Variational methods for the problems of nonconservative force fields in the micropolar elastodynamics

Based on the properties of the convolution and the convolute commutation, some quasi-variational principles for the problems of nonconservative force field in the micropolar elastodynamics are given and verified in this paper. The theorem given in this paper can be applied to the theories of the nonlocal elastic mediums and the nonlocal micropolar elastic mediums.     

A finite element explicit algorithm for solving the temporal temperature fields

Practical calculations and numerical experiments in this paper have shown that in elements relating to a common node it is acceptable and reasonable for derivaties of temperature with respect to time on nodes of those elements to be presented with one on common node, if linear interpolation shape function is taken. The relation between the derivative of temperature to time on a certain node and the temperature on other nodes around that node may therefore be established after discretization of the differential equation is made in space by the finite element method. Then an explicit scheme for calculating the temperature fields may be constructed. The obtained algebraic equations. being simple and the procedure being straight will be its two tangible advantages and its calculating will, therefore, be fast. The stability analysis by the maximum principle, as in the example quoted, proves that the stability condition is similar to that in implicit algorithms.     

Singularly perturbed nonlinear second order elliptic equation

In this paper, we study singular perturbation problems of some semi-linear second order elliptic equations with nonlinear boundary value conditions: where ε is a small positive parameter and u/ l is a directional derivative, which lies on an oblique vector (x,ε). We have given a construction of the asymptotic solutions and proof of their asymptotic correctness, which is based on the principle of contraction mapping.     

Eigenvalue problem for integro-differential equation of supersonic panel,flutter

The dynamic stability of a thin plate in supersonic flow based on 2-dimensional linear theory leads to the study of a new problem in mathematical physics: complex eigenvalue prob-lem for a non-self-adjoint fourth-order integro-differential equation of Volterra’s type.Exact solutions of the aeroelastic system is obtained. In contrast to various approximate analyses, our critical curve agrees satisfactorily with experimental data, being free from divergence in the low supe’rsonic region. Moreover, we observe some notable physical behaviors: (1) mutual separation of flutter and vacuum frequency spectrums, (2) degeneracy of critical Mach number. The present method may be generalized in solving the supersonic flutter for 3-dimensional airfoil model as well as blade cascade in turbo-generator.     

Statistical mechanics of temporary polymer networks I. The equilibrium theory

In part I of this work (the present article) the equilibrium state of temporary polymer networks is treated in the framework of thermodynamics and statistical mechanics. The network is described as an open system. Thereby we use a modified spring-bead model in which the beads represent junctions that decay and reform thus adding a viscous component to the assumed elastic behaviour of the permanent network. The relevant statistical equation — analogous to Liouville's equation — is solved. The grand-canonical probability density function and two of three equations of state are derived. Explicit formulae are given for several relevant probabilities. For instance the probabilityw (z)dz that a network chain connecting two junctions has a contour length betweenz andz +dz is given by the Wien type formulaw(z) =A z ³ exp {–B z} whereA andB do not depend onz.     

Principles of instrumentation and signal processing method of PLDA

It is shown in this paper that in geometrical space two polarization planes of thelinearly polarized light waves scattered by particles in measuring ellipsoid constitute anangle of π/2. while in sequence of time the signals sent out by two symmetricphotodetectors in PLDA ard separated by a phase angle π.This property of PLDAenables the improvement of SNR.The similarity between power spectrum of photoelectrical current of PLDA andprobability density function P_d(u_c)of investigated flow velocity has been provedtheoretically and checked by agreement of obtained results with classical theory andgenerally accepted experiments.     

Some problems for viscoelastic rods

Using an approach proposed in [3],we consider some linear and nonlinear problems forviscoelastic rods.Results in [1]for linear case are affirmed more elamentarily and simplyhere.We also treat linear problem with damping term and nonlinear problem with powernonlinearity Pu~3. Some new results are established.     

The method of matrices conjoint multiplication for the problem of circular arc corrugated diaphragm

The circular are corrugated diaphragins are taken in this paper and structures of several sections of the ring shells and a central cireular plale I matrices and link matrices are derived by using Prof. Chuen Hei-zang’s general the ring shell[1] and perturbation theory of the circular thin plates. Throngh the meined of matrices conjoint multiplication, the linear exact solution and nonlinear soluaen are obtained. The resutts agree with that of the experiments presented by W. A. Wildhack..     

Time correlation functions of a one-dimensional infinite system

We investigate the time evolution of a simple one-dimensional system with an infinite number of particles. We calculate some time correlation functions and show that they behave asymptotically as 1/t.     

Quantum statistical hierarchy equation in nonequilibrium systems

An extension is given for the Fourier expansion method with the contraction technique, which was introduced by Balescu for quantum statistical systems. This is attained by introducing a diagrammatic method with a concept of moving contraction. Then the hierarchy equation for the Contracted Fourier coefficient of the Wigner distribution function is obtained. As an application, a generalized master equation involvingn-body collision effects and quantum statistical effects is also derived.