Table of Content

01 July 2009, Volume 30 Issue 7

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Articles

Chaotic motions of the L-mode to H-mode transition model in tokamak

CHEN Fang-Qi;ZHOU Liang-Qiang;WANG Xia;CHEN Yu-Shu

2009, 30(7):  811-820.  doi:10.1007/s10483-009-0701-z

Abstract ( 1878 )   PDF (283KB) ( 952 )  

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The chaotic dynamics of the transport equation for the L-mode to H-mode near the plasma in a tokamak is studied in detail with the Melnikov method. The transport equations represent a system with external and parametric excitation. The critical curves separating the chaotic regions and nonchaotic regions are presented for the system with periodically external excitation and linear parametric excitation, or cubic parametric excitation, respectively. The results obtained here show that there exist uncontrollable regions in which chaos always take place via heteroclinic bifurcation for the system with linear or cubic parametric excitation. Especially, there exists a controllable frequency, excited at which chaos does not occur via homoclinic bifurcation no matter how large the excitation amplitude is for the system with cubic parametric excitation. Some complicated dynamical behaviors are obtained for this class of systems.

Boundary conditions for porous solids saturated with viscous fluid

M.D.Sharma

2009, 30(7):  821-832.  doi:10.1007/s10483-009-0702-6

Abstract ( 1572 )   PDF (288KB) ( 1377 )  

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Boundary conditions are derived to represent the continuity requirements at the boundaries of a porous solid saturated with viscous fluid. They are derived from the physically grounded principles with a mathematical check on the conservation of energy. The poroelastic solid is a dissipative one for the presence of viscosity in the interstitial fluid. The dissipative stresses due to the viscosity of pore-fluid are well represented in the boundary conditions. The unequal particle motions of two constituents of porous aggregate at a boundary between two solids are explained in terms of the drainage of pore-fluid leading to imperfect bonding. A mathematical model is derived for the partial connection of surface pores at the porous-porous interface. At this interface, the loose-contact slipping and partial pore opening/connection may dissipate a part of strain energy. A numerical example shows that, at the interface between water and oil-saturated sandstone, the modified boundary conditions do affect the energies of the waves refracting into the isotropic porous medium.

Improved spatial decay bounds in the plane Stokes flow

J.C.Song

2009, 30(7):  833-838.  doi:10.1007/s10483-009-0703-z

Abstract ( 1484 )   PDF (118KB) ( 878 )  

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This paper investigates spatial decay bounds and a decay rate for the timedependent Stokes flow of a viscous fluid in a semi-infinite channel. We show how to obtain a near optimal decay rate that is independent of the Reynolds number. We also show that a modification to an analysis given in the literature and a better choice of arbitrary constants yield a decay rate 1.328, which is clearly an improvement compared to 0.91 obtained in the referenced work.

A new full discrete stabilized viscosity method for transient Navier-Stokes equations

QIN Yan-Mei;FENG Min-Fu;ZHOU Tian-Xiao

2009, 30(7):  839-852.  doi:10.1007/s10483-009-0704-z

Abstract ( 1918 )   PDF (245KB) ( 1472 )  

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A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number (small viscosity coefficient) is proposed based on the pressure projection and the extrapolated trapezoidal rule. The transient Navier- Stokes equations are fully discretized by the continuous equal-order finite elements in space and the reduced Crank-Nicolson scheme in time. The new stabilized method is stable and has many attractive properties. First, the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pressure projection term. Second, the artifical viscosity parameter is added to the viscosity coefficient as a stability factor, so the system is antidiffusive. Finally, the method requires only the solution to a linear system at every time step. Stability and convergence of the method is proved. The error estimation results show that the method has a second-order accuracy, and the constant in the estimation is independent of the viscosity coefficient. The numerical results are given, which demonstrate the advantages of the method presented.

Classification using least squares support vector machine for reliability analysis

GUO Zhi-Wei;BAI Guang-Chen

2009, 30(7):  853-864.  doi:10.1007/s10483-009-0705-x

Abstract ( 1523 )   PDF (784KB) ( 1163 )  

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In order to improve the efficiency of the support vector machine (SVM) for classification to deal with a large amount of samples, the least squares support vector machine (LSSVM) for classification methods is introduced into the reliability analysis. To reduce the computational cost, the solution of the SVM is transformed from a quadratic programming to a group of linear equations. The numerical results indicate that the reliability method based on the LSSVM for classification has higher accuracy and requires less computational cost than the SVM method.

Blow-up rate and profile for a class of quasilinear parabolic system

CHEN Yu-Juan;ZHU Yue-Ping

2009, 30(7):  865-874.  doi:10.1007/s10483-009-0706-y

Abstract ( 1426 )   PDF (185KB) ( 890 )  

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This paper deals with positive solutions to a class of nonlocal and degenerate quasilinear parabolic system with null Dirichlet boundary conditions. The blow-up rate and blow-up profile are gained if the parameters and the initial data satisfy some conditions.

Statistical detection of structural damage based on model reduction

YIN Tao;LIN Xiang-Hui;SHU Hong-Ping

2009, 30(7):  875-888.  doi:10.1007/s10483-009-0707-7

Abstract ( 1758 )   PDF (296KB) ( 907 )  

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This paper proposes a statistical method for damage detection based on the finite element (FE) model reduction technique that utilizes measured modal data with a limited number of sensors. A deterministic damage detection process is formulated based on the model reduction technique. The probabilistic process is integrated into the deterministic damage detection process using a perturbation technique, resulting in a statistical structural damage detection method. This is achieved by deriving the firstand second-order partial derivatives of uncertain parameters, such as elasticity of the damaged member, with respect to the measurement noise, which allows expectation and covariance matrix of the uncertain parameters to be calculated. Besides the theoretical development, this paper reports numerical verification of the proposed method using a portal frame example and Monte Carlo simulation.

Gas-kinetic numerical schemes for one- and two-dimensional inner flows

LI Zhi-Hui;BI Lin;TANG Zhi-Gong

2009, 30(7):  889-904.  doi:10.1007/s10483-009-0708-x

Abstract ( 1666 )   PDF (390KB) ( 1069 )  

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Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated and analyzed based on the computed results. The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed.

Nonempty intersection theorems in topological spaces with applications

FANG Min;HUANG Nan-Jing

2009, 30(7):  905-914.  doi:10.1007/s10483-009-0709-2

Abstract ( 1982 )   PDF (172KB) ( 1475 )  

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In this paper, we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces. As applications, an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces. Our results generalize some known results in the literature.

The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters

SU Chun-Hua;LIU Si-Feng

2009, 30(7):  915-924.  doi:10.1007/s10483-009-0710-x

Abstract ( 1887 )   PDF (181KB) ( 1086 )  

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The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov- Krasovskii functional and employing the decomposition technique of interval matrix and Itˆo’s formula, the delay-dependent criteria for the p-moment exponential robust stability are obtained. Numerical examples show the validity and practicality of the presented criteria.

Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

LIU Ying

2009, 30(7):  925-932.  doi:10.1007/s10483-009-0711-y

Abstract ( 1867 )   PDF (148KB) ( 898 )  

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In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others.

Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield

ZHANG Hong;Paul Georgescu;Juan J.Nieto;CHEN Lan-Sun

2009, 30(7):  933-944.  doi:10.1007/s10483-009-0712-x

Abstract ( 1878 )   PDF (275KB) ( 961 )  

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In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nutrient refilling and the periodic antibiotic injection occur with the same periodicity, but not simultaneously. The model is then formulated in terms of autonomous differential equations subject to impulsive perturbations. It is observed that either the population of microorganisms essentially washes out, or more favorably, the system is permanent. To describe this dichotomy, some biologically significant integral conditions are introduced. Further, it is shown that in a certain critical situation, a nontrivial periodic solution
emerges via a bifurcation phenomenon. Finally, the dynamics of the model is illustrated with numerical experiments and computer simulations.