Table of Content

01 August 2009, Volume 30 Issue 8

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Articles

Asymptotic behavior of 2D generalized stochastic Ginzburg-Landau equation with additive noise

LI Dong-Long;GUO Bo-Ling

2009, 30(8):  945-956.  doi:10.1007/s10483-009-0801-x

Abstract ( 1554 )   PDF (193KB) ( 1013 )  

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The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H^1₀

Prediction of nanoparticle transport and deposition in bends

LIN Pei-Feng;LIN Jian-Zhong

2009, 30(8):  957-968. 

Abstract ( 1705 )   PDF (355KB) ( 1303 )  

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Nanoparticle transport and deposition in bends with circular cross-section are solved for different Reynolds numbers and Schmidt numbers. The perturbation method is used in solving the equations. The results show that the particle transport patterns are similar and independent of the particle size and other parameters when suspended nanoparticles flow in a straight tube. At the outside edge, particle deposition is the most intensive, while deposition at the inside edge is the weakest. In the upper and lower parts of the tube, depositions are approximately the same for different Schmidt numbers. Curvatures of tube, Reynolds number, and Schmidt number have second-order, forthorder, and first-order effects on the relative deposition efficiency, respectively.

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

LI Shi-Rong;SU Hou-De;CHENG Chang-Jun

2009, 30(8):  969-982.  doi:10.1007/s10483-009-0803-7

Abstract ( 2396 )   PDF (1240KB) ( 2390 )  

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Free vibration of statically thermal postbuckled functionally graded material (FGM) beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric layers subject to thermo-electromechanical loadings are formulated. It is assumed that the material properties of the middle FGM layer vary continuously as a power law function of the thickness coordinate, and the piezoelectric layers are isotropic and homogenous. By assuming that the amplitude of the beam vibration is small and its response is harmonic, the above mentioned non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations. One is for the postbuckling, and the other is for the linear vibration of the beam superimposed upon the postbuckled configuration. Using a shooting method to solve the two sets of ordinary differential equations with fixed-fixed boundary conditions numerically, the response of postbuckling and free vibration in the vicinity of the postbuckled configuration of the beam with fixed-fixed ends and subject to transversely nonuniform heating and uniform electric field is obtained. Thermo-electric postbuckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity, and the material gradient parameters are plotted. It is found that the three lowest frequencies of the prebuckled beam decrease with the increase of the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.

Fractal geometry and topology abstracted from hair fibers

YIN Ya-Jun;YANG Fan;LI Ying;FAN Qin-Shan

2009, 30(8):  983-990.  doi:10.1007/s10483-009-0804-5

Abstract ( 2098 )   PDF (361KB) ( 968 )  

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Based on the concepts of fractal super fibers, the (3, 9+2)-circle and (9+2,3)-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the (3)-circle and the (9+2)-circle fractal sets as subsets. As far as the (9+2) topological patterns are concerned, the following propositions are proved: The (9+2) topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent (or fundamental). Besides, we demonstrate that the (3, 9+2)-circle and (9+2, 3)-circle fractal sets are golden ones with symmetry breaking.

Numerical method and analysis of computational fluid mechanics for photoelectric semiconducting detector

YUAN Yi-Rang;LI Chang-Feng;LIU Yun-Xin;MA Li-Qin

2009, 30(8):  991-1002.  doi:10.1007/s10483-009-0805-x

Abstract ( 1841 )   PDF (332KB) ( 1101 )  

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We propose a modified upwind finite difference fractional step scheme for the computational fluid mechanics simulations of a three-dimensional photoelectric semiconductor detector. We obtain the optimal l2-norm error estimates by using the techniques including the calculus of variations, the energy methods, the induction hypothesis, and a priori estimates. The proposed scheme is successfully applied to the simulation of the
photoelectric semiconductor detectors.

Asymptotic solution of nonlocal nonlinear reaction-diffusion Robin problems with two parameters

MO Jia-Qi

2009, 30(8):  1003-1008.  doi:10.1007/s10483-009-0806-x

Abstract ( 1805 )   PDF (142KB) ( 1153 )  

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In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed in relation to two small parameters.The asymptotic solutions of the problem are given.

Solar radiation pressure used for formation flying control around the Sun-Earth libration point

GONG Sheng-Ping;LI Jun-Feng;BAO Yin-He-Xi

2009, 30(8):  1009-1016.  doi:10.1007/s10483-009-0807-z

Abstract ( 1826 )   PDF (361KB) ( 1239 )  

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Solar radiation pressure is used to control the formation flying around the L2 libration point in the Sun-Earth system. Formation flying control around a halo orbit requires a very small thrust that cannot be satisfied by the latest thrusters. The key contribution of this paper is that the continuous low thrust is produced by solar radiation pressure to achieve the tight formation flying around the libration point. However, only certain families of formation types can be controlled by solar radiation pressure since the direction of solar radiation pressure is restricted to a certain range. Two types of feasible formations using solar radiation pressure control are designed. The conditions of feasible formations are given analytically. Simulations are presented for each case, and the results show that the formations are well controlled by solar radiation pressure.

Symmetry solutions of a nonlinear elastic wave equation with third-order anharmonic corrections

M.Tahir Mustafa;Khalid Masood

2009, 30(8):  1017-1026.  doi:10.1007/s10483-009-0808-z

Abstract ( 1919 )   PDF (161KB) ( 1350 )  

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Lie symmetry method is applied to analyze a nonlinear elastic wave equation for longitudinal deformations with third-order anharmonic corrections to the elastic energy. Symmetry algebra is found and reductions to second-order ordinary differential equations (ODEs) are obtained through invariance under different symmetries. The reduced ODEs are further analyzed to obtain several exact solutions in an explicit form. It was observed in the literature that anharmonic corrections generally lead to solutions with time-dependent singularities in finite times. Along with solutions with time-dependent singularities, we also obtain solutions which do not exhibit time-dependent singularities.

Multi-symplectic Runge-Kutta methods for Landau-Ginzburg-Higgs equation

HU Wei-Peng;DENG Zi-Chen;HAN Song-Mei;FAN Wei

2009, 30(8):  1027-1034.  doi:10.1007/s10483-009-0809-x

Abstract ( 2071 )   PDF (203KB) ( 2078 )  

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Nonlinear wave equations have been extensively investigated in the last several decades. The Landau-Ginzburg-Higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic theory in the Hamilton space. The multi-symplectic Runge-Kutta method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the first-order partial differential equations (PDEs) derived from the Landau-Ginzburg-Higgs equation. The numerical results for the soliton solution of the Landau-Ginzburg-Higgs equation are reported, showing that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.

A wavelet multiscale method for inversion of Maxwell equations

DING Liang;HAN Bo;LIU Jia-Qi

2009, 30(8):  1035-1044.  doi:10.1007/s10483-009-0810-1

Abstract ( 1651 )   PDF (444KB) ( 1230 )  

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This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.

Boundary value problems for nonlinear second-order difference equations with impulse

Huseyin Bereketoglu;Aydin Huseynov

2009, 30(8):  1045-1054.  doi:10.1007/s10483-009-0811-z

Abstract ( 1789 )   PDF (158KB) ( 1076 )  

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In this paper, we consider a boundary value problem with impulse (BVPI) for nonlinear second-order difference equations. Existence and uniqueness of solutions of  the considered BVPI are established.

Solvability of a class of second-order quasilinear boundary value problems

TAO Qing-Liu

2009, 30(8):  1055-1062.  doi:10.1007/s10483-009-0812-y

Abstract ( 1951 )   PDF (134KB) ( 851 )  

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The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution if the integration of the limit growth function has an appropriate value.

A difference equation approach to statistical mechanics of complex networks

GUO Jin-Li

2009, 30(8):  1063-1068.  doi:10.1007/s10483-009-0813-6

Abstract ( 1559 )   PDF (123KB) ( 1083 )  

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In this paper, we propose a difference equation approach to the estimation of the degree distributions in growing networks after having analyzed the disadvantages of some existing approaches. This approach can avoid logic conflicts caused by the continuum of discrete problems, and does not need the existence assumption of the stationary degree distribution in the network analysis. Using this approach, we obtain a degree distribution formula of the Poisson growth and preferential attachment network. It is rigorously shown that this network is scale-free based on the Poisson process theory and properties of Γ-distribution.

Finite-time stability with respect to a closed invariant set for a class of discontinuous systems

CHENG Gui-Fang;MU Xiao-Wu

2009, 30(8):  1069-1075.  doi:10.1007/s10483-009-0814-y

Abstract ( 1818 )   PDF (150KB) ( 947 )  

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This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.