On the stability of the solution to a gonorrhea discrete mathematical model

ＯＮＴＨＥＳＴＡＢＩＬＩＴＹＯＦＴＨＥＳＯＬＵＴＩＯＮＴＯＡＧＯＮＯＲＲＨＥＡＤＩＳＣＲＥＴＥＭＡＴＨＥＭＡＴＩＣＡＬＭＯＤＥＬＪｉｎＪｕｎ（金均）（ＳｈａｎｇｈａｉＴｅａｃｈｅｒｓＵｎｉｖｅｒｓｉｔｙ,Ｓｈａｎｇｈａｉ）（ＲｅｃｅｉｖｅｄＭａｒｃｈ...     

On the closure problem of turbulence model theory

ＯＮＴＨＥＣＬＯＳＵＲＥＰＲＯＢＬＥＭＯＦＴＵＲＢＵＬＥＮＣＥＭＯＤＥＬＴＨＥＯＲＹＴｓａｉＳｈｕ－ｔａｎｇ（蔡树棠）ＬｉｕＹｕ－ｌｕ（刘宇陆）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ;ＳｈａｎｑｈａｉＩｎｓｔｏｆＡｐｐｌ．Ｍａｔｈ．ａｎｄＭｅｃｈ．,...     

On the Somigliana dislocations associated with applications of the Neuber–Papkovich solution in multiply-connected regions

Summary The study aims to explain the problem of single-valuedness of the mean stress and dilatation in multiply-connected regions. It is shown that in multiply-connected regions, displacement representation potentials, in particular the Neuber–Papkovich potentials, have to be submitted to the integral conditions in order to avoid the many-valuedness. Received 8 September 1998; accepted for publication 8 April 1999     

The existence and uniqueness of weak solution of the flow between two concentric rotating spheres

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｔｕｄｙｔｈｅｕｎｓｔｅａｄｙａｘｉｓｙｍｍｅｔｒｉｃｉｎｃｏｍｐｒｅｓｓｉｂｌｅｆｌｏｗｂｅｔｗｅｅｎｔｗｏｃｏｎｃｅｎｔｒｉｃｓｐｈｅｒｅｓ．Ｔｈｉｓｆｌｏｗｉｓｃａｌｌｅｄａｓｓｐｈｅｒｉｃ...     

ON THE EXISTENCE AND STABILITY OF SOLUTION FOR SEMI－HOMOGENEOUS BOUNDARY VALUE PROBLEM

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＦＯＲＳＥＭＩ－ＨＯＭＯＧＥＮＥＯＵＳＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＤｏｎｇＱｉｎｘｉ（董勤喜）;ＨｕａｎｇＸｉａｎｋａｉ（黄先开）（ＲｅｃｅｉｖｅｄＪｕｌｙ．４．１９...     

A formula of solution to the integral of rational functions

ＡＦＯＲＭＵＬＡＯＦＳＯＬＵＴＩＯＮＴＯＴＨＥＩＮＴＥＧＲＡＬＯＦＲＡＴＩＯＮＡＬＦＵＮＣＴＩＯＮＳＧｕｉＺｕ－ｈｕａ（桂祖华）（ＴｈｅＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ＳｈａｎｇｈａｉＪｉａｏ－ｔｏｎｇＵｎｉｖｅｒｓｉｔ...     

On the multiple solutions to a three-coefficient spectral model of wind-driving ocean current equation

In this paper, a research on the problem of multiple solutions of the three-coefficient low-spectrum model for the quasi-geostrophic ocean current equation with forcing and dissipation terms is carried out. The state of the ocean current under wind conditions such as those of typhoon is discussed carefully and the relations between the multiple solutions and the coefficientsR and ε are analyzed. It is seen that in an approximate triangular region with the Rossby-coefficientR less than 0.5, and the friction-coefficient ε less than 0.22, there exist three equilibrium solutions, among which two are stable and one is unstable. For the former, the coefficientA orB in the expansion is rather large, while for the latter.A orB is relatively small. They respectively imply how much the ocean energy is fed back from the wind stress and the solution with a largeA is much more stable than that with a largerB. Institute of Systems Science, Academia Sinica The project partly supported by the national project of 75-76-01-03 “Study on numerical prediction of the South China Sea current”.     

Polymer contribution to the thermal conductivity and viscosity in a dilute solution (Fraenkel Dumbbell model)

The phase-space kinetic theory for polymeric liquid mixtures is used to obtain an expression for the polymer contribution to the thermal conductivity of a nonflowing, dilute solution of polymers, where the polymer molecules are modeled as Fraenkel dumbbells. This theory takes into account three mechanisms for the energy transport: diffusion of kinetic energy (including the Öttinger-Petrillo term), diffusion of intramolecular energy, and the work done against the intramolecular forces. This paper is an extension of previous developments for the Hookean dumbbell model and the finitely-extensible dumbbell model. A comparison among the dumbbell results suggests that the thermal conductivity increases with chain stiffness. In addition, the zero-shear-rate viscosity and first normal-stress coefficient are also given for the Fraenkel dumbbell model.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Comparing analytical and numerical solution of nonlinear two and three‐dimensional hydrostatic flows

New test cases for frictionless, three‐dimensional hydrostatic flows have been derived from some known analytical solutions of the two‐dimensional shallow water equations. The flow domain is a paraboloid of revolution and the flow is determined by the initial conditions, the nonlinear advective terms, the Coriolis acceleration and by the hydrostatic pressure. Wetting and drying is also included. Some specific properties of the exact solutions are discussed under different hypothesis and relative importance of the forcing terms. These solutions are proposed for testing the stability, the accuracy and the efficiency of numerical models to be used for simulating environmental hydrostatic flows. The computed solutions obtained with a semi‐implicit finite difference—finite volume algorithm on unstructured grid are compared with the corresponding analytical solutions in both two and three space dimension. Excellent agreement are obtained for the velocity and for the resulting water surface elevation. Comparison of the computed inundation area also shows a good agreement with the analytical solution with degrading accuracy observed when the inundation area becomes relatively large and for long simulation time. Copyright © 2006 John Wiley & Sons, Ltd.     

New exact solution of the problem of rotationally symmetric Couette-Poiseuille flow

An exact solution is obtained for the problem of steady-state viscous incompressible flow under a pressure difference in the gap between coaxial cylinders for the case where the inner cylinder rotates at a constant angular velocity. The solution differs from the classical Couette-Poiseuille result by the presence of radial mass transfer, which provides for interaction between the poloidal and azimuthal circulations. The flow rate is found to depend linearly on the angular velocity of rotation of the inner cylinder. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 71–77, September–October, 2007.     

Unsteady flow of viscoelastic fluid between two cylinders using fractional Maxwell model

The unsteady flow of an incompressible fractional Maxwell fluid between two infinite coaxial cylinders is studied by means of integral transforms.The motion of the fluid is due to the inner cylinder that applies a time dependent torsional shear to the fluid.The exact solutions for velocity and shear stress are presented in series form in terms of some generalized functions.They can easily be particularized to give similar solutions for Maxwell and Newtonian fluids.Finally,the influence of pertinent parameters on the fluid motion,as well as a comparison between models,is highlighted by graphical illustrations.     

Optimal harvesting of a two species competition model with imprecise biological parameters

In this paper a two competing species harvesting model with imprecise biological parameters has been developed. We have developed a method to handle these imprecise parameters and discuss the dynamical behaviour of the model. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. Also the bionomic equilibrium of the harvesting model has been analysed. Next the equilibrium solution of the control problem has been derived, and then dynamical optimization of the harvest policy is carried out taking combined harvesting effort as a dynamic variable by invoking Pontryagin’s Maximum Principle. Our important analytical findings are illustrated through computer simulation using MATLAB followed by discussions and conclusions.     

A uniformly valid asymptotic solution of the Navier-Stokes equations

ＡＵＮＩＦＯＲＭＬＹＶＡＬＩＤＡＳＹＭＰＴＯＴＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳＱｉｎＳｈｅｎｇ－ｌｉ（秦圣立）ＺｈａｎｇＡｉ－ｓｈｕ（张爱淑）（Ｄｅｐｔ．ＯｆＰｈｙｓｉｃｓ,ＱｕｆｕＴｅａｃｈｅｒｓＵｎｉｖｅ...     

On the numerical solution to two fluid models via a cell centered finite volume method

A new method for the discretization of nonlinear systems of partial differential equations occurring in the numerical simulation of two phase flows is proposed. This method is based on a cell centered finite volume discretization on possibly unstructured meshes and aims to approximate three-dimensional stationary and evolution problems in arbitrary geometries. We are able to consider conservative and non-conservative systems of equations and the method belongs to the class of shock-capturing upwind ones. In the paper we put the emphasis on the treatment of terms involving first-order derivatives since we deal with the change of type (hyperbolic to non-hyperbolic). One of the features of the method is that it does not rely a priori on the hyperbolic character of the convection operator. The method is illustrated on a classical numerical benchmark and we refer to the bibliography concerning various and numerous applications in the context of two phase flows.     

THE QUALITATIVE ANALYSIS OF TWO SPECIES PREDATOR-PREY MODEL WITH ROLLING’S TYPE III FUNCTIONAL RESPONSE

This paper is denoted to the qualitative analysis of two species predator-prey model with Boiling’s type III functional response. Conditions for the global stability ofnontrivial equilibrium points and conditions for the existence and uniqueness of limit cycles around the positive equilibrium point are obtained. The biological interpretations of these conditions are discussed. The authors believe that the conditions established in this paper are new to literature.     

Existence of a Solution for a Nonlinearly Elastic Plane Membrane Subject to Plane Forces

The two-dimensional nonlinear ‘membrane’ equations for a plate made of a Saint Venant–Kirchhoff material have been justified by D. Fox, A. Raoult and J.C. Simo (1993) by means of the method of formal asymptotic expansions applied to the three-dimensional equations of nonlinear elasticity. This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of R³, is equivalent to finding the critical points of a functional whose nonlinear part depends on the first fundamental form of the unknown deformed surface. We establish here a local existence result for these equations in the case of the membrane subject to forces parallel to its plane and we give qualitative properties of the solutions found in this fashion in terms of injectivity and of minimization. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analysis of the wave solution of the elastokinetic equations of a Cosserat continuum for the case of bulk plane waves

A study is made of waves in a Cosserat continuum, whose strain state is characterized by independent displacement and rotation vectors. The propagation of longitudinal and transverse bulk waves is considered. Wave solutions are sought in the form of wave trains specified by a Fourier spectrum of arbitrary shape. It is shown that if the solution is sought in the form of three components of the displacement vector and three components of the rotation vector which depend on time and the longitudinal coordinate, the initial system is split into two systems, one of which describes longitudinal waves, and the other transverse waves. For waves of both types, dispersion relations and analytical solutions in displacement are obtained. The dispersion characteristics of the solutions obtained differ from the dispersion characteristics of the corresponding classical elastic solutions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 196–203, March–April, 2008.     

含两类附加函数的扩展等参有限元法

基于扩展有限元的基本思想,提出一类指数型间断函数来模拟。由于裂纹或节理等非连续结构所导致的位移不连续现象,该附加函数是以到间断处的垂直距离为自变量,且随距离的增大而呈指数衰减,同时,在非连续结构末端引入能反映其奇异场特性的三角基函数。本文用弱解形式推导了扩展有限元格式,并论证了两类附加函数在单元公共边上能够保持位移连续性这一要求。最后,编制了二维4节点和三维8节点的扩展等参有限元程序,并分别给出了算例,结果表明在模拟裂纹追踪时,扩展有限元法可行且有效。     

On the solution of the Darboux problem

We consider the problem of determining the angular position of a rigid body in space from its known angular velocity and initial position (the Darboux problem) in quaternion setting. For an arbitrary angular velocity vector of the body, we present a solution based on Lappo-Danilevskii’s recursion relations [1]. New special cases of solvability of the Darboux problem in closed form are obtained.