Table of Content

18 May 2008, Volume 29 Issue 5

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Articles

Optimal obstacle control problem

ZHU Li;LI Xiu-hua;GUO Xing-ming

2008, 29(5):  559-570 .  doi:10.1007/s10483-008-0501-5

Abstract ( 1316 )   PDF (148KB) ( 725 )  

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In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality. Existence, uniqueness and regularity of the optimal control problem are established. In addition, the approximation of the optimal obstacle problem is also studied.

Algorithms of common solutions to quasi variational inclusion and fixed point problems

ZHANG Shi-sheng;LEE Joseph H. W.;CHAN Chi Kin

2008, 29(5):  571-582 .  doi:10.1007/s10483-008-0502-y

Abstract ( 1519 )   PDF (143KB) ( 1263 )  

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The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multi-valued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich (Ekonomika i Matematicheskie Metody, 1976, 12(4):747--756), but also extend and replenish the corresponding results obtained by Iiduka and Takahashi (Nonlinear Anal TMA, 2005,61(3):341--350), Takahashi and Toyoda (J Optim Theory Appl, 2003,118(2):417--428), Nadezhkina and Takahashi (J Optim Theory Appl, 2006,128(1):191--201), and Zeng and Yao (Taiwanese Journal of Mathematics, 2006,10(5):1293--1303).

Terminal sliding mode control for coordinated motion of a space rigid manipulator with external disturbance

GUO Yi-shen;CHEN Li

2008, 29(5):  583-590 .  doi:10.1007/s10483-008-0503-1

Abstract ( 1572 )   PDF (187KB) ( 1146 )  

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The control problem of coordinated motion of a free-floating space rigid manipulator with external disturbance is discussed. By combining linear momentum conversion and the Lagrangian approach, the full-control dynamic equation and the Jacobian relation of a free-floating space rigid manipulator are established and then inverted to the state equation for control design. Based on the terminal sliding mode control (SMC) technique, a mathematical expression of the terminal sliding surface is proposed. The terminal SMC scheme is then developed for coordinated motion between the base's attitude and the end-effector of the free-floating space manipulator with external disturbance. This proposed control scheme not only guarantees the existence of the sliding phase of the closed-loop system, but also ensures that the output tracking error converges to zero in finite time. In addition, because the initial system state is always at the terminal sliding surface, the control scheme can eliminate reaching phase of the SMC and guarantee global robustness and stability of the closed-loop system. A planar free-floating space rigid manipulator is simulated to verify the feasibility of the proposed control scheme.

Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

YUAN Si;XING Qin-yan;WANG Xu;YE Kang-sheng

2008, 29(5):  591-602 .  doi:10.1007/s10483-008-0504-8

Abstract ( 1632 )   PDF (245KB) ( 757 )  

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Based on the newly-developed element energy projection (EEP) method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method (FEM) is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

Aerodynamic optimization of 3D wing based on iSIGHT

YIN Bo;XU Dian;AN Yi-ran;CHEN Yao-song

2008, 29(5):  603-610 .  doi:10.1007/s10483-008-0505-y

Abstract ( 1804 )   PDF (2178KB) ( 1733 )  

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A method for combining the CFD software, Fluent, with the iSIGHT design platform is presented to optimize a three-dimensional wing to ameliorate its aerodynamics performance. In the optimization design, two kinds of genetic algorithms, the Neighborhood Cultivation Genetic Algorithm (NCGA) and the Non-dominated Sorting Genetic Algorithm (NSGAII), are employed and the Navier-Stoke (N-S) equations are adopted to derive the aerodynamics functions of the 3D wing. The aerodynamic performance of the optimized wing has been significantly improved, which shows that the approach can be extended and employed in other cases.

Characteristic finite difference method and application for moving boundary value problem of coupled system

YUAN Yi-rang;LI Chang-feng;YANG Cheng-shun;HAN Yu-ji

2008, 29(5):  611-624 .  doi:10.1007/s10483-008-0506-x

Abstract ( 1549 )   PDF (186KB) ( 634 )  

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The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. A kind of characteristic finite difference schemes is put forward, from which optimal order estimates in norm are derived for the error in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method and software development.

A moving screw dislocation near interfacial rigid lines in two dissimilar anisotropic media

LIU You-wen;LI Bo;FANG Qi-hong

2008, 29(5):  625-638 .  doi:10.1007/s10483-008-0507-7

Abstract ( 1391 )   PDF (457KB) ( 643 )  

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This paper attempts to investigate the problem for the interaction between a uniformly moving screw dislocation and interface rigid lines in two dissimilar anisotropic materials. Integrating Riemann-Schwarz's symmetry principle with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interfaces containing one and two rigid lines. The expressions of stress intensity factors at the rigid line tips and image force acting on moving dislocation are derived explicitly. The results show that dislocation velocity has an antishielding effect on the rigid line tip and a larger dislocation velocity leads to the equilibrium position of dislocation closing with the rigid line. The presented solutions contain previously known results as the special cases.

Numerical method for nonlinear two-phase displacement problem and its application

YUAN Yi-rang;LIANG Dong;RUI Hong-xing;DU Ning;WANG Wen-qia

2008, 29(5):  639-652 .  doi:10.1007/s10483-008-0508-x

Abstract ( 1705 )   PDF (261KB) ( 682 )  

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For the three-dimensional nonlinear two-phase displacement problem, the modified upwind finite difference fractional steps schemes were put forward. Some techniques, such as calculus of variations, induction hypothesis, decomposition of high order difference operators, the theory of prior estimates and techniques were used. Optimal order estimates were derived for the error in the approximation solution. These methods have been successfully used to predict the consequences of seawater intrusion and protection projects.

Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey

JIAO Jian-jun;CHEN Lan-sun;Juan J. Nieto;Torres Angela

2008, 29(5):  653-664 .  doi:10.1007/s10483-008-0509-x

Abstract ( 1389 )   PDF (621KB) ( 958 )  

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We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the
global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system.

Alternative principles and minimax inequalities in G-convex spaces

Mircea Balaj

2008, 29(5):  665-672 .  doi:10.1007/s10483-008-0510-x

Abstract ( 1526 )   PDF (133KB) ( 691 )  

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Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.

Computation of compressible flows with high density ratio and pressure ratio

CHEN Rong-san

2008, 29(5):  673-682 .  doi:10.1007/s10483-008-0511-y

Abstract ( 1573 )   PDF (1534KB) ( 858 )  

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The WENO method, RKDG method, RKDG method with original ghost fluid method, and RKDG method with modified ghost fluid method are applied to single-medium and two-medium air-air, air-liquid compressible flows with high density and pressure ratios. We also provide a numerical comparison and analysis for the above methods. Numerical results show that, compared with the other methods, the RKDG method with modified ghost fluid method can obtain high resolution results and the correct position of the shock, and the computed solutions are converged to the physical solutions as the mesh is refined.

Optimal harvesting for an age-dependent n-dimensional food chain model

LUO Zhi-xue;DU Ming-yin

2008, 29(5):  683-695 .  doi:10.1007/s10483-008-0512-y

Abstract ( 1262 )   PDF (150KB) ( 696 )  

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This paper is concerned with optimal harvesting policy for an age-dependent n-dimensional food chain model. The existence and uniqueness of non-negative solution of the system are proved using the fixed point theorem. By Mazur's theorem, the existence of optimal control strategy is demonstrated and optimality conditions derived by means of normal cone.