应用数学和力学

2009 Vol. 30, No. 7

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Chaotic Motions for the Model of the L-Mode to H-Mode in Tokamak

CHEN Fang-qi, ZHOU Liang-qiang, WANG Xia, CHEN Yu-shu

2009, 30(7): 757-765. doi: 10.3879/j.issn.1000-0887.2009.07.001

Abstract(2148) PDF(698)

Abstract:
The chaotic dynamics of the transport equation for the L-mode to H-mode near plasma in Tokamak is studied in detail with Melnilov method.The transport equations represent a system with external and parametric excitation.The critical curves separating the chaotic regions and non-chaotic regions were 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 takes place via heteroclinic bifurcation for the system with linear or cubic parametric excitation.Especially,there exists a "controllable frequency" excited at which chaos doesn.toccur via homoclinic bifurcation no matter how large the excitation amplitude is for the system with cubic parametric excitation.Some complicated dynamical behaviors were obtained for this class of systems.

Boundary Conditions for Porous Solids Saturated With Viscous Fluid

M. D. Sharma

2009, 30(7): 766-776. doi: 10.3879/j.issn.1000-0887.2009.07.002

Abstract(1883) PDF(750)

Abstract:
Boundary conditions were derived to represent the continuity requirements at the boundaries of a porous solid saturated with viscous fluid.These were 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 inter stitial 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 were explained interms of drainage of pore-fluid leading to imperfect bonding.Mathematical model was 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.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): 777-782. doi: 10.3879/j.issn.1000-0887.2009.07.003

Abstract(1191) PDF(743)

Abstract:
Spatial decay bounds and a decay rate for the time-dependent Stokes flow of a viscous fluid was investigated in a semi-infinite channel.It is shown how to obtain a near optimal decay rate that is independent of the Reynolds number.It is also shown that a modification of the analysis given by Lin-Song and a somewhat better choice of arbitrary constants yield the decay rate 1.328 which clearly improves upon that 0.91 obtained by Lin.

A New Full Discrete Stabilized Viscosity Method for the Transient Navier-Stokes Equations

QIN Yan-mei, FENG Min-fu, ZHOU Tian-xiao

2009, 30(7): 783-798. doi: 10.3879/j.issn.1000-0887.2009.07.004

Abstract(1958) PDF(1057)

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

Classification Using Least Squares Support Vector Machine for Reliability Analysis

GUO Zhi-wei, BAI Guang-chen

2009, 30(7): 799-810. doi: 10.3879/j.issn.1000-0887.2009.07.005

Abstract(1915) PDF(750)

Abstract:
In order to improve efficiency of support vector machine for classification on dealing with large amount of samples,least squares support vector machine for classification method was introduced into the reliability analysis,in which the solving of support vector machine was transformed from a quadratic programming to a group of linear equations to reduce computational cost.The numerical results indicate that the reliability method based on least squares vector for classification has excellent accuracy and a smaller computational cost than support vector machine method.

Blow-up Rate and Profile for a Class of Quasilinear Parabolic System

CHEN Yu-juan, ZHU Yue-ping

2009, 30(7): 811-820. doi: 10.3879/j.issn.1000-0887.2009.07.006

Abstract(1821) PDF(777)

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

Statistical Damage Detection of Structures Based on Model Reduction

YIN Tao, LAM Heung-fai, ZHU Hong-ping

2009, 30(7): 821-832. doi: 10.3879/j.issn.1000-0887.2009.07.007

Abstract(3586) PDF(682)

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

Study of Gas-Kinetic Numerical Schemes for One-and Two-Dimensional Inner Flows

LI Zhi-hui, BI Lin, TANG Zhi-gong

2009, 30(7): 833-846. doi: 10.3879/j.issn.1000-0887.2009.07.008

Abstract(1806) PDF(1009)

Abstract:
Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions were designed with different-order precision by analyzing the inner characteristic of the gas-kinetic numerical algorithm for Boltzmann model equation.The peculiar flow phenomena and mechanism from various flow regimes were revealed by the numerical simulation of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers,and the numerical remainde-reffects of the difference schemes were investigated and analyzed on computed results.The ways of improving the computational efficiency of the gas-kinetic numerical method and the computing principles of difference discretization were discussed on the Boltzmann model equation.

Some Nonempty Intersection Theorems in Topological Spaces With Applications

FANG Min, HUANG Nan-jing

2009, 30(7): 847-855. doi: 10.3879/j.issn.1000-0887.2009.07.009

Abstract(1812) PDF(994)

Abstract:
The some new nonempty intersection theorems for generalized L-KKM mappings were established and some new fixed point theorems for set-valued mappings were proved 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 were obtained in topological spaces.The results generalize some known results in recent literature.

p-Moment Exponential Robust Stability for Stochastic Systems With Distributed Delays and Interval Parameters

SU Chun-hua, LIU Si-feng

2009, 30(7): 856-864. doi: 10.3879/j.issn.1000-0887.2009.07.010

Abstract(1538) PDF(1033)

Abstract:
The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied.By constructing Liapunov-Krasovskii functional and employing the decomposition technique of interval matrix and using It's formula,the easily verified delay-dependent criteria for p-moment exponential robust stability were obtained.Numerical examples show the effectiveness and practicality of the presented criteria.

Strong Convergence Theorems for Relatively Nonexpansive Mappings and Inverse-Strongly-Monotone Mappings in a Banach Space

LIU Ying

2009, 30(7): 865-872. doi: 10.3879/j.issn.1000-0887.2009.07.011

Abstract(1698) PDF(774)

Abstract:
An iterative sequence is introduced 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 it is shown that the sequence converges strongly to a common element of two sets.Results improve and extend the corresponding results announced by many others.

On the 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): 873-882. doi: 10.3879/j.issn.1000-0887.2009.07.012

Abstract(1818) PDF(655)

Abstract:
A new model of a chemostat with variable yield and non-synchronous impulsive effect was proposed and investigated.It is observed that a set of threshold-like conditions guaranteeing the global stability of semi-trivial periodic solution,the permanence of the system and then a bifurcation of a nontrivial solution arises.Finally,the dynamics of the model was also illustrated by means of a few numerical experiments and computational simulations.