2010 Vol. 31, No. 4

Display Method:
Global Existence of Solutions of the Periodic Initial Value Problems for Two-Dimensional Newton-Boussinesq Equations
FANG Shao-mei, JIN Ling-yu, GUO Bo-ling
2010, 31(4): 379-388. doi: 10.3879/j.issn.1000-0887.2010.04.001
Abstract(1502) PDF(913)
Abstract:
A class of periodic initial value problems for two-dmiensional Newton-Bouss inesqequations was investigated.First the Newton-Boussinesq equations were turned into the equivalent integral equations,then by the iteration methods the local existence of the solutions was obtained.Finally using the method of a priori estimates,the global existence of the solutions was proved.
Linear Rayleigh-Taylor Instability Analysis of a Double-Shell Kidder’s Self-Similar Implosion
HU Jun, YIN Xie-yuan, HANG Yi-hong, ZHANG Shu-dao
2010, 31(4): 399-410. doi: 10.3879/j.issn.1000-0887.2010.04.002
Abstract(1482) PDF(838)
Abstract:
By generalizing the single-shell Kidder's self-similar solution to double-shell with a discontinuity for density across the interface,an isentropic implosion model was constructed to study the Rayleigh-Taylor instability for the miplosion compression.A Godunov-type method in Lagrangian coordinates was used to compute the one-dmiensional Euler equation with the initial conditions and boundary conditions of the double-shell Kidder's self-similar solution in spherical geometry,and numerical results were obtained to validate the double-shell miplosion model. By programming and using the linear perturbation code,a linear stability analysis on the Rayleigh-Taylor instability for the double-shellisen tropic miplosion model was performed.It is found that when the initial perturbation concentrates much closer to the inter face of the two shells,or when the spherical wave number becomes much smaller,the interface modal radius grows much faster,i.e.more unstable.In addition,from the spatial point of view for the compressibility effect on the perturbation evolution,it is found that the compressibility of the outer shell has destabilization effect on Rayleigh-Taylor instability,while the compressibility of the inner shell has stabilization effect.
Effect of the Slip Condition on the MHD Stagnation-Point Flow Over a Power-Law Stretching Sheet
ZHU Jing, ZHENG Lian-cun, ZHANG Zhi-gang
2010, 31(4): 411-419. doi: 10.3879/j.issn.1000-0887.2010.04.003
Abstract(1346) PDF(1227)
Abstract:
The steady two-dimensionalm agnetohyd rodynamic stagnation flow towards a nonlinear stretching surface was studied.The no slip condition on the solid boundary was replaced by the partial slip cond ition.A scaling group of transformations was applied to get the invariants. Using the invariants,a third order ordinary differential equation corresponding to the momentum was obtained.The analytical solution was obtained in the series form with the help of homotopy analysis method.The reliability and efficiency of series solutions were illustrated by good agreement with numerical results in the literature.Besides,the effects of the slip parameter,the magnetic field parameter,velocity ratio parameter,suction velocity parameter and the power law exponent on the flow were investigated.Results show that the velocity and shear stress pro files are greatly in fluenced by these parameters.
Numerical Simulation of the Bubble Breakup Phenomena in the Narrow Flow Field
ZHANG A-man, NI Bao-yu, SONG Bing-yue, YAO Xiong-liang
2010, 31(4): 420-432. doi: 10.3879/j.issn.1000-0887.2010.04.004
Abstract(1427) PDF(1058)
Abstract:
Based on boundary in tegral method,the 3D bubble breakup model in the narrow flow field was erected and corresponding computing program was developed to smiulate symmetrical and unsymm etrical bubble breakup.The calculated results are compared with the expermiental results and agree with them very well, which indicates the numerical model is valid. Starting with the basic behavior of bubble in the narrow flow field,the symmetrical and unsymmetrical bubble breakup was studied systematically with the program developed,and feasible rule of 3D bubble breakup was presented based on the published numerical results and experimental data.Besides,the dynamics of sub-bubbles after splitting was studied,and the influence of characteristic parameters on the bubble breakup and sub-bubbles dynamics was analyzed.
Simulation on Motion of Particles in Vortex Merging Process
HUANG Hai-ming, XU Xiao-liang
2010, 31(4): 433-442. doi: 10.3879/j.issn.1000-0887.2010.04.005
Abstract(988) PDF(809)
Abstract:
In two-phase flow,the vortex merging in fluences both flow evolution and particles motion.With the help of the blobs-splitting-and-merging scheme,the vortex merging was calculated by using a corrected core spreading vortex method(CC SVM);based on these,the particlesmotion in vortex merging process was calculated according to the particle kinetic model. As the results indicate,the particle traces are spiral lines,keeping the same rotation direction with the spinning vortex;the center of particles group is in agreement with that of the merged vortex;the merging tmie is determined by the circulation and initial ratio of the vortex radius and vortex centerd istance;and in a certain initial condition,a stretched particle trail is generated,which is determined by the viscosity,the relative position between particles and vortex, and the unsymm etrical circulation of the two merging vortexes.
Generalized Variational Principles for Boundary Value Problem of Electromagnetic Field in Electrodynamics
ZHENG Cheng-bo, LIU Bin, WANG Zuo-jun, ZHENG Shi-ke
2010, 31(4): 443-450. doi: 10.3879/j.issn.1000-0887.2010.04.006
Abstract(1710) PDF(956)
Abstract:
The expression of the generalized principle of virtual work for the boundary value problem of linear and aniso tropic electromagnetic field was given.Using Pro.fW.Z.Chien's method,a pair of generalized variational principles(GVP s)were established,which could directly lead to all four Maxwell equations,two intensity-potential equations,two constitutive equations and eight boundary conditions.A family of constrained variational principles was deduced sequentially.As the additional verifications,two degenerated forms were obtained,which were equivalent to two known variational principles.Two modified GVPs were given to provide the hybrid finite element models for the present problem.A more complete theoretical foundation for the finite element applications was provided for the discussed 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): 451-462. doi: 10.3879/j.issn.1000-0887.2010.04.007
Abstract(1531) PDF(791)
Abstract:
The torsional surface wave propagation in an initially stressed aniso tropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface was studied.The irregularity had been taken in the half-space in the form of arectangle.It is observed that to rsional surface waves propagate in this assumed medium.In the absence of irregularity the velocitye quation of torsional surface wave has also been obtained.Further,it has been seen that for a layer over a homogeneous half space,the velocity of torsional surface waves coincides with that of Love waves.
Effect of Relaxation Times on Circular Crested Waves in Thermoelastic Diffusive Plate
Rajneesh Kumar, Tarun Kansal
2010, 31(4): 463-471. doi: 10.3879/j.issn.1000-0887.2010.04.008
Abstract(1518) PDF(796)
Abstract:
The propagation of circularly crested the rmoelasticd iffusive waves in an infinite homogeneous transversely isotropic plate subjected to stress free,isothermal/insulated and chemical potential conditions was investigated in the framework of different theories of thermoelastic diffusion.The dispersion equations of therm oelastic diffusive Lamb type waves were derived'some special cases of dispersion equation were also deduced.
Generalized H-η-Accretive Operators in Banach Spaces With an Application to Variational Inclusions
LUO Xue-ping, HUANG Nan-jing
2010, 31(4): 472-480. doi: 10.3879/j.issn.1000-0887.2010.04.009
Abstract(1315) PDF(801)
Abstract:
A new notion of generalizedH-η-accretive operator which provided a unifying framework for the generalizedm-accretive operator and theH-η-mono tone operator in Banach spaces was introduced and studied.A resolvent operator associated with the generalizedH-η-accretive operator was defined and its Lipschitz continuity was shown.As an application,the solvability for a class of variational inclusion sinvolving the generalizedH-η-accretive operators in Banach spaces was considered.By using the technique of resolvent mapping,aniterative algorithm for solving the variational inclusion in Banach space was constructed.Under some suitable conditions,the existence of solution for the variational inclusion and the convergence of iterative sequence generated by the algorithm were proved.
Bifurcation Method for Solving Multiple Positive Solutions to Boundary Value Problem of p-Henon Equation on the Unit Disk
LI Zhao-xiang, YANG Zhong-hua
2010, 31(4): 481-490. doi: 10.3879/j.issn.1000-0887.2010.04.010
Abstract(1137) PDF(954)
Abstract:
An algorithm which was applied to solving theO(2)symmetric positive solutions to the boundary value problem ofp-Henon equation was proposed.Taking linp-Henon equation as a bifurcation parameter,the symmetry-breaking bifurcation point on the branch of theO(2) symmetric positive solutions was found via the extended systems.Finally,other symmetric positive solutions were computed by the branch switching method based on the Liapunov-Schmid treduction.
Nonlinear Schrdinger Equation With Combined Power-Type Nonlinearities and Harmonic Potential
XU Run-zhang, XU Chuang
2010, 31(4): 491-498. doi: 10.3879/j.issn.1000-0887.2010.04.011
Abstract(1412) PDF(847)
Abstract:
A class of nonlinear SchrLdinger equations with combined power-type nonlinearities and harmonic potential are discussed.By constructing a variational problem the potential well method is applied.The structure of the potential well and the properties of 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 either in the potential well or out of it respectively.By convexity method,the sharp condition of the global well-posedness is given.
Optimal Control Problem for Bio-Heat Equation Due to Induced Microwave
Piyanka Dhar, Ranjit Dhar
2010, 31(4): 499-504. doi: 10.3879/j.issn.1000-0887.2010.04.012
Abstract(1265) PDF(809)
Abstract:
A distributed optimal control problem for a system described by bio-heat equation for a homogeneous plane slab of tissue was analytically investigated so that a required temperature of the tissue at a particular point of location of tumor in hyperthermia could be attained with in a total time of operation of the process due to induced microwave radiation which was taken as control. Here the temperature of the tissue against the length of the tissue at different tmies of operation of the process was considered for investigation to atta in the desired temperature of the tumor.