应用数学和力学

2007 Vol. 28, No. 12

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Molecular Dynamics of Dewetting of Ultra-Thin Water Films on a Solid Substrate

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

2007, 28(12): 1387-1391.

Abstract(3603) PDF(803)

Abstract:
Molecular dynamics simulation was 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 interactions between solid and liquid have less in fluences 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 the time, 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): 1392-1399.

Abstract(3191) PDF(745)

Abstract:
First, the notions of the measure of noncompactness and condensing set-valued mappings were 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 was proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings were 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 the results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.

Maximal Elements and Generalized Games Involving Condensing Mappings in Locally FC-Uniform Spaces and Applications(Ⅱ)

DING Xie-ping

2007, 28(12): 1400-1410.

Abstract(3438) PDF(671)

Abstract:
Some new systems of generalized vector quasi-equilibrium problems involving condensing mappings were introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems were proved in locally FC-uniform spaces. These results improve and generalize some recent known results in literature to locally FC-uniform spaces.

Analytical Modeling of Sandwich Beam for Piezoelectric Bender Elements

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

2007, 28(12): 1411-1416.

Abstract(3291) PDF(590)

Abstract:
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 compare well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.

Nonlinear Mathematical Model for Large Deflection of Incompressible Saturated Poroelastic Beams

YANG Xiao, WANG Chen

2007, 28(12): 1417-1424.

Abstract(3610) PDF(587)

Abstract:
Nonlinear governing equations were 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, was 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 were shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam were 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.

Genetic Algorithm Optimization for a Finned Channel Performance

S. S. Mousavi, K. Hooman, S. J. Mousavi

2007, 28(12): 1425-1432.

Abstract(3566) PDF(550)

Abstract:
Compared to a smooth channel, a finned-channel provides higher heat transfer coefficient and increasing the fin height enhances the heat transfer. However, this heat transfer enhancement is associated with an increase in the pressure drop. This leads to an increased pumping power requirement so that one may seek an optimum design for such systems. The main goal of this paper is to define the exact location and size of fins in such a way that a minimal pressure drop coincides with an optimal heat transfer based on the genetic algorithm. Each arrangement of fins was considered as a solution of the problem (an individual for genetic algorithm). An initial population was generated randomly at the first step. Then the algorithm had searched among these solutions and made new solutions iteratively by its functions to find an optimum design as reported.

Adaptive Genetic Algorithm for Solving Bilevel Linear Programming Problem

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

2007, 28(12): 1433-1440.

Abstract(3247) PDF(603)

Abstract:
An adaptive genetic algorithm is proposed for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes may be infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.

On the Stability of Discontinuous Systems via Vector Liapunov Functions

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

2007, 28(12): 1441-1447.

Abstract(3359) PDF(770)

Abstract:
The stability of systems with discontinuous right-hand side (with solutions in Filippov's sense) via locally Lipschitz continuous and regular vector Liapunov functions are discussed. A new type of "set-valued derivative" of vector Liapunov functions was introduced, some generalized comparison principles on discontinuous systems were shown. Furthermore Liapunov stability theory was developed for a class of discontinuous systems based on locally Lipschitz continuous and regular vector Liapunov functions.

Sliding State Stepping Algorithm Solving Impact Problems of Multi-Rigid-Body System With Joint Friction

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

2007, 28(12): 1448-1454.

Abstract(3001) PDF(624)

Abstract:
Impact dynamics of multi-rigid-body systems with joint friction was considered. Based on traditional approximate assumption dealing with impact problem, a general numerical method called sliding state stepping algorithm was introduced. This method can avoid the difficulties in solving di-f ferential equations with variable scale and the result can avoid the energy inconsistency before and a-f ter impact due to considering the complex of the tangential sliding mode. An example was given to describe the concrete details dealing with these difficulties.

Closed Form Stress Distribution in 2D Elasticity for all Boundary Conditions

A. Y. T. Leung, ZHENG Jian-jun

2007, 28(12): 1455-1467.

Abstract(3371) PDF(600)

Abstract:
A Hamiltonian method was applied to study analytically the stress distributions of orthotropic two-dimensional elasticity in (x, z) plane for arbitrary boundary conditions without beam assumptions. It is a method of separable variables for partial differential equations using displacements and their conjugate stresses as unknowns. Since coordinates (x, z) cannot be easily separated, an alternative symplectic expansion was used. Similar to the Hamiltonian formulation in classical dynamics, the x coordinate as time variable so that z becomes the only independent coordinate in the Hamiltonian matrix differential operator. The exponential of the Hamiltonian matrix is symplectic. There are homogenous solutions with constants to be determined by the boundary conditions and particular integrals satisfying the loading conditions. The homogenous solutions consist of the eigen-solutions of the derogatory zero eigenvalues (zero eigen-solutions) and that of the wellbehaved nonzero eigenvalues (nonzero eigen-solutions). The Jordan chains at zero eigenvalues give the classical Saint Venant solutions associated with averaged global behaviors such as rigid-body translation, rigid-body rotation or bending. On the other hand, the nonzero eigen-solutions describe the exponentially decaying localized solutions usually ignored by Saint-Venant's principle. Completed numerical examples were newly given to compare with established results.

Model for Dependent Default With Hyperbolic Attenuation Effect and the Valuation of CDS

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

2007, 28(12): 1468-1474.

Abstract(2680) PDF(851)

Abstract:
A hyperbolic attenuation function was introduced to reflect the effect of one firm's default to its partner. If the two firms are competitors (copartners), the default intensity of one firm will decrease (increase) abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinction. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, so the fair swap premium of a CDS can be valued.

Analysis of Phase Transformation From Austenite to Martensite in NiTi Alloy Strips Under Uniaxial Tension

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

2007, 28(12): 1475-1482.

Abstract(3401) PDF(589)

Abstract:
Phase transformation from austenite to martensite in NiTi alloy strips under uniaxial tension has been observed in experiments and has been numerically simulated as a localized deformation. This work presented an analysis of that using the theory of phase transformation. The jump of deformation gradient across interface between the two phases and the Maxwell relation were considered. Governing equations for the phase transformation were derived. The analysis was reduced to finding the minimum value of the loading at which the governing equations have a unique, real, physically acceptable solution. The equations were solved numerically and it is verified that the unique solution exists definitely. The Maxwell stress, the stresses and strains inside both austenite and martensite phases, and the transformation-front orientation angle were determined that are in reasonably good agreement with experimental observations.

Improved Proximal-Based Decomposition Method for Structured Monotone Variational Inequalities

LI Min, YUAN Xiao-ming

2007, 28(12): 1483-1492.

Abstract(3039) PDF(628)

Abstract:
The proximal-based decomposition method was originally proposed by Chen and Teboulle (Math. Programming, 1994, 64(1):81-101) for solving convex minimization problems. This paper extended to solve monotone variational inequalities associated with separable structures with the improvements that the restrictive assumptions on the involved parameters are much relaxed, and thus makes it practical to solve the involved subproblems easily. Without additional assumptions, global convergence of the new method is proved under the same mild assumptions on the problem's data as the original method.

On the L_p Intersection Body

ZHU Xian-yang, LENG Gang-song

2007, 28(12): 1493-1501.

Abstract(2601) PDF(701)

Abstract:
By using 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 I_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): 1502-1512.

Abstract(3329) PDF(612)

Abstract:
A delayed stage-structured pest management predator-prey system with impulsive transmitting on predators and chemical on prey concern was considered. Sufficient conditions of the global attractivity of pest-extinction boundary periodic solution and permanence of the system were obtained. It was also proved that all solutions of the system are uniformly ultimately bounded. The results provide reliable tactical basis for the practical pest management.