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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

ANALYTICAL SOLUTION OF FILLING AND EXHAUSTING PROCESS IN PNEUMATIC SYSTEM

The filling and exhausting processes in a pneumatic system are involved with many factors, and numerical solutions of many partial differential equations are always adapted in the study of those processes, which have been proved to be troublesome and less intuitive. Analytical solutions based on loss-less tube model and average friction tube model are found respectively by using fluid net theory, and they fit the experimental results well. The research work shows that： Fluid net theory can be used to solve the analytical solution of filling and exhausting processes of pneumatic system, and the result of loss-less tube model is close to that of average friction model, so loss-less tube model is recommended since it is simpler, and the difference between filling time and exhausting time is determined by initial and final pressures, the volume of container and the section area of tube, and has nothing to do with the length of the tube.

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.

A MODEL FOR THE ACTIVITY COEFFICIENTS OF WATER IN THE AQUEOUS SOLUTION OF HCl-MCl_n (M=Ni, Cu, Na AND Fe) WITHCONSTANT CONCENTRATION RATIO XHCl/XMCl_n

In orber to calculate the activity coefficients of water in the aqueous solution systems of double electrolytes, HCl and MCln (M=Ni, Cu,Na and Fe), a simplified regular solution model has been derived based on the assumption that the electrolytes in the aqueous solution are treated as independent particles instead of their ion forms, and that the interaction of the component pair HCl-MCln in the aqueous solution is very weak as compared with the component pairs HCl-H2O and H2 O-MCln. The interchange energies of the component pairs in the discussed systems, ωWCl-H2o, ωH2o-NiCl2,ωH2o-CuCl2, ωH2o-NaCl and ωH2O-FeCl3, have been evaluated from the experimental data to be-69800, -212600, -90550, -42450 and -198310J·mol-1.

A General Representation of Geometrical Solution Model for Predicting Ternary Thermodynamic Properties

The existing geometrical solution models for predicting ternary thermodynamic properties from relevant binary ones have been analysed,and a general representation was proposed in an integral form on the bases of these models.

AN IMPROVED MODEL FOR COMPUTING SOLUTION DYNAMICS OF NATURAL PRODUCTS WITH ^(13)C NUCLEAR MAGNETIC RELAXATION

The fully anisotropic molecular overall tumbling model with methyl conformation jumps internal rotation among three equivalent sites is proposed,the overall tumbling rotation rates and the methyl internal rotation rates of ponicidin are computed with this model from ~C relaxation parameters.

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.

DISTRIBUTION OF REACHABLE WORKSPACE AREAS IN PHYSICAL MODEL OF THE SOLUTION SPACE OF 2-DOF PARALLEL PLANAR MANIPULATORS

The expressions for calculating the values of the workspace areas of 2-DOF parallel planar manipulators (PPM) is derived. By the aid of computer, the values are calculated and plotted on the physical model of the solution space of the 2-DOF PPMs,so the workspaee-area-property atlas is obtained. The atlas delineates the relationship between the workspace areas and the link lengths of the 2-DOF PPMs all-sidedly. It is very useful for designers overalI to understand and know welI the relationship.

Calculation of thermodynamic properties in liquid phase for ternary Al-Ni-Zn alloys

The results of the calculation of thermodynamic properties in liquid state for ternary Al-Ni-Zn alloys using the newest version of the general solution model for thermodynamic prediction are presented. Nine sections with different molar ratios of Ni to Zn, Zn to Al and Al to Ni were investigated in a temperature interval of 1800-2000 K. Partial and integral molar thermodynamic properties in liquid phase for the Al-Ni-Zn ternary system are determined and discussed.