应用数学和力学

2008 Vol. 29, No. 6

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Phase Synchronization Between Nonlinearly Coupled R^L ssler Systems

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

2008, 29(6): 631-638.

Abstract(2619) PDF(545)

Abstract:
Phase synchronization between nonlinearly coupled systems with 1:1 and 1:2 resonances is investigated. By introducing the conception of phase for a chaotic motion, it demonstrates that for the different internal resonances, with relatively small parameter epsilon, both differences between the mean frequencies of the two sub-oscillators approach zero, implying phase synchronization can be achieved for weak interaction between the two oscillators. With the increase of the 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 with the case with frequency ratio 1:2, even with weak coupling strength. Unlike the enhance effect on the synchronization for linear coupling, the increase of nonlinear coupling strength results in the transition from phase synchronization to non-synchronized state. Further investigation reveals that the states from phase synchronization to non-synchronization are related to the critical changes of the Liapunov exponents, which can also be explained by the diffuse clouds.

Analytical and Numerical Method of Symplectic System for Stokes Flow in the Two-Dimensional Rectangular Domain

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

2008, 29(6): 639-648.

Abstract(2912) PDF(645)

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

Periodical Streaming Potential and Electro-Viscous Effects in Microchannel Flow

GONG Lei, WU Jian-kang, Wang Lei, CHAO Kan

2008, 29(6): 649-656.

Abstract(3103) PDF(1060)

Abstract:
An analytical solution of periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in two-dimensional uniform microchannel based on Poisson-Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow was presented. Dimensional analysis indicates that electric-viscous force depends on three factors: 1) Electricviscous coefficient representing a ratio of maximum of electric-viscous force to pressure gradient in steady state; 2) Profile function describing distribution profile of electrio-viscous force in channel section; 3) Coupling coefficient reflecting behavior of the amplitude damping and the phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number. Flowinduced electric field varies very slowly when frequency Reynolds number is less than 1, and rapidly decreases when frequency Reynolds number is larger than 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.

Research of New-Type Flying Control for Spinning TVC Vehicle

LIU Xin-jian, YUAN Tian-bao

2008, 29(6): 657-662.

Abstract(2435) PDF(589)

Abstract:
A new kind of problem for TVC vehicle spinning in the boost stage is researched. On the basis of research of the non-linear flying dynamics modeling and dynamic properties of TVC vehicle, the dominant coupled factors which affected the attitude stability and attitude precision of pitch channel and yaw channel were found. The inertial delay coupled effects between pitch servo system and yaw servo system were emphasized, which were ever neglected, and the uncoupled plan and control algorithm were put forward from the point of engineering realization. It is to provide the theoretical guidance and reference for the furthermore research of this complicated flying control.

Effects of Unsteady Deformation of a Flapping Wing on Its Aerodynamic Forces

LIU Xin-jian, YUAN Tian-bao

2008, 29(6): 663-675.

Abstract(2715) PDF(595)

Abstract:
The effects of unsteady deformation of a flapping model insect wing on its aero dynamic force production were studied by solving the Navier-Stokes equations on a dynamically deforming grid. Aerodynamic forces on the flapping wing are little affected by consider abletwist, but are affected by camber deformation; the effect of combined camber and twist deformation is similar to that of camber deformation. With a de formation of 6% camber and 20 degrees twist (typical values observed forwings of many insects), lift is increased by 10~20% and lift-to-dragratio by around 10% compared with the case of rigid flat-plate wing. As a result, the deformation canincrease the maximum lift coefficient of aninsect, and candecrease its power requirement of flight, e. g., for a hovering bumblebee with dynamically deforming wings (6% camber and 20 degrees twist), aerodynamic power required is de creased by about 16% compared with the case of rigid wings.

Hamiltonian Long Wave Expansions for Internal Waves Over a Periodically Varying Bottom

ZHOU Hong-yan, PIAO Da-xiong

2008, 29(6): 676-686.

Abstract(2859) PDF(589)

Abstract:
A Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom was derived. From the formulation, using the Hamiltonian perturbation theory, 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 were obtained. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.

Computational Model for Short-Fiber Composites With Eigen-Strain Formulation of Boundary Integral Equations

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

2008, 29(6): 687-695.

Abstract(2933) PDF(742)

Abstract:
A computational model was proposed for shortfiber reinforced materials with the eigenstrain formulation of the boundary integral equations (BIE) and solved with the newly developed boundary point method (BPM). The model comes intimately from the concept of the equivalent inclusion of Eshelby with eigenstrains to be determined in an iterative way for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand through either analytical or numerical means. As the unknowns 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 to be significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with the 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 model and the solution procedure.

Reconstruction of High Order Derivatives by New Mollification Methods

ZHAO Zhen-yu, HE Guo-qiang

2008, 29(6): 696-704.

Abstract(2671) PDF(615)

Abstract:
The problem of reconstructing numerical derivatives from noisy data is considered. A new framework of mollification methods based on L-generalized solution regularization methods was proposed. A concrete algorithm for the first three derivatives was presented, in which a modification of TSVD (called cTSVD (canonical truncated singular value decomposition)) is chosen as the needed regularization technique. The numerical examples given verify the theoretical results and show the efficiency of the new method.

Approximate Analysis for the Scattering of SH-Wave by an Interface Cylindrical Elastic Inclusion With a Semicircular Disconnected Curve

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

2008, 29(6): 705-712.

Abstract(2899) PDF(527)

Abstract:
The scattering of SH-wave by an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated and the solution of dynamic stress concentration factor is given by Green's function, complex function method. Firstly, the space can be divided into up-and-down parts along the interface. In the lower half space, a suitable Green's function for the present problem were constructed, which is the essential solution of displacement field for an elastic half space with a semicylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at horizontal surface. Thereby the semicircular disconnected curve can be constructed when the two parts are bonded which is continuous in the interface loading the undetermined anti- plane forces on the horizontal surfaces. And the expressions of displacement field and stress field were obtained under this situation. Finally, some examples and results of dynamic stress concentration factor were given, and the influences by the cylindrical inclusion and the difference parameters of the two mediators were discussed.

Stabilization and Control for the Subcritical Semilinear Wave Equation in a Bounded Domain With a Cauchy-Ventcel Boundary Conditions

A. Kanoune, N. Mehidi

2008, 29(6): 713-725.

Abstract(2781) PDF(549)

Abstract:
The exponential decay property of solutions of the semilinear wave equation in bounded domain of R^N(N is equals or greater than 1) with a damping term which is effective on the exterior of a ball and with boundary conditions of Cauchy-Ventcel type was analyzed. Under suitable and natural assumptions on the nonlinearity, it was proved that the exponential decay holds locally uniformly for finite energy solutions that provided the nonlinearity is subcritical at infinity. Subcriticality means, roughly speaking, that the nonlinearity grows at infinity atmost as a power is less than 5. The results obtained in R³ and R^N (N equals to or greater than 1) by B. Dehman, G. Le beau 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 contro llability of the semilinear wave equation in abounded domain of R^N (N equals to orgreater than 1) with a subcritical nonlinearity on the domain and its boundary and with conditions on the boundary of Cauchy-Ventcel type.

Stochastic Level-Value Approximation for Quadratic Integer Convex Programming

PENG Zheng, WU Dong-hua

2008, 29(6): 726-734.

Abstract(3159) PDF(590)

Abstract:
A stochastic level value approximating method for quadratic integer convex minimizing problem was proposed. This method applies the importance sampling technique, and uses the main idea of the cross-entropy method to update the sample density functions. The asymptotic convergence of this algorithm was also proved, and some numerical results to illuminate its efficiency was reported.

Generalized LMI-Based Approach to the Global Asymptotic Stability of Cellular Neural Networks With Delay

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

2008, 29(6): 735-740.

Abstract(2346) PDF(515)

Abstract:
The global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition was presented based on Liapunov-Krasovskii method, which is dependent on the size of delay. The result is given in the form of LMI(linear matric inequality), and the admitted upper bound of the delay can be obtained easily. The time delay dependent and independent results can be obtained, which include some results in the former literature. Finally, a numerical example was given to illustrate the effectiveness of the main results.

Positive Solutions of Three-Point Boundary Value Problems

MIAO Ye-hong, ZHANG Ji-hui

2008, 29(6): 741-748.

Abstract(2983) PDF(619)

Abstract:
The existence of single or multiple positive solutions of three-point boundary value problems involving one dimensional p-Laplacian was considered. Then the existence of solution when the problems is in resonance case was studied. The approach is based on the Krasnoselskii's fixed point theorem and the coincidence degree theory.

Diffusion-Driven Instability and Hopf Bifurcation in the Brusselator System

LI Bo, WANG Ming-xin

2008, 29(6): 749-756.

Abstract(3014) PDF(866)

Abstract:
The Hopf bifurcation for the Brusselator ODE model and the corresponding PDE model are investigated by using the Hopf bifurcation theorem. The stability of the Hopf bifurcation periodic solution was 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. The results show that if parameters are properly chosen, Hopf bifurcation does not occur for the ODE system, but occurs for the PDE system.