New Developments on Existence and Uniqueness of Solutions to Some Models in Atmospheric Dynamics

This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical instability and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.

Prediction of Henry's constant in polymer solutions using PCOR equation of state coupled with an activity coefficient model

In this paper,the polymer chain of rotator(PCOR) equation of state(EOS) was used together with an EOS/G^E mixing rule(MHV1) and the Wilson's equation as an excess-Gibbs-energy model in the proposed approach to extend the capability and improve the accuracy of the PCOR EOS for predicting the Henry's constant of solutions containing polymers.The results of the proposed method compared with two equation of state(van der Waals and GC-Flory) and three activity coefficient models(UNIFAC,UNIFAC-FV and Entropic-FV) indicated that the PCOR EOS/Wilson's equation provided more accurate results.The interaction parameters of Wilson's equation were fitted with Henry's constant experimental data and the property parameters of PCOR,a and b,were fitted with experimental volume data(Tait equation).As a result,the present work provided a simple and useful model for prediction of Henry's constant for polymer solutions.

THE WEAK DETONATION SOLUTIONS TO THE SIMPLEST COMBUSTION MODEL

In the present paper the authors prove that all the generalised entropy,solutions of the CJ-model, which for the given Riemann initial data are a oneparameter family u(eta) characterised by weak detonation discontinuity point eta, are just the limits of the admissible solutions u(ek) Of the selfsimilar combustion model. In fact, the authors prove that for any possible eta, there exists a constant B>0 s.t.

EXISTENCE OF GENERALIZED SOLUTIONS TO A HYPERBOLIC MODEL OF COMBUSTION

In this paper we obtain the existence of the generalized solutions to the Cauchy problem for a model of combustion provided that the function f is of nonconvexity and initial values lie in the bounded, measurable class.

Application of LINGO to the Solution of the Water Supply System′s Optimal Operation Model

In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model was transformed to LINGO form and solved successfully. Secondly, the research on the interface between LINGO and the popular office software was made. The optimization software was developed, which had Excel as the workspace and LINGO as the core of computation. Through practice, this software was found stable, easy to use and suitable for the application to the water supply corporations.

Adsorption Kinetics of β-Carotene and Chlorophyll onto Acid-activated Bentonite in Model Oil

The textural properties of acid-activated bentonite （AAB）, which were prepared using four different concentrations of sulfuric acid, were analyzed by adsorption-desorption isotherm of nitrogen using an automated specific surface area and porosity analyzer. The total pore volume, specific surface area and average pore diameter of these four kinds of AAB show a regular changing trend, increasing first and then decreasing, the optimum of which can be achieved at a sulfuric acid concentration of 25% （sample A25）. The kinetic analysis of the adsorption of β-carotene and chlorophyll in model oil solutions, namely, xylene and edible oil solution, has been investigated by using AAB. Experimental results indicated that the adsorption data fit the pseudo-second-order model well. The whole adsorption process of the two pigments on AAB was divided basically into two parts： the initial adsorption of pigments was rapid in the first l0 rain, followed by a slower adsorption process till equilibrium was attained at 60 rain. In addition, the amount and rate of adsorption on A25 increase synchronously with the initial pigment concentration and temperature. The results showed that the adsorption kinetics behavior of AAB with respect to the pigments is not influence by the xylene and edible oil solution.

Numerical Modelling of Dissolving and Driving Exploitation of Potash Salt in the Qarhan Playa——A Coupled Model of Reactive Solute Transport and Chemical Equilibrium in a Multi-component Underground Brine System

Firstly, the macroscopic chemical equilibrium state of a series of chemical reactions between intercrystal brine and its media salt layer （salt deposit） in Qarhan Salt Lake was studied by using the Pitzer theory. The concept of macroscopic solubility product and its relation with accumulated ore dissolving ratio were presented, which are used in the numerical model of dissolving and driving exploitation of potassium salt in Qarhan Salt Lake. And secondly, with a model forming idea of transport model for reacting solutes in the multi-component fresh groundwater system in porous media being a reference, a two-dimensional transport model coupled with a series of chemical reactions in a multi-component brine porous system （salt deposits） was developed by using the Pitzer theory. Meanwhile, the model was applied to model potassium/magnesium transport in Qarhan Salt Lake in order to study the transfer law of solid and liquid phases in the dissolving and driving process and to design the optimal injection/abstraction strategy for dissolving and capturing maximum Potassium/ Magnesium in the mining of salt deposits in Qarhan Salt Lake.

Asymptotic solution of a weak nonlinear model for the mid-latitude stationary wind field of a two-layer barotropic ocean

A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the corresponding problem is discussed.

Improved frequency modeling and solution for parallel liquid-filled pipes considering both fluid-structure interaction and structural coupling

The dynamic characteristics of a single liquid-filled pipe have been broadly studied in the previous literature.The parallel liquid-filled pipe(PLFP)system is also widely used in engineering,and its structure is more complex than that of a single pipe.However,there are few reports about the dynamic characteristics of the PLFPs.Therefore,this paper proposes improved frequency modeling and solution for the PLFPs,involving the logical alignment principle and coupled matrix processing.The established model incorporates both the fluid-structure interaction(FSI)and the structural coupling of the PLFPs.The validity of the established model is verified by modal experiments.The effects of some unique parameters on the dynamic characteristics of the PLFPs are discussed.This work provides a feasible method for solving the FSI of multiple pipes in parallel and potential theoretical guidance for the dynamic analysis of the PLFPs in engineering.

AN ANALYTICAL SOLUTION FOR THE MODEL OF DRUG DISTRIBUTION AND ABSORPTION IN SMALL INTESTINE

According to the physiological and anatomical characteristics of small intestine,neglecting the effect of its motility on the distribution and absorption of drug and nutrient,Y.Miyamoto et al.proposed a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drugby numerical analysis.In this paper,we give a steady-state analytical solution of the above model including deactivationterm.The obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence pro- vides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments.

Calculation of Activity Coefficient from Immiscible Binary Alloy Phase Diagram by Means of Modified Sub-regular Solution Model

The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 and λ 2, which are represented as a linear function of temperature, T . The molar excess Gibbs free energy, G m E, can be written in the form G m E= x A x B[( λ 11 + λ 12 T )+( λ 21 + λ 22 T ) x B ] The calculation is carried out numerically for three immiscible binary alloy systems, Al Pb, Cu Tl and In V. The agreement between the calculated and experimentally determined values of activity coefficient is excellent.

Adsorption of Protein from Model Wine Solution by Different Bentonites

The adsorption of protein from model wine was investigated under different temperatures, pH values, contact times, and concentrations of ethanol, by certain bentonites. The results showed that ethanol molecules could broaden the protein molecules＇ channel to the interlayer of bentonite, and the maximum protein adsorption amount occurred under an ethanol concentration of 12% （by volume） and a pH value of 3.56. The increased single point Brunauer-Emmitt-Teller （BET） surface area （SBET） and adsorption pore volume （VAds） suggested a larger amount of active adsorption sites of the bentonite surface and a wider protein channel from the surface to the inner adsorption sites of bentonite, respectively. At the same time, higher methylene blue test （MBT） and swelling index （Sw） indicated that it was easy for the entrance of water and the absorbance of protein. Higher temperature was found favorable to eliminate more proteins and it took about 20 to 40min to arrive at the maximum adsorption.

A SIMPLIFIED SUBREGULAR SOLUTION MODEL DESCRIBING THE ACTIVITES OF MgCl_2 IN BOTH KCl-MgCl _2-LiCl AND CaCl_2-MgCl_2-NaCl MOLTEN SALT SYSTEMS

A simplified subregular solution model was developed for describing the activities of MgCl 2 in both KCl MgCl 2 LiCl and CaCl 2 MgCl 2 NaCl systems on the assumption that the electrolytes in the solution are treated as independent particles in stead of their ion forms and the interchange energy between the KCl LiCl (or CaCl 2 NaCl) pair is ignored as compared to those of the KCl MgCl 2(or CaCl 2 MgCl 2) and MgCl 2 LiCl (or MgCl 2 NaCl) pairs. The calculating results on the model agree with the observed very well.

General solution model and its new progress

The physicochemical properties of multicomponent systems are involved in all fields of chemistry and have received attention from various related areas such as minerals,metallurgy,material science,environment,biology,and agriculture.At present,the relevant data can be obtained by using two major calculation methods,namely,the first principle method and the empirical method.Though the former has achieved recent great progress,it is still a long way to offer practical data;while the latter has not received progress for almost half a century.Therefore,a new method that is theoretically reasonable and accurate in practical application is necessary to obtain practical and precise physicochemical data for ternary and multicomponent systems.In this paper,a new theoretical model is suggested based on its corresponding binary ones.The feasibility of this theoretical model is discussed in terms of both theoretical analysis and practical performance.

THE BASIC CONSIDERATIONS OF SELF-SReM AND SELF-BoSS MODELS

Model Investigation is the only feasible way to solve the problem about the component activities in concentrated multicomponent alloys and molten slags at present. The basic characteristic of SELF-SReM model is briefly introduced in this paper. It intends to give out the systematical value of component activities in the whole homogeneous region of a concentrated multicomponent melt, then to provide a reliable database for the description of the equilibrium conditions associated with metallurgy processes. For molten slags, the key issue is to distinguish the accuracy of thermodynamic properties in binary systems. The fundamental approach for this task is to link the microscopic bond structure and macroscopic activity based on both of the measurement of high tem- perature Raman spectroscopy and the corresponding computation simulation according to molecular dynamics and quantum chemistry.

A UNIFIED RETENTION MODEL OF SOLUTE IN LIQUID CHROMATOGRAPHY

Based on six thermodynamic equilibria,a unified retention model of solute in liquid chromatography(LC)is first proposed.The unified model was tested and proved to be valid for a LC sys- tem with mobile phase consisting of a complete range of multiple,ternary or binary components and each kind of LC except size exclusion chromatography.In addition,so long as making some assumptions and mathematical conversions,the expressions of various popular models in LC can be derived by using the unified model.

Evaluation of Component Activities in C-Mn-Fe-Si with Model Self-SReM4

A sub-regular solution model SELFSReM4 used to evaluate activities of the components in a homogeneous region of a quaternary system has been developed in Shanghai Enhanced Lab of Ferrometallurgy. This paper introduces the application of SELFSReM4 in evaluating activities of the components in C-Mn-Fe-Si system without SiC precipitation.

Evaluation of Component Activity in Molten MnO-SiO_(2)-Al_(2)O_(3)-CaO System with Model SELF-SReM4

A sub-regular solution model SELF-SReM4 used to evaluate activity of the components in a homogeneous region of a quaternary system has been developed in Shanghai Enhanced Laboratory of Ferrometallurgy.The application of SELF-SReM4 in C-Mn-Fe-Si system without the SiC formation has been introduced in previous paper.It’s application for molten slag of MnO-SiO2-Al2O3-CaO was introduced in this paper.They provide a basis for the prediction of the metal-slag equilibrium conditions.

Calculation of Interaction Parameters from Immiscible Phase Diagram of Alkali Metal or Alkali Earth Metal-Halide System by Means of Subregular Solution Model

In this paper, the interaction parameters in the subregular solution model, λ1 and λ2, are regarded as a linear function of temperature, T. Therefore, the molar excess Gibbs energy of A-B binary system may be reexpressed as follows:Gm^E=xAxB[(λ11+λ12T)+(λ21+λ22T)xB]The calculation of the model parameters, λ11, λ12, λ21and λ22, was carried out numerically from the phase diagrams for 11 alkali metal-alkali halide or alkali earth metal-halide systems. In addition, artificial neural network trained by known data has been used to predict the values of these model parameters. The predicted results are in good agreement with the .calculated ones. The applicability of the subregular solution model to the alkali metal-alkali halide or alkali earth metal-halide systems were tested by comparing the available experimental composition along the boundary of miscibility gap with the calculated ones which were obtained by using genetic algorithm. The good agreement between the calculated and experimental results across the entire liquidus is valid evidence in support of the model.

Modeling the Migration of Soluble Methanol in Unsaturated Soil Zone

A combined model of solute transport and water flow was developed to simulate the migration of methanol, a soluble organic chemical, in unsaturated soil zone. The solute transport equation considered convective-dispersive transport in the liquid phase as well as diffusion in the gas phase. The effect of rainfall and evapotranspiration on transport was considered at the boundary conditions of the governing equations. Data on the characteristics of a loam soil and the climatic conditions in southern California were also introduced to compare the results with those from a study in the USA in which the profiles of methanol distribution and water content in the soil zone at different times had been depicted. This comparison showed that there was good agreement between the two studies. The results showed that methanol contamination reached a depth of about 250 cm after 8 760 h. In contrast, if rainfall and evapotranspiration were not considered, the depth was only about 140 cm. The model therefore confirmed that rainfall strongly affected solute transport.