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2010年 第31卷 第4期    刊出日期：2010-04-20

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Articles

Global existence of solutions to the periodic initial value problems for two-dimensional Newton-Boussinesq equations

房少梅 金玲玉 郭柏灵

2010, 31(4):  405-414.  doi:10.1007/s10483-010-0401-9

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A class of periodic initial value problems for two-dimensional Newton-Boussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With iteration methods, the local existence of the solutions is obtained. Using the method of a priori estimates, the global existence of the solution is proved.

Intuitionistic Menger inner product spaces and applications to integral equations

张石生 M.Goudarzi R.Saadati S.M.Vaezpour

2010, 31(4):  415-424.  doi:10.1007/s10483-010-0402-z

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In this paper, first introduce and define an intuitionistic Menger inner product space, and then, obtain a new fixed point theorem in a complete intuitionistic Menger inner product space. As an application, the results are used to study the existence and uniqueness of the solution to a linear Volterra integral equation.

Linear Rayleigh-Taylor instability analysis of double-shell Kidder’s self-similar implosion solution

胡军 尹协远 杭义洪 张树道

2010, 31(4):  425-438.  doi:10.1007/s10483-010-0403-x

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This paper generalizes the single-shell Kidder’s self-similar solution to the double-shell one with a discontinuity in density across the interface. An isentropic implosion model is constructed to study the Rayleigh-Taylor instability for the implosion compression. A Godunov-type method in the Lagrangian coordinates is used to compute the one-dimensional Euler equation with the initial and boundary conditions for the double-shell Kidder’s self-similar solution in spherical geometry. Numerical results are obtained to validate the double-shell implosion model. By programming and using the linear perturbation codes, a linear stability analysis on the Rayleigh-Taylor instability for the double-shell isentropic implosion model is performed. It is found that, when the initial perturbation is concentrated much closer to the interface of the two shells, or when the spherical wave number becomes much smaller, the modal radius of the interface grows much faster, i.e., more unstable. In addition, from the spatial point of view for the compressibility effect on the perturbation evolution, the compressibility of the outer shell has a destabilization effect on the Rayleigh-Taylor instability, while the compressibility of the inner shell has a stabilization effect.

论文

Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet

朱婧 郑连存 张志刚

2010, 31(4):  439-448.  doi:10.1007/s10483-010

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The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.

Articles

Numerical simulation of bubble breakup phenomena in a narrow flow field

张阿漫 倪宝玉 宋炳月 姚熊亮

2010, 31(4):  449-460.  doi:10.1007/s10483-010-0405-z

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Based on the boundary integral method, a 3D bubble breakup model in a narrow flow field is established, and a corresponding computation program is developed to simulate the symmetrical and asymmetrical bubble breakup. The calculated results are compared with the experimental results and agree with them very well, indicating that the numerical model is valid. Based on the basic behavior of bubbles in a narrow flow field, the symmetrical and asymmetrical bubble breakup is studied systematically using the developed program. A feasibility rule of 3D bubble breakup is presented. The dynamics of sub-bubbles after splitting is studied. The influences of characteristic parameters on bubble breakup and sub-bubble dynamics are analyzed.

Simulation on motion of particles in vortex merging process

黄海明 徐晓亮

2010, 31(4):  461-470.  doi:10.1007/s10483-010-0406-x

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In a two-phase flow, the vortex merging influences both the flow evolution and he particle motion. With the blobs-splitting-and-merging scheme, the vortex merging is alculated by a corrected core spreading vortex method (CCSVM). The particle motion n the vortex merging process is calculated according to the particle kinetic model. The esults indicate that the particle traces are spiral lines with the same rotation direction is the spinning vortex. The center of the particle group is in agreement with that of the merged vortex. The merging time is determined by the circulation and the initial ratio of the vortex radius and the vortex center distance. Under a certain initial condition, a stretched particle trail is generated, which is determined by the viscosity, the relative position between the particles and the vortex, and the asymmetrical circulation of the two merging vortices.

Generalized variational principles for boundary value problem of electromagnetic field in electrodynamics

郑成博 刘彬 王作君 郑世科

2010, 31(4):  471-480.  doi:10.1007/s10483-010-0407-9

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An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien’s method, a pair of generalized variational principles (GVPs) are established, which directly leads to all four Maxwell’s equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem.

Effect of irregularity on the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer

S.Gupta A.Chattopadhyay D.K.Majhi

2010, 31(4):  481-492.  doi:10.1007/s10483-010-0408-9

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The paper studies the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface. The irregularity is taken in the half space in the form of a rectangle. It is observed that torsional surface waves propagate in this assumed medium. In the absence of the irregularity, the velocity equation of the torsional surface wave is also obtained. For a layer over a homogeneous half space, the velocity of torsional surface waves coincides with that of the Love waves.

Effect of relaxation times on circular crested waves in thermoelastic diffusive plate

Rajneesh Kumar Tarun Kansal

2010, 31(4):  493-500.  doi:10.1007/s10483-010-0409-6

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The propagation of circularly crested thermoelastic diffusive waves in an infinite homogeneous transversely isotropic plate subjected to stress free, isothermal/insulated and chemical potential conditions is investigated in the framework of different thermoelastic diffusion theories. The dispersion equations of thermoelastic diffusive Lamb type waves are derived. Some special cases of the dispersion equations are also deduced.

Generalized H-η-accretive operators in Banach spaces with application to variational inclusions

罗雪萍 黄南京

2010, 31(4):  501-510.  doi:10.1007/s10483-010-0410-6

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In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.

Bifurcation method for solving multiple positive solutions to boundary value problem of p-Henon equation on the unit disk

李昭祥 杨忠华

2010, 31(4):  511-520.  doi:10.1007/s10483-010-0411-6

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In this paper, an algorithm is proposed to solve the O(2) symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking l in the p-Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O(2) symmetric positive solutions is found via the extended systems. The other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.

Nonlinear Schr¨odinger equation with combined power-type nonlinearities and harmonic potential

徐润章 徐闯

2010, 31(4):  521-528.  doi:10.1007/s10483-010-0412-7

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This paper discusses a class of nonlinear Schr¨odinger equations with combined power-type nonlinearities and harmonic potential. By constructing a variational problem the potential well method is applied. The structure of the potential well and the properties of the depth function are given. The invariance of some sets for the problem is shown. It is proven that, if the initial data are in the potential well or out of it, the solutions will lie in the potential well or lie out of it, respectively. By the convexity method, the sharp condition of the global well-posedness is given.

Optimal control for bio-heat equation due to induced microwave

Piyanka Dhar Ranajit Dhar

2010, 31(4):  529-534.  doi:10.1007/s10483-010-0413-x

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A distributed optimal control problem for a system described by a bio-heat equation for a homogeneous plane slab of tissue is analytically investigated. The required tissue temperature at a particular location of the tumour in hyperthermia can be attained within the total operation time of the process due to induced microwave radiation which is taken as control. The tissue temperature against the tissue length at different operation time of the process is considered to attain the desired temperature of the tumor.