Applied Mathematics and Mechanics (English Edition)

Molecular dynamics of dewetting of ultra-thin water films on solid substrate

XU Ai-jin;ZHOU Zhe-wei;HU Guo-hui

2007, 28(12): 1555-1559 . doi:10.1007/s10483-007-1201-z

Abstract ( 1226 )

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Molecular dynamics simulation is applied to study the instability and rupture process of ultra-thin water films on a solid substrate. Results show the small disturbance of the film will develop linearly due to the spinodal instability, whereas the interaction between solid and liquid has less influences on the initial growth. Then the rupture occurs and the rim recedes with a dynamic contact angle. The radius of the rim varies with time as the square root of t, which is consistent with the macroscopic theory available. Stronger interaction between solid and liquid will postpone rupture time, decline the dynamic contact angle and raise the density of water near the interface between solid and liquid.

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications (I)

DING Xie-ping

2007, 28(12): 1561-1568 . doi:10.1007/s10483-007-1202-y

Abstract ( 1378 )

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First, the notions of the measure of noncompactness and condensing set-valued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.

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DING Xie-ping

2007, 28(12): 1569-1579 . doi:10.1007/s10483-007-1203-y

Abstract ( 1615 )

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Analytical modeling of sandwich beam for piezoelectric bender elements

ZHOU Yan-guo;CHEN Yun-min;DING Hao-jiang

2007, 28(12): 1581-1586 . doi:10.1007/s10483-007-1204-z

Abstract ( 1308 )

PDF (347KB) ( 572 )

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Piezoelectric bender elements are widely used as electromechanical sensors and actuators. An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory (FSDT), which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simply-supported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.

A nonlinear mathematical model for large deflection of incompressible saturated poroelastic beams

YANG Xiao;WANG Chen

2007, 28(12): 1587-1595 . doi:10.1007/s10483-007-1205-3

Abstract ( 1355 )

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Nonlinear governing equations are established for large deflection of incompressible fluid saturated poroelastic beams under constraint that diffusion of the pore fluid is only in the axial direction of the deformed beams. Then, the nonlinear bending of a saturated poroelastic cantilever beam with fixed end impermeable and free end permeable, subjected to a suddenly applied constant concentrated transverse load at its free end, is examined with the Galerkin truncation method. The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam are compared, and the differences between them are revealed. It is shown that the results of the large deflection theory are less than those of the corresponding small deflection theory, and the times needed to approach its stationary states for the large deflection theory are much less than those of the small deflection theory.

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S. S. Mousavi;K. Hooman;S. J. Mousavi

2007, 28(12): 1597-1604 . doi:10.1007/s10483-007-1206-z

Abstract ( 1533 )

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An adaptive genetic algorithm for solving bilevel linear programming problem

WANG Guang-min;WANG Xian-jia;WAN Zhong-ping;JIA Shi-hui

2007, 28(12): 1605-1612 . doi:10.1007/s10483-007-1207-1

Abstract ( 1354 )

PDF (473KB) ( 698 )

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MU Xiao-wu;CHENG Gui-fang;DING Zhi-shuai

2007, 28(12): 1613-1619 . doi:10.1007/s10483-007-1208-x

Abstract ( 1492 )

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Sliding state stepping algorithm for solving impact problems of multi-rigid-body system with joint friction

YAO Wen-li;CHEN Bin;LIU Cai-shan;XU Jian

2007, 28(12): 1621-1627 . doi:10.1007/s10483-007-1209-x

Abstract ( 1134 )

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LEUNG A. Y. T.;ZHENG Jian-jun

2007, 28(12): 1629-1642 . doi:10.1007/s10483-007-1210-z

Abstract ( 1201 )

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BAI Yun-fen;HU Xin-hua;YE Zhong-xing

2007, 28(12): 1643-1649 . doi:10.1007/s10483-007-1211-9

Abstract ( 1212 )

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XIE Yu-xin;ZHANG Yi-tong;XU Jia-fu

2007, 28(12): 1651-1658 . doi:10.1007/s10483-007-1212-x

Abstract ( 1233 )

PDF (192KB) ( 559 )

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LI Min;YUAN Xiao-ming

2007, 28(12): 1659-1668 . doi:10.1007/s10483-007-1213-y

Abstract ( 1504 )

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On the L_p intersection body

ZHU Xian-yang;LENG Gang-song

2007, 28(12): 1669-1678 . doi:10.1007/s10483-007-1214-x

Abstract ( 1299 )

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In this paper, by using the Brunn-Minkowski-Firey mixed volume theory and dual mixed volume theory, associated with L_p intersection body and dual mixed volume, some dual Brunn-Minkowski inequalities and their isolate
forms are established for L_p intersection body about the normalized L_p radial addition and L_p radial linear combination. Some properties of operator L_p are given.

Delayed stage-structured predator-prey model with impulsive perturbations on predator and chemical control on prey

JIAO Jian-jun;CHEN Lan-sun

2007, 28(12): 1679-1689 . doi:10.1007/s10483-007-1215-y

Abstract ( 1281 )

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We consider a delayed stage-structured pest management predator-prey system with impulsive transmitting on predator and chemical control on prey. Sufficient conditions of the global attractiveness of the pest-extinction boundary periodic solution and permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for practical pest management.

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