Table of Content

18 June 2008, Volume 29 Issue 6

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Articles

Phase synchronization between nonlinearly coupled Rösslersystems

LIU Yong;BI Qin-sheng;CHEN Yu-shu

2008, 29(6):  697-704 .  doi:10.1007/s10483-008-0601-x

Abstract ( 1655 )   PDF (1595KB) ( 1139 )  

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Phase synchronization between nonlinearly coupled systems with 1:1 and 1:2 resonances is investigated. By introducing a concept of phase for a chaotic
motion, it is demonstrated that for different internal resonances,with relatively small parameter epsilon, the difference between the mean frequencies of the two sub-oscillators approaches zero. This implies that phase synchronization can be achieved for weak interaction between the two oscillators. With the increase in coupling strength, fluctuations of the frequency difference can be
observed, and for the primary resonance, the amplitudes of the fluctuations of the difference seem much smaller compared to the case with frequency ratio 1:2, even with the weak coupling strength. Unlike the enhanced effect on synchronization for linear coupling, the increase in nonlinear coupling strength results in the transition from phase synchronization to a non-synchronized state. Further investigation reveals that the states from phase synchronization to non-synchronization are related to the critical
changes of the Lyapunov exponents, which can also be explained with
the diffuse clouds.

Analytical and numerical methods of symplectic system for Stokes flow

XU Xin-sheng;WANG Ga-ping;SUN Fa-ming

2008, 29(6):  705-714 .  doi:10.1007/s10483-008-0602-3

Abstract ( 1591 )   PDF (434KB) ( 1289 )  

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In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint
relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is
presented based on completeness of the symplectic eigensolution
space. The results show that fundamental flows can be described by
zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems.

Periodical streaming potential and electro-viscous effects

GONG Lei;WU Jian-kang;WANG Lei;CHAO Kan

2008, 29(6):  715-724 .  doi:10.1007/s10483-008-0603-7

Abstract ( 1653 )   PDF (288KB) ( 1136 )  

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This paper presents an analytical solution to periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in two-dimensional uniform microchannel based on the Poisson-Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow. Dimensional analysis indicates that electric-viscous force depends on three factors: (1) Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state, (2) profile function describing the distribution profile of electro-viscous force in channel section, and (3) coupling coefficient reflecting behavior of amplitude damping and phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number (R_e = wh²/v). Flow-induced electric field varies very slowly with R_e when R_e < 1 , and rapidly decreases when R_e<1. Electro-viscous effect on flow-induced electric field and flow velocity are very significant when the rate of the channel width to the thickness of electric double layer is small.

New-type of flying control for spinning TVC vehicle

LIU Xin-jian;YUAN Tian-bao

2008, 29(6):  725-730 .  doi:10.1007/s10483-008-0604-2

Abstract ( 1800 )   PDF (133KB) ( 847 )  

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A new kind of problem for TVC vehicle spinning in the boost stage had been researched. The study of non-linear flying dynamics modeling and dynamic properties of TVC vehicles reveal dominant coupled factors that affect the attitude stability and attitude precision of the pitch channel and yaw
channel. The paper emphasizes the inertial delay coupled effects between vehicle's pitch servo system and yaw servo system, which have always been neglected. An uncoupled plan and control algorithm are put forward from the standpoint of engineering implementation to provide theoretical guidance and reference for further research on this complicated flying control.

Effects of unsteady deformation of flapping wing on its aerodynamic forces

DU Gang;SUN Mao

2008, 29(6):  731-743 .  doi:10.1007/s10483-008-0605-9

Abstract ( 1592 )   PDF (547KB) ( 1072 )  

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Effects of unsteady deformation of a flapping model insect wing on its aerodynamic force production are studied by solving the Navier-Stokes equations on a dynamically deforming grid. Aerodynamic forces on the flapping wing are not much affected by considerable twist, but affected by camber deformation. The effect of combined camber and twist deformation is similar to
that of camber deformation. With a deformation of 6% camber and 20^。 twist (typical values observed for wings of many insects), lift is increased by 10%-20% and lift-to-drag ratio by around 10\% compared with the case of a rigid flat-plate wing. As a result, the deformation can increase the maximum lift
coefficient of an insect, and reduce its power requirement for flight. For example, for a hovering bumblebee with dynamically deforming wings (6\% camber and 20^。 twist), aerodynamic power required is reduced by about 16% compared with the case of rigid wings.

Hamiltonian long wave expansions for internal waves

ZHOU Hong-yan;PIAO Da-xiong

2008, 29(6):  745-756 .  doi:10.1007/s10483-008-0606-x

Abstract ( 1957 )   PDF (166KB) ( 699 )  

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We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective
Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.

Computational model for short-fiber composites

MA Hang;XIA Li-wei;QIN Qing-hua

2008, 29(6):  757-767 .  doi:10.1007/s10483-008-0607-4

Abstract ( 1907 )   PDF (290KB) ( 953 )  

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A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations (BIE) and solved with the newly developed boundary point method (BPM). The model is closely derived from the concept of the equivalent inclusion of Eshelby tensors.
Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally
time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element (RVE), showing the validity and the effectiveness of the proposed computational modal and the solution procedure.

Reconstruction of high order derivatives by new mollification methods

ZHAO Zhen-yu;HE Guo-qiang

2008, 29(6):  769-778 .  doi:10.1007/s10483-008-0608-y

Abstract ( 1396 )   PDF (305KB) ( 1041 )  

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In this paper, the problem of reconstructing numerical derivatives from noisy data is considered. A new framework of mollification methods based on the L
generalized solution regularization methods is proposed. A specific algorithm for the first three derivatives is presented in the paper, in which a modification of TSVD, termed cTSVD is chosen as the regularization technique. Numerical examples given in the paper verify the theoretical results and show efficiency of the new method.

Scattering of SH-waves from interface cylindrical elastic inclusion

ZHAO Jia-xi;QI Hui;SU Sheng-wei

2008, 29(6):  779-786 .  doi:10.1007/s10483-008-0609-1

Abstract ( 1772 )   PDF (495KB) ( 719 )  

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Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated. The solution of dynamic stress
concentration factor is given using the Green's function and the method of complex variable functions. First, the space is divided into upper and lower parts along the interface. In the lower half space, a suitable Green's function for the problem is constructed. It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic
inclusion while bearing out-plane harmonic line source load at the horizontal surface. Thus, the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces. Also, the expressions of displacement and stress fields are obtained in this situation. Finally, examples and results of dynamic stress concentration factor are given. Influences of the cylindrical inclusion and the difference parameters of the
two mediators are discussed.

Stabilization and control of subcritical semilinear wave equation in bounded domain with Cauchy-Ventcel boundary conditions

A. Kanoune;N. Mehidi

2008, 29(6):  787-800 .  doi:10.1007/s10483-008-0610-x

Abstract ( 1670 )   PDF (170KB) ( 750 )  

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We analyze the exponential decay property of solutions of the semilinear wave equation in bounded domain Ω of R^N with a damping term which is effective on the exterior of a ball and boundary conditions of the Cauchy-Ventcel type. Under suitable and natural assumptions on the nonlinearity, we prove that the exponential decay holds locally uniformly for finite energy
solutions provided the nonlinearity is subcritical at infinity. Subcriticality means, roughly speaking, that the nonlinearity grows at infinity at most as a power p<5. The results obtained in R³ and R^N by B. Dehman, G. Lebeau and E. Zuazua on the inequalities of the classical energy (which estimate the total
energy of solutions in terms of the energy localized in the exterior of a ball) and on Strichartz's estimates, allow us to give an application to the stabilization controllability of the semilinear wave equation in a bounded domain of R^N with a subcritical nonlinearity on the domain and its boundary, and conditions on the boundary of Cauchy-Ventcel type.

Stochastic level-value approximation for integer programming

PENG Zheng;WU Dong-hua

2008, 29(6):  801-809 .  doi:10.1007/s10483-008-0611-y

Abstract ( 1727 )   PDF (145KB) ( 705 )  

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We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and report some numerical results to illuminate
its effectiveness.

Global asymptotic stability of cellular neural networks with delay

LIU De-you;ZHANG Jian-hua;GUAN Xin-ping;XIAO Xiao-dan

2008, 29(6):  811-816 .  doi:10.1007/s10483-008-0612-x

Abstract ( 1878 )   PDF (139KB) ( 874 )  

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A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper
bound of the delay can be easily obtained. The time delay dependent
and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.

Positive solutions of three-point boundary value problems

MIAO Ye-hong;ZHANG Ji-hui

2008, 29(6):  817-823 .  doi:10.1007/s10483-008-0613-y

Abstract ( 1772 )   PDF (128KB) ( 733 )  

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In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional $p$-Laplacian. We then study existence of solutions when the problems are in resonance cases. The proposed approach is based on the Krasnoselskii's fixed point theorem and the coincidence degree.

Diffusion-driven instability and Hopf bifurcation in Brusselator system

LI Bo;WANG Ming-xin

2008, 29(6):  825-832 .  doi:10.1007/s10483-008-0614-y

Abstract ( 2117 )   PDF (128KB) ( 1403 )  

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The Hopf bifurcation for the Brusselator ordinary-differential-equation (ODE) model and the corresponding partial-differential-equation (PDE)
model are investigated by using the Hopf bifurcation theorem. The stability of the Hopf bifurcation periodic solution is discussed by applying the normal form theory and the center manifold theorem. When parameters satisfy some
conditions, the spatial homogenous equilibrium solution and the
spatial homogenous periodic solution become unstable. Our results
show that if parameters are properly chosen, Hopf bifurcation does
not occur for the ODE system, but occurs for the PDE system.