EQUATION OF STATE FOR POLYMERS

In the theoretical study on equation of state for polymers, much attention has been paid to the polymer in liquid state, but less to that in solid state. Therefore, some empirical and semi-empirical equations of state have been used to describe its pressure-volume-temperature (P-V-T) relations.

Modification to the Hardisty equation, regarding the relationship between sediment transport rate and particle size

Bagnold-type bed-load equations are widely used for the determination of sediment transport rate in marine environments. The accuracy of these equations depends upon the definition of the coefficient k(1) in the equations, which is a function of particle size. Hardisty (1983) has attempted to establish the relationship between k(1) and particle size, but there is an error in his analytical result. Our reanalysis of the original flume data results in new formulae for the coefficient. Furthermore, we found that the k(1) values should be derived using u(1) and u(1cr) data; the use of the vertical mean velocity in flumes to replace u(1) will lead to considerably higher k(1) values and overestimation of sediment transport rates.

The nonlinear evolution equation on the shallow water wave

Based on the variation principle, the nonlinear evolution model for the shallow water waves is established. The research shows the Duffing equation can be introduced to the evolution model of water wave with time.

Asymptotic periodicity of the Volterra equation with infinite delay

For some species, hereditary factors have great effects on their population evolution, which can be described by the well-known Volterra model. A model developed is investigated in this article, considering the seasonal variation of the environment, where the diffusive effect of the population is also considered. The main approaches employed here are the upper-lower solution method and the monotone iteration technique. The results show that whether the species dies out or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the hereditary effects. The evolution of the population may show asymptotic periodicity, provided a certain condition is satisfied for the above factors. (c) 2006 Elsevier Ltd. All rights reserved.

Asymptotic weighted-periodicity of the impulsive parabolic equation with time delay

The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted. The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner-called "asymptotic weighted-periodicity".

Traveling wave front for the Fisher equation on an infinite band region

Instead of discussing the existence of a one-dimensional traveling wave front solution which connects two constant steady states, the present work deals with the case connecting a constant and a nonhomogeneous steady state on an infinite band region. The corresponding model is the well-known Fisher equation with variational coefficient and Dirichlet boundary condition. (c) 2006 Elsevier Ltd. All rights reserved.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

人工源频率域大地电磁法正反演研究

The CSAMT method is playing an important role in the exploration of geothermal and the pre-exploration in tunnel construction project recently. In order to instruct the interpretation technique for the field data, the forward method from ID to 3D and inversion method in ID and 2D are developed in this paper for the artificial source magnetotelluric in frequency domain. In general, the artificial source data are inverted only after the near field is corrected on the basis of the assumption of half-homogeneous space; however, this method is not suitable for the complex structure because the assumption is not valid any more. Recently the new idea about inversion scheme without near field correction is published in order to avoid the near field correction error. We try to discuss different inversion scheme in ID and 2D using the data without near field correction.The numerical integration method is used to do the forward modeling in ID CSAMT method o The infinite line source is used in the 2D finite-element forward modeling, where the near-field effect is occurred as in the CSAMT method because of using artificial source. The pseudo-delta function is used to modeling the source distribution, which reduces the singularity when solving the finite-element equations. The effect on the exploration area is discussed when anomalous body exists under the source or between the source and exploration area; A series of digital test show the 2D finite element method are correct, the results of modeling has important significant for CSAMT data interpretation. For 3D finite-element forward modeling, the finite-element equation is derived by Galerkin method and the divergence condition is add forcedly to the forward equation, the forward modeling result of the half homogeneous space model is correct.The new inversion idea without near field correction is followed to develop new inversion methods in ID and 2D in the paper. All of the inversion schemes use the data without near field correction, which avoid introducing errors caused by near field correction. The modified grid parameter method and the layer-by-layer inversion method are joined in the ID inversion scheme. The RRI method with artificial source are developed and finite-element inversion method are used in 2D inversion scheme. The inversion results using digital data and the field data are accordant to the model and the known geology data separately, which means the inversion without near field correction is accessible. The feasibility to invert the data only in exploration area is discussed when the anomalous body exists between the source and the exploration area.

An empirical equation for the calculation of retention time with extrapolation of temperature in gas chromatography

An empirical equation is proposed to accurately correlate isothermal data over a wide range of temperature With the equation ln k = A* + B*/T-lambda the retention times of different solutes tested on OV-101, SE-54 and PEG 20M capillary columns have been achieved even when lambda is assigned a constant value of 1.7 Comparison with ln k = A + B/T and in k = c + d/T+ h/T-2, shows that the proposed equation is of higher accuracy and is applicable to extrapolation calculation, especially from data at high temperature to those at low temperature. Parameters A* and B* as well as A and B are also discussed. The linear correlation of A* and B* is weaker than that of A and B.

The Image Irradiance Equation: Its Solution and Application

How much information about the shape of an object can be inferred from its image? In particular, can the shape of an object be reconstructed by measuring the light it reflects from points on its surface? These questions were raised by Horn [HO70] who formulated a set of conditions such that the image formation can be described in terms of a first order partial differential equation, the image irradiance equation. In general, an image irradiance equation has infinitely many solutions. Thus constraints necessary to find a unique solution need to be identified. First we study the continuous image irradiance equation. It is demonstrated when and how the knowledge of the position of edges on a surface can be used to reconstruct the surface. Furthermore we show how much about the shape of a surface can be deduced from so called singular points. At these points the surface orientation is uniquely determined by the measured brightness. Then we investigate images in which certain types of silhouettes, which we call b-silhouettes, can be detected. In particular we answer the following question in the affirmative: Is there a set of constraints which assure that if an image irradiance equation has a solution, it is unique? To this end we postulate three constraints upon the image irradiance equation and prove that they are sufficient to uniquely reconstruct the surface from its image. Furthermore it is shown that any two of these constraints are insufficient to assure a unique solution to an image irradiance equation. Examples are given which illustrate the different issues. Finally, an overview of known numerical methods for computing solutions to an image irradiance equation are presented.