The mirror relations and nonlinear viscoelasticity of polymer melts

An attempt is made to incorporate into a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type the two mirror relations of Gleissle, as well as his relation between the steady-state first normal-stress difference and the shear viscosity curve. It is shown that the three relations can hold separately within this constitutive model, but not simultaneously, because they require a different nonlinear strain measure, namelyS ₁₂ () = – a ( – 1) (a = 0 for 1,a = 1 for 1) for the mirroring of the viscosities,S ₁₂ () = – a (–k ²/) (a = 0 for k, a = 1 for k) for the mirroring of the first normal-stress coefficients, and for the third relation. Here denotes the shear strain and erf the error function. Experimental data on melts of a low-density polyethylene, a high-density polyethylene and a polypropylene show that the mirror relations are passable approximations, but that the third relation meets reality surprisingly close if the right value ofk is used.     

An example of applications of the elementary catastrophe theory in Hamiltonian systems

The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems.     

从相关测量的数据恢复超短激光脉冲的波形

本文证明了,只要测量了脉冲光强的二阶相关函数G~(2)(τ)和单延迟的三阶相关函数G~(3)(τ),便可以恢复超短激光脉冲的强度波形。并提出一种恢复脉冲波形的计算方法,编制了计算机程序,对实验数据作了处理,证实这种计算方法是可行的。在此基础上建议一种通过相关测量确定超短激光脉冲波形的新型仪器。     

On the structure of continua and the mathematical properties of algebraic elastodynamic of a triclinic structural system

This paper is neither laudatory nor derogatory but it simply contrasts with what might be called elastostatic (or static topology), a proposition of the famous six equations. The extension strains and the shearing strains which were derived by A.L. Cauchy, are linearly expressed in terms of nine partial derivatives of the displacement function (u _i ,u _j ,u _h )=u(x ⁱ ,x ^j ,x ^k ) and it is impossible for the inverse proposition to sep up a system of the above six equations in expressing the nine components of matrix (∂(u _i ,u _j ,u _h )/∂(x ⁱ ,x ^j ,x ^k )). This is due to the fact that our geometrical representations of deformation at a given point are as yet incomplete^[1]. On the other hand, in more geometrical language this theorem is not true to any triangle, except orthogonal, for “squared length” in space^[2]. The purpose of this paper is to describe some mathematic laws of algebraic elastodynamics and the relationships between the above-mentioned important questions.     

Laminar boundary layer between two planes perpendicular to each other

In this paper, we obtain a third-order approximate solution for the laminar boundary layer between two planes perpendicular to each other.In boundary layer equations, the viscous and the inertial terms have the same quantity step. In this paper, at first, supposing that the inertial terms are bigger than the viscous terms, we solve the boundary layer equations, and then we suppose that the viscous terms are bigger than the inertial terms. At last, we take the mean value as the valid solution of the boundary layer equations.The first- and the second-order approximate solutions obtained in this paper coincide with the results in ref. [1], while the third-order solution obtained in this paper is better than that in ref. [1].     

On singularly perturbed quasilinear systems

In this paper, the objective is to give sufficient conditions for the existence of solution of the nonlinear two-point boundary value problem(1.1). And we employ these results to consider the boundary layer phenomena of the quasilinear weakly coupled singularly perturbed system (DP)_q.     

Load supporting prefabricated wall reinforced by a frame

This load supporting prefabricated wall consists of a thin plate reinforced along its boundaries by a frame. With the loads acting on the frame, the plate has its boundary conditions defined neither by forces nor by displacements. On the basis of satisfying the biharmonic equation of the stress function for the plate, we make the total strain energy to be minimum to ensure the compatibility of displacements for the two elastic bodies. Thus we get a set of infinite simultaneous equations. The results obtained indicate the method of solution is effective.     

An approximate solution considering flow inertia between spherical surfaces

In this paper, the analytical expressions of the pressure distribution, velocity distribution and discharge of the flow between spherical surfaces are found by using the method of iterative approximate solution when the inertia terms of Navier-Stokes equations in spherical coordinates are taken into consideration. Furthermore, using these expressions, we can directly obtain the corresponding analytical expressions of the laminar radial flow between parallel disks, which are fully identical with corresponding results presented by refs. [3,4].     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

一种基于复数域微分的资料同化新方法

提出了一种基于复数域微分的资料同化新方法. 针对变分资料同化中目标泛函梯度计算复杂和精度不高的问题, 首先利用复变量求导法把梯度分析过程转化为复变泛函的数值计算, 进而高效和高精度地获得梯度值; 然后结合经典的最优化方法, 给出了非线性物理系统资料同化问题的新求解算法; 最后对典型混沌系统和包含“开关”现象的单格点比湿发展方程进行了资料同化数值实验, 结果表明新方法能非常有效地估计出非线性动力预报模式的初始条件. 关键词： 资料同化 复数域微分 非线性物理系统 梯度分析