应用数学和力学

1988 Vol. 9, No. 9

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The Effect of the Vasomotion on the Mass Transfer in Microcirculation

Wu Wang-yi, Cheng He-ping

1988, 9(9): 763-769.

Abstract(1805) PDF(601)

Abstract:
This paper deals with the mass transfer in the microcirculation with vasomotion. The effect of the vasomotion on the mass transfer is analysed. It is shown that the vasomotion is of great importance to accelerate the mass transfer.

Structure of the Attracting Set of a Piecewise Linear Henon Mapping

Zhu Zhao-xuan, Liu Zeng-rong

1988, 9(9): 771-770.

Abstract(2456) PDF(498)

Abstract:
Detailed structure of the attracting set of the piecewise linear Henon mapping(x, y)→(1-a|x|+by,x)with a=8/5 and b=9/25 is described in this paper using the method of dual line mapping. Let A and B denote the fixed saddles in the first quadrant, and in the third quadrant, respectively. It is claimed that(1)the attracting set is the closure of the unstable manifold of saddle B, which includes the unstable manifold of A as its subset, and(2)the basin of attraction is the closure of the stable manifold of A, bounded by the stable manifold of B, which is in the limiting set of the stable manifold of A.Relations of the manifolds of the periodic saddles with the manifolds of the fixed point are given. Symbolic dynamics notations are adopted which renders possible the study of the dynamical behavior of every piece of the manifolds and of every homoclinic or heteroclinic point.

Vibration Analysis of a Rod with Complex Boundary Conditions

Tang Jia-shi, Li Li Huo, Quan-zhong

1988, 9(9): 781-791.

Abstract(2124) PDF(644)

Abstract:
This paper deals with the forced longitudinal vibration of a rod carrying a concentrated mass and supported by a spring at one end. The vibration of the rodis excited by the motion of the support point at the other end Since the boundary conditions of the problem are complex and it is necessary to consider the damping, we determine only the steady state periodic solution. First the linear system is analysed; then the material nonlinearity is considered and the approximate analytic solution of nonlinear partial differential equation with nonlinear boundary conditions is obtained by the perturbation method.

Tension of a Clamped Rectangular Plate Containing a Central Crack

Tang Ren-ji, Wang Yi-qing

1988, 9(9): 793-801.

Abstract(1835) PDF(454)

Abstract:
Using the fundamental solution of a single crack and the Fourier transform solution of an infinite strip, the tension problem of a clamped rectangular plate containing a central crack is reduced to solve a system of singular integral equations. Then, the normal stress on clamped side and the stress intensity factors of the central crack are carried out by means of Gauss-Jacobi integration formulas. The comparison of numerical results is shown in the "table of stress intensity factors".

A Class of Three-Level Explicit Schemes with Higher Stability Properties for a Dispersive Equation u_t=au_xxx

Lin Peng-cheng

1988, 9(9): 803-808.

Abstract(2232) PDF(525)

Abstract:
In this paper, a class of three level explicit schemes for a dispersive equation u_t =au_xxx with stability condition |r|=|a|△t/(△x)³≤2.382484, are considered. The stability condition for this class of schemes is much better than |r|≤0.3849 in [1], [2] and |r|≤0.701658 in [3], and |r|≤l.1851 in [4].

Thermodynamic Entropy Models of the Frozen-Wall System(Ⅱ)

Zan Ting-quan

1988, 9(9): 809-815.

Abstract(1819) PDF(447)

Abstract:
This paper is a further research of reference [1]. At first, the author analyzes the force-energetics basis of the frozen-wall system. By quantitative discussion of Model(Ⅰ)in reference [1], we get a thermal stability entropy model of the frozen-wall system(called Model(Ⅱ)). At last, we check the models by the field observed data in Anhui Province. P.R.C. The result is greatly satisfactory.

Singular Perturbation of Nonlinear Vector Boundary Value Problem

Kang Sheng-liang, Chen Qi

1988, 9(9): 817-824.

Abstract(2015) PDF(424)

Abstract:
In this paper we study the perturbed boundary value problem of the form in which x,f β∈E^m and a₁(ε),a₂(ε),b₁(ε) and b₂(ε) are matrices of the appropriate size. Under the condition that g_y(t) is nonsingular and other suitable restrictions, the existence of the solution is proved, the asymptotic expansion of solution of order n is constructed, and the remainder term is estimated.

A Stack Protocol of CTM Type with Quartet Feedback

Chen Yong-yi, You Chuan-hua

1988, 9(9): 825-834.

Abstract(2192) PDF(515)

Abstract:
In this paper, we analysed a stack protocol of the CTM(Capetanakis-Tsybakov-Mikhailov)type with quartet feedback. We obtained the explicit expression of the expectation of CRI(Collision Resolution Interval)duration for the delayed access case. By means of numerical calculation we gave respectively the maximal capacities of channel of 0.4140 and 0.41445 packets/slot for both the delayed case and immediate cases.

Application of Reciprocal Theorem for Caculating the Transverse Displacement Equations of the Thin Elastic Circular Plates

Li Nong, Fu Bao-lian

1988, 9(9): 835-842.

Abstract(2141) PDF(558)

Abstract:
On the basis of [1] and [2], this paper further extends the Reciprocal Theorem to the thin elastic circular plates and proposes a general convenient new method, which can easily solve the transverse displacement equations of the circular plates with various complex edges and loads.

A Discrete Nonlinear Stepping Optimization Method and Its Application

Xia De-lin, Zhou Jin-fang

1988, 9(9): 843-850.

Abstract(2329) PDF(498)

Abstract:
Most of the practical design variables should always be discrete quantity within engineering optimization design problems. To obtain the true optimization solution, a discrete optimization method must be used. In this paper, a new method called step optimization search method is presented to solve the discrete quantity mathematic programming problems. The basic idea of this method is to find out an initial feasible point and then to search the optimum point step by step in the neighbouring region of this point so as to obtain an improved new discrete point. Respectively, the new point can be taken as initial one, and the whole process can be carried out once more until the optimum solution of the problem is obtained.Some results of numerical examples of practical problems show that this new method can solve problems quickly and simply and can be applied in a lot of engineering design problems.

Determination of Buckling Mode and Explicit Expression of Critical Load for Simply Supported Rectangular Orthotropic Plates under Biaxial Compression

Li Shu-guang

1988, 9(9): 851-856.

Abstract(2101) PDF(468)

Abstract:
C. Libove[1]proved that at least one of the halfwave numbers m and n in x and y directions of the buckling mode will be I for simply supported rectangular ort hot ropic plates under biaxial compression. This paper will give the physical conditions of m=1or n=1, and, at the same time, show the way of finding appropriate value of m when n=1 and that of n when m=1 and even lead to explicit expression for m and n. Thus, the buckling mode may be determined completely and the expression of critical load may beformlated explicitly.