应用数学和力学

1998 Vol. 19, No. 9

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Two-Dimensional Cellular Automaton Traffic Model with Randomly Switching Traffic Lights

Gu Guoqing, Hui Pakming, Wang Binghong, Dai Shiqiang

1998, 19(9): 752-772.

Abstract(2013) PDF(752)

Abstract:
Cellular automaton traffic models can include various facotrs in traffic systems and the corresponding computational simulations are rather simple and effective.The Biham-MiddletonLevine model (BML model) facilitates the simulation of two-dimensional traffic flow problems via the cellular automaton models.In this paper,the BML model is improved by removing its limitation of synchronized change of traffic lights.In the new model,the traffic light at each crossing could arbitrarily change its starting time and tempo of variation,and hence the model could more realistically describe the influence of traffic lights on the performance of traffic systems.Some new effects appearing in the new model are also elucidated.

Nonlinear Semigroups and Differential Inclusions in Probabilistic Normed Spaces

Zhang Shisheng, Chen Yuqing

1998, 19(9): 759-772.

Abstract(1829) PDF(525)

Abstract:
The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces.As applications,these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.

Best Approximation Theorem for Set-Valued Mappings without Convex Values and Continuity

Ding Xieping, He Yiran

1998, 19(9): 773-778.

Abstract(1855) PDF(645)

Abstract:
In this paper,a new concept of weakly convex graph for set-valued mappings is introduced and studied.By using the concept,some new coincidence,the best approximation and fixed point theorems are obtained.

Connections and Geodesic Characteristic of Equations of Motion for Constrained Mechanical Systems

Luo Shaokai, Guo Yongxin, Mei Fengxiang

1998, 19(9): 779-783.

Abstract(2016) PDF(792)

Abstract:
The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry.A necessary and sufficient condition for the dynamical flow of nonautonomous mechanical system with geodesic characteristic was obtained with respect to a connection on 1-jet bundle.The dynamical flow concerning the non-autonomous case was always of geocesic characteristic with regard to torsionfree connections.Thus the motion of any nonautonomous mechanical system with constraints can be always represented by the motion along the geodesic line of torsion-connection on 1-jet bundle,which is different from the case in an autonomous mechaincal system.

Szebehely’s Problem for Nonholonomic Systems with a Given First Integral

Zhu Haiping

1998, 19(9): 785-790.

Abstract(2590) PDF(541)

Abstract:
An inverse problem for nonholonomic systems is studied.The equations of motion of nonholonomic systems are given,and the Szebehely's problem for a mechanical system with homogeneous nonholonomic constraints is considered,and the general nonholonomic systems with a given first integral are studied.

On Analysis of the Steady Flow in an Irrectangular Parallel-Plate Flow Chamber

Qin Kairong, Jiang Weiyuan, Li Xixi, Liu Zhaorong

1998, 19(9): 791-798.

Abstract(1843) PDF(604)

Abstract:
The parallel-plate flow chamber (PPFC),of which the height is far smaller than its own length and width,is one of the main apparatus for the in vitro study of the mechanical behaviors of cultured cells at the bottom of PPFC undergoing shear stress.The PPFC of which the upper and lower plates are rectangular is usually used by research workers,and the flow field in this kind of PPFC (except for the regions near the entrance and exit) is uniform^[1],so only the effect the shear stress with one value has on cultured cells can be observed during each experiment.A kind of PPFC of which the upper and lower plates are not rectangular is proposed in this paper.The distributions of the velocities inside and the shear stresses at the bottom of the chamber are given by analyzing the flow field of the steady flow in the PPFC.The results show that the mechanical behaviors of cultured cells undergoing the shear stresses with various values may be simultaneously observed by the use of this kind of irrectangular PPFC.The theoretical and experimental results obtained by the use of Ultrasonic Doppler show good agreement.

Disturbances to a Rotating Fluid with a Sphere Moving along the Axis of Rotation

Le Jiachun

1998, 19(9): 799-804.

Abstract(2103) PDF(1088)

Abstract:
In this paper,the disturbaces to a uniformly rotating idealfluid,with a sphere moving steadily along the axis of rotation are analysed by using linearization theory,the equations of disturbance pressure and distur bance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric.The equation of distur bance stream function is analysed with the method of normal modes,and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral distur bances are obtained.The conclusion is drawn that there are three kinds of possible forms of ne utral disturblances.

Differential Geometrical Method in Elastic Composite with Imperfect Interfaces

Tong Jinzhang, Guan Lingyun, Zhang Qingjie

1998, 19(9): 805-814.

Abstract(1831) PDF(576)

Abstract:
A differential geonmetrical method is for the first time used to calculate the effective moduli of a two-plaste elastic composite materials with imperfect interface which the inclusions are assumed to be ellipsoidal of revolutions.All of the interface integral items participating in forming the potential and complementary energy functionals of the composite materials are expressed in terms of intrinsic quantities of the ellipsoidal of revolutions.Based on this,the upper and the lower bound for the effective elastic moduli of the composite materials with inclusions described above have been derived.Under three limiting conditions of sphere,disk and needle shaped inclusions,the results of this paper will return to the bounds obtained by Hashin^[6] (1992).

CML Models and the Nonlinearity of Turbulence

Liu Zhaocun

1998, 19(9): 815-820.

Abstract(1853) PDF(575)

Abstract:
Some new coupled map lattice (CML) models are developed for simulating both convection,diffusion terms and weakly or strongly coupled terms.The structure and features of model are analysed.Numerical results show that the new models are effective for studying spatiotemporal chaos.Finally,the of mechanism turbulence is analysed via the numerical results.

On the Solution of Nonlinear Two-Point Boundary Value Problem u"+g(t, u)=f(t), u(0)=u(2π)=0

Huang Wenhua, Cao Jusheng, Shen Zuhe

1998, 19(9): 821-826.

Abstract(2257) PDF(769)

Abstract:
In this paper,a non-variational version of a max-min principle is proposed,and an existence and uniqueness result is obtained for the nonlinear two-point boundary value problem u"+g(t,u)=f(t),u(0)=u(2π)=0.

Higher-Order Multivariable Euler’s Polynomial and Higher-Order Multivariable Bernoulli’s Polynomial

Liu Guodong

1998, 19(9): 827-836.

Abstract(1866) PDF(706)

Abstract:
In this paper,the definitions of both higher-order multivariable Euler's numbers and polynomial,higher-order multivariable Bernoulli's numbers and polynomial are given and some of their important properties are expounded.As a resut,the mathematical relationship between higher-order multivariable Euler's polynomial (numbers) and higher-order multivariable Bernoulli's polynomial (numbers) are thus obtained.

A New Technique for Solving Non-Axially Symmetrical Large Deflection of Elastic and Thin Circular Plates

Guo Yi, Wang Guifang

1998, 19(9): 837-845.

Abstract(2343) PDF(646)

Abstract:
A new technique for solving large deflection problem of circular plates flexural non-axisy mmetrically is proposed in this paper.The large deflection problem of a circular plate with built-in edge under non-axisymmetrical load is taken as an example to clarify the principle and proce dure of the technique mentioned here.The technique given here can also be used to solve large deflection problem of circular plates under other non-axisy mmetrical loads and boundary conditions.