STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .3. BINARY MIXTURE OF POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION WITH STRONG-INTERACTIONS

For a binary mixture of polydisperse polymers with strong interactions, the free energy, the equation of state, the chemical potentials and the spinodal are formulated on the basis of the lattice fluid model. Further, the spinodal curves for the system wi

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER MIXTURES

A statistical thermodynamics theory of polydisperse polymer blends based on a lattice model description of a fluid is formulated. Characterization of a binary polydisperse polymer mixture requires a knowledge of the pure polymer system and the interaction energy. It is assumed that the intrinsic and interactive properties of polymer (for example, T*, P*, rho*, and epsilon(ij)*) are independent of molecular size. Thermodynamic properties of ternary and higher order mixtures are completely defined in terms of the pure fluid polymer parameters and the binary interaction energies. Thermodynamic stability criteria for the phase transitions of a binary mixture are shown. The binodal and spinodal of general binary systems and of special binary systems are discussed.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER BLENDS WITH STRONG INTERACTION

A statistical thermodynamics theory of polydisperse polymer mixtures with strong interaction between dissimilar components based on a lattice fluid model is formulated. Expressions for the free energy, equation of state, phase stability and spinodal for a polydisperse, binary polymer mixture with strong interaction are derived.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMERS

A statistical thermodynamics theory of polydisperse polymers based on a lattice model of fluids is formulated. Pure polydisperse polymer can be completely characterized by three scale factors and the molecular weight distribution of the system. The equation of state does not satisfy a simple corresponding-states principle, except for a polymer fluid of sufficiently high molecular weight. The relationships between thermal expansion coefficient alpha and isothermal compressibility beta with reduced variables are also predicted.

STATISTICAL THERMODYNAMICS OF A LATTICE FLUID - PURE POLYMER

A statistical thermodynamics theory of a polydisperse polymer based on a lattice model of a fluid is formulated. The pure polydisperse polymer is completely characterized by three scale factors and the distribution law of the system. The equation of state does not satisfy a simple corresponding state principle, except for the polymer fluid with sufficiently high molecular weight.

ADVANCED ELECTROANALYTICAL CHEMISTRY IN CHINA .1. GENERAL ASPECT AND SOME METHODOLOGIES

The Research on Electroanalytical chemistry in China started mainly from the beginning of new China in 1949. It has already good basis and development nowadays. A review with references to the end of seventies has been published in "Reviews in Analytical Chemistry" 1) and in a book titled "Fifty years of Chinese Chemistry" edited by the Chinese Chemical Society in 1985 2). Since then more than thousand papers have been published, and it is impossible and also not necessary to describe all of them. This review only deals with the main progress of electroanalytical chemistry in China in recent years. Some new developed methodologies will be reviewed by S. Dong in the next article.

Substrate induction and statistical optimization for the production of chitosanase from Microbacterium sp OU01

The chitosanase production was markedly enhanced by substrate induction, statistical optimization of medium composition and culture conditions by Microbacteritan sp. OU01 in shake-flask. A significant influence of (NH4)(2)SO4, MgSO4 center dot 7H(2)O and initial pH on chitosanase production was noted with Plackett-Burman design. It was then revealed with the method of steepest ascent and response surface methodology (RSM) that 19.0 g/L (NH4)(2)SO4, 1.3 g/L MgSO4 and an initial pH of 2.0 were optimum for the production of chitosanase; colloidal chitosan appeared to be the best inducer for chitosanase production by Microbacterium sp. OU01. This optimization strategy led to the enhancement of chitosanase from 3.6 U/mL to 118 U/mL. (c) 2006 Elsevier Ltd. All rights reserved.

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied. (C) 2003 Elsevier B.V. All rights reserved.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins's linear,model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper. (C) 2002 Elsevier Science Ltd. All rights reserved.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

人口统计信息空间可视化系统研究

Population research is a front area concerned by domestic and overseas, especially its researches on its spatial visualization and its geo-visualization system design, which provides a sound base for understanding and analysis of the regional difference in population distribution and its spatial rules. With the development of GIS, the theory of geo-visualization more and more plays an important role in many research fields, especially in population information visualization, and has been made the big achievements recently. Nevertheless, the current research is less attention paid to the system design for statistical-geo visualization for population information. This paper tries to explore the design theories and methodologies for statistical-geo-visualization system for population information. The researches are mainly focused on the framework, the methodologies and techniques for the system design and construction. The purpose of the research is developed a platform for population atlas by the integration of the former owned copy software of the research group in statistical mapping system. As a modern tool, the system will provide a spatial visual environment for user to analyze the characteristics of population distribution and differentiate the interrelations of the population components. Firstly, the paper discusses the essentiality of geo-visualization for population information and brings forward the key issue in statistical-geo visualization system design based on the analysis of inland and international trends. Secondly, the geo-visualization system for population design, including its structure, functionality, module, user interface design, is studied based on the concepts of theory and technology of geo-visualization. The system design is proposed and further divided into three parts: support layer, technical layer, user layer. The support layer is a basic operation module and main part of the system. The technical layer is a core part of the system, supported by database and function modules. The database module mainly include the integrated population database (comprises spatial data, attribute data and geographical features information), the cartographic symbol library, the color library, the statistical analysis model. The function module of the system consists of thematic map maker component, statistical graph maker component, database management component and statistical analysis component. The user layer is an integrated platform, which provides the functions to design and implement a visual interface for user to query, analysis and management the statistic data and the electronic map. Based on the above, China's E-atlas for population was designed and developed by the integration of the national fifth census data with 1:400 million scaled spatial data. The atlas illustrates the actual development level of the population nowadays in China by about 200 thematic maps relating with 10 map categories(environment, population distribution, sex and age, immigration, nation, family and marriage, birth, education, employment, house). As a scientific reference tool, China's E-atlas for population has already received the high evaluation after published in early 2005. Finally, the paper makes the deep analysis of the sex ratio in China, to show how to use the functions of the system to analyze the specific population problem and how to make the data mining. The analysis results showed that: 1. The sex ratio has been increased in many regions after fourth census in 1990 except the cities in the east region, and the high sex ratio is highly located in hilly and low mountain areas where with the high illiteracy rate and the high poor rate; 2. The statistical-geo visualization system is a powerful tool to handle population information, which can be used to reflect the regional differences and the regional variations of population in China and indicate the interrelations of the population with other environment factors. Although the author tries to bring up a integrate design frame of the statistical-geo visualization system, there are still many problems needed to be resolved with the development of geo-visualization studies.