A CLOSED SYSTEM OF EQUATIONS FOR DENSE TWO-PHASE FLOW AND EXPRESSIONS OF SHEARING STRESS OF DISPERSED PHA’E AT A WALL

In this paper, each of the two phases in dense two-phase flow is considered as continuous medium and the fundamental equations for two-phase flow are described in Eulerian form. The generalized constitutive relation of the Bingham fluid is applied to the dispersed phase with the analysis of physical mechanism of dense two-phase flow. The shearing stress of dispersed phase at a wall is used to give a boundary condition. Then a mathematical model for dense two-phase flow is obtained. In addition, the expressions of shearing stress of dispersed phase at a wall is derived according to the fundamental model of the factional collision between dispersed-phase particles and the wall.     

SOLUTIONS FOR A SYSTEM OF NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS

ＳＯＬＵＴＩＯＮＳＦＯＲＡＳＹＳＴＥＭＯＦＮＯＮＬＩＮＥＡＲＲＡＮＤＯＭＩＮＴＥＧＲＡＬＡＮＤＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＤｉｎｇＸｉｅｐｉｎｇ（丁协平）ＷａｎｇＦａｎ（王凡）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｉｃｈ...     

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θmodel of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θmodel in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θmodel has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θmodel was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.     

K-ε-T MODEL OF DENSE LIQUID-SOLID TWO-PHASE TURBULENT FLOW AND ITS APPLICATION TO THE PIPE FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＬｉｑｕｉｄ＿ｓｏｌｉｄｔｗｏ＿ｐｈａｓｅｆｌｏｗｅｘｉｓｔｓｗｉｄｅｌｙｉｎｎａｔｕｒｅａｎｄｍａｎｙｉｎｄｕｓｔｒｉａｌｍｉｎｉｓｔｒｉｅｓ,ｆｏｒｅｘａｍｐｌｅ,ｓｅｄｉｍｅｎｔ＿ｌａｄｅｎｗａｔｅｒｆｌｏｗｉｓａｃｈａｒａｃｔｅｒｉｓｔｉｃｌｉｑｕｉｄ＿ｓｏｌｉｄｔｗｏ＿ｐｈａｓｅｆｌｏｗｉｎｎａｔｕｒｅａｎｄｈｙｄｒａｕｌｉｃｔｒａｎｓｐｏｒｔｏｆｓｏｌｉｄｍａｔｅｒｉａｌｉｓａｃｈａｒａｃｔｅｒｉｓｔｉｃｉｎｄｕｓｔｒｉａｌａｐｐｌｉｃａｔｉｏｎ.Ｔｈｅｓｔｕｄ…     

THE EQUATIONS OF MOTION FOR A NONHOLONOMIC SYSTEM UNDER THE ACTION OF IMPULSIVE FORCES

The equations of impact for a nonholonomic system described with generalizedcoordinated have been discussed in detail in the general references of classical dynamics.But these equations contain undetermined multipliers which made the problem complicatedThrough the appropiate treatment of mathematics,using the δ-function andexpression of matrix in this paper,the author derived equations of impact for anonholonomic system without undetermined multipliers.Therefore.the problem can besolved more simply.     

DIFFERENTIAL EQUATIONS OF MOTION FOR A VARIABLE-MASS HOLONOMIC SYSTEM WITH A UNIFORMLY ROTATING CONSTRAINT

In this paper,the differential equations of motion will be established for variable-massholonomic mechanical systems constrained to the uniform rotation.including the equationsin Lagrange form,Nielsen form and Appell form.The application of these new equations isillustrated with an example.     

REFLECTION AND RADIATION OF A WAVE SYSTEM AT THE OPEN END OF A SUBMERGED ELASTIC PIPE

The reflection and radiation of a wave system at the open end of a submerged.semi-infinite elastic pipe are studicd.This wave system consists of a flexural wave in the pipe,anacoustic surface wave in the fluid exterior to the pipe and an acoustit wave in the pipe’sinterior.Fourier transfrom techniques are used to formulate this semi-infinite geometryproblem rigorously as a Wiener-Hopf type equation.An approximate solution is obtainedby using a perturbation method in which the ratio of the massdensities of the fluid and thepipe material is regarded as a small parameter.The calculation of the reflection coefficientis emphasized,and the polar plots of the radiation coefficient are also presented.     

THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATION

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＡＮＤＴＨＥＩＲＡＰＰＬＩＣＡＴＩＯＮＺｈａｏＪｉｅ－ｍｉｎ（赵杰民）;ＨｕａｎｇＫｅ－ｌｅｉ（黄克累）...     

ASYMPTOTIC NON-STABILITY AND BLOW-UP AT BOUNDARY FOR SOLUTIONS OF A FILTRATION EQUATION

For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.     

SECOND-ORDER CNOIDAL WAVES AT THE FREE SURFACE AND INTERFACE OF A TWO-FLUID SYSTEM

In this paper, using the PLK method and reductive perturbation method,we obtainedthe second approximation to cnoidal waves at the free surface and ihterface for the two-fluid system considered in[1].The corresponding results in[3]and[4]may be obtained asspecial cases in this paper.     

A NECESSARY AND SUFFICIENT CONDITION FOR THEOSCILLATION OF SOLUTIONS OF LIENARD TYPE SYSTEM WITH MULTIPLE SINGULAR POINTS

I.IntroductionJ.R.Graer']andG.VillariI2]gavenecessar\JandsufficientconditionsfortheoscillationofsolutionofLienardsystemf~])~F(x),y~~glXJ(l.l)HanMaoanI3]gaveoscillatirytheoremsforLienardt}'pesystemt'.ithasingularpointi~h(.t/)~F(x),#~~g(x)(1.2)Whereas,aloto…     

AN ANALYSIS FOR DIFFRACTION OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN THICK PLATES WITH A CAVITY

By using the complex variable method and conformal mapping,the diffraction of flexu-ral waves and dynamic stress concentrations in thick plates with a cavity have been studied.A generalsolution of the stress problem of the thick plate satisfying the boundary conditions on the contour of anarbitrary cavity is obtained.By employing the orthogonal function expansion technique,the dynamicstress problem can be reduced to the solution of an infinite algebraic equation series.As an example,the numerical results for the dynamic stress concentration factor in thick plates with a circular,ellipticcavity are graphically presented.The numerical results are discussed.     

FREE CONVECTION FLOW OF WATER AT 4℃ PASSING AN INFINITE POROUS PLATE WITH CONSTANT SUCTION IN A ROTATING SYSTEM

In this work an analysis of steady free convection flow of waterat 4℃ passing a vertical infinite porous plate in a rotating systemis considered.Approximate solutions for the coupled nonlinear equa-tions are obtained for the velocity and the temperature.The effectof E’(Eckman number) is discussed,when P (Prandtl number)=11.4,which corresponds to water at 4℃.     

FREE CONVECTION FLOW OF WATER AT 4℃ PASSING AN INFINITE POROUS PLATE WITH CONSTANT SUCTION IN A ROTATING SYSTEM

In this work an analysis of steady free convection flow of water at 4℃ passing a vertical infinite porous plate in a rotating system is considered. Approximate solutions for the coupled nonlinear equations are obtained for the velocity and the temperature. The effect of E’ (Eckman number) is discussed, when P (prandtl number)=11.4, which corresponds to water at 4℃.     

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM (Ⅰ)

Based on the mathematical model of a kind of complicated financial system, all possible things that the model shows in the operation of our country’s macro-financial system were analyzed, such as balance, stable periodic, fractal, Hopf-bifurcation, the relationship between parameters and Hopf-bifurcations,and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior were analyzed. This study will deepen people’s understanding of the lever function of all kinds of financial policies.     

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅱ)

ＩｎｔｒｏｄｕｃｔｉｏｎＣｈａｏｔｉｃｉｓｔｈｅｉｎｈｅｒｅｎｔｒａｎｄｏｍｎｅｓｓｉｎｔｈｅｄｅｆｉｎｉｔｅｓｙｓｔｅｍ .Ｔｈｅｄｅｆｉｎｉｔｅｎｅｓｓｉｓｃａｕｓｅｄｂｙｔｈｅｓｙｓｔｅｍｉｎｔｅｒｎａｌｓｂｕｔｎｏｔｂｙｔｈｅｅｘｔｅｒｎａｌｄｉｓｔｕｒｂａｎｃｅ,ｗｈｉｌｅｔｈｅｉｎｈｅｒｅｎｔｒａｎｄｏｍｎｅｓｓｉｓｔｈｅｉｒｒｅｇｕｌａｒａｎｄｄｉｆｆｉｃｕｌｔ＿ｔｏ＿ｂｅ＿ｐｒｅｄｉｃｔｅｄｂｅｈａｖｉｏｒｏｆｔｈｅｓｙｓｔｅｍ .Ｗｈａｔｉｓｍｏｓｔａｔｔｒａｃｔｉｖｅｏｆｔｈｅｃ…     

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅱ)

Based on the work discussed on the former study, this article first starts from the mathematical model of a kind of complicated financial system, and analyses all possible things that the model shows in the operation of our country’s macro-financial system: balance, stable periodic, fractal, Hopf-bifurcation, the relationship between parameters and Hopf-bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior have been analyzed. This study will deepen people’s understanding of the lever function of all kinds of financial policies.     

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅰ)

ＩｎｔｒｏｄｕｃｔｉｏｎＣｈａｏｔｉｃｉｓｔｈｅｉｎｈｅｒｅｎｔｒａｎｄｏｍｎｅｓｓｉｎｔｈｅｄｅｆｉｎｉｔｅｓｙｓｔｅｍ .Ｔｈｅｄｅｆｉｎｉｔｅｎｅｓｓｉｓｃａｕｓｅｄｂｙｔｈｅｓｙｓｔｅｍｉｎｔｅｒｎａｌｓｂｕｔｎｏｔｂｙｔｈｅｅｘｔｅｒｎａｌｄｉｓｔｕｒｂａｎｃｅ[1- 4],ｗｈｉｌｅｔｈｅｉｎｈｅｒｅｎｔｒａｎｄｏｍｎｅｓｓｉｓｔｈｅｉｒｒｅｇｕｌａｒａｎｄｄｉｆｆｉｃｕｌｔ＿ｔｏ＿ｂｅ＿ｐｒｅｄｉｃｔｅｄｂｅｈａｖｉｏｒｏｆｔｈｅｓｙｓｔｅｍ[5 ,6 ].Ｗｈａｔｉｓｍｏｓｔａｔｔｒａｃｔｉｖｅ…     

A STUDY OF THE CATASTROPHE AND THE CAVITATION FOR A SPHERICAL CAVITY IN HOOKE’S MATERIAL WITH 1/2 POISSON’S RATIO

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓ,ｔｈｅｒｅｓｅａｒｃｈｅｓｏｎｃａｖｉｔａｔｉｏｎａｎｄｃａｔａｓｔｒｏｐｈｅｏｆａｃａｖｉｔｙｈａｖｅｓｕｐｐｌｉｅｄａｎｅｗｍｅｔｈｏｄｆｏｒｉｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｍｅｃｈａｎｉｃｓｏ...     

ON EXACT SOLUTION OF KRMN’S EQUATIONS OF RIGID CLAMPED CIRCULAR PLATE AND SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD

It is extremely difficult to obtain an exact solution of von Kármán’s equationsbecause the equations are nonlinear and coupled.So far many approximate methods havebeen used to solve the large deflection problems except that only a few exact solutions havebeen investigated but no strict proof on convergence is presented yet.In this paper,first ofall,we reduce the von Kármán’s equations to equivalent integral equations which arenonlinear,coupled and singular.Secondly the sequences of continuous function withgeneral form are constructed using iterative technique.Based on the sequences to beuniformly convergent,we obtain analytical formula of exact solutions to von Kármán’sequations related to large deflection problems of circular plate and shallow spherical shellwith clamped boundary subjected to a concentrated load at the centre.