phenomena is considered.By using dynamical systems method,specifically the geometric singular perturbation method,the existence of traveling wave solutions of the equation when the dissipative terms have sufficiently small coefficients was investigated.It was shown that the traveling waves exist on a two-dimensional slow manifold in a three-dimensional system of ODEs.Then,by using the Melnikov method,the existence of a homoclinic orbit in this manifold,which corresponds to a solitary wave solution of the equation,was established.Furthermore,some numerical computations were presented to show approximations of such wave orbits.

Solutions of General Forward-Backward Doubly Stochastic Differential Equations

ZHU Qing-feng, SHI Yu-feng, GONG Xian-jun

2009, 30(4): 484-494.

Abstract(2708) PDF(643)

Abstract:
A general type of forward-backward doubly stochastic differential equations(FBDSDEs in short) was studied,which extends many important equations well studied before,including stochastic Hamiltonian systems.Under some much weaker monotonicity assumptions,the existence and uniqueness results for measurable solutions were established by means of a method of continuation.Furthermore the continuity and differentiability of the solutions of FBDSDEs depending on parameters were discussed.

Positive Solutions for(n-1,1) m-Point Boundary Value Problems With Dependence on the First Order Derivative

JI Yu-de, GUO Yan-ping, YU Chang-long

2009, 30(4): 495-504.

Abstract(3281) PDF(781)

Abstract:
Using the extension of Krasnoselskii's fixed point theorem in a cone,the existence of at least one positive solution to the nonlinear n th order m-point boundary value problem with dependence on the first order derivative was proved.The associated Green's function for the n th order mpoint boundary value problem was given,and growth conditions were imposed on nonlinear term f which ensure existence of at least one positive solutions.A simple example was presented to illustrate applications of the obtained results.