应用数学和力学

2008 Vol. 29, No. 2

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Initial-Boundary Value Problem of One Class Nonlinear Schrêdinger Equations Described in Molecular Crystals

FANG Shao-mei, GUO Bo-ling

2008, 29(2): 127-132.

Abstract(2799) PDF(607)

Abstract:
The initial-boundary value problem of one class nonlinear Schrêdinger equations described in molecular crystals is studied.Furthermore,the existence of the global solution is obtained by means of interpolation inequality and a priori estimation.

Influences of Marangoni Effect on Solidification of Curved Interfaces With Constant Curvature

HU Guo-hui, ZHOU Zhe-wei

2008, 29(2): 133-139.

Abstract(2898) PDF(548)

Abstract:
The asymptotic method and phase field simulation were applied to study the influences of variation of the surface tension with temperature on the movements of solid-liquid interfaces in the solidification process of spherical and cylindrical nuclei respectively.Results indicate that Marangoni effect will increase the critical nucleation radius,slow up the movement of interface.The tip speed of dendrite decreases linearly with Marangoni number for melt without convection.The results of phase field simulation are qualitatively in accordance with that of asymptotic method.

Research on the Nucleation and Coagulation of Nanoparticles in the Parallel Twin Jets

YIN Zhao-qin, LIN Jian-zhong, ZHOU Kun

2008, 29(2): 140-148.

Abstract(2433) PDF(494)

Abstract:
The large eddy simulation method has been used to simulate the diffusion of H₂SO₄ vapor in the parallel twin jets.The distributions of number concentration and size of nanoparticles produced by nucleation and coagulation in sulfuric acid/water system were given.The functions of the sulfur content,relative humidity and jet Reynolds number were evaluated according to the distributions of number concentration and size of nanoparticles.The results show that the nucleation in sulfuric acid/water system produces large number of nanoparticles,and ga-sto-nanoparticle conversion mostly takes place in the middle and interface of the twin jets.The coagulation process of particles reduces the number concentration but increases the mean particle size.For the case with higher sulfur content,more number and smaller size nanoparticles are produced by nucleation and coagulation.There is also a larger number of nanoparticles for the cases with higher relative humidity and jet Reynolds number.

Theoretical Prediction of the Stiffness and Strength of Three-Dimensional and Four-Directional Braided Composites

LI Dian-sen, LU Zi-xing, LU Wen-shu

2008, 29(2): 149-156.

Abstract(2889) PDF(685)

Abstract:
Based on unit cell model,the 3D 4-directional braided composites can be simplified as unidirectional composites with different local axial coordinate system and the compliance matrix of unidirectional composites can be defined utilizing the bridge model.The total stiffness matrix of braided composites can be obtained by the volume average stiffness of unidirectional composites with different local axial coordinate systems and the engineering elastic constants of braided composites were computed further.Based on the iso-strain assumption and the bridge model,the stress distribution of fiber bundle and matrix of different unidirectional composites can be determined and the tensile strength of 3D 4-directional braided composites was predicted by means of the Hoffman.s failure criterion for the fiber bundle and Mises.failure criterion for the matrix.

Discontinuous Element Pressure Gradient Stabilizations for the Compressible Navier-Stokes Equations Based on Local Projections

LUO Yan, FENG Min-fu

2008, 29(2): 157-168.

Abstract(3489) PDF(945)

Abstract:
A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations based on local projections was derived.The resulting finite element formulation is stable and uniquely solvable without requiring a B-B stability condition.An error estimate was obtained.

Robust Attitude Control for Rapid Multi-Target Tracking in Spacecraft Formation Flying

YUAN Chang-qing, LI Jun-feng, WANG Tian-shu, BAOYIN He-xi

2008, 29(2): 169-180.

Abstract(2963) PDF(487)

Abstract:
A robust attitude tracking control scheme for spacecraft formation flying is presented.The leader spacecraft with a rapid mobile antenna and a camera was modeled.While the camera is tracking the ground target,the antenna is tracking the follower spacecraft.By an angular velocity constraint and an angular constraint,two methods were proposed to compute the reference attitude profiles of the camera and antenna,respectively.To simplify the control design problem,the desired inverse system(DIS),which can convert the attitude tracking problem of 3D space into the regulator problem,was derived.Based on DIS and sliding mode control(SMC),a robust attitude tracking controller was developed in the presence of mass parameter uncertainties and external disturbance.By Liapunov stability theory,the closed loop system stability can be achieved.The numerical simulations show that the proposed robust control scheme exhibits significant advantages for the multi-target attitude tracking of a two-spacecraft formation.

Supercritical as Well as Subcritical Hopf Bifurcation in Nonlinear Flutter Systems

CHEN Yan-mao, LIU Ji-ke

2008, 29(2): 181-187.

Abstract(4884) PDF(819)

Abstract:
The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated with the flow speed as a bifurcation parameter.The center manifold theory and complex normal form method were used to obtain the bifurcation equation.Interestingly,for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical.It is found,mathematically,this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter.The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.

Two-Dimensional Interactions Due to Moving Load in Generalized Thermoelastic Solid With Diffusion

Sunita Deswal, Suman Choudhary

2008, 29(2): 188-202.

Abstract(2929) PDF(523)

Abstract:
Disturbances in a homogeneous,isotropic elastic medium with generalized thermoelastic diffusion,when a moving source is acting along one of the co-ordinate axis on the boundary of the medium,are investigated.Eigen value approach was applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem.The analytical expressions for displacement components,stresses,temperature field,concentration and chemical potential were obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques.These expressions were calculated numerically for a copper like material and depicted graphically.As special cases,the results in generalized thermoelastic and elastic media were obtained to depict the diffusion and thermal effects in the medium theoretically and numerically.

A New Modification of False Position Method Based on the Homotopy Analysis Method

S. Abbasbandy, LIAO Shi-jun

2008, 29(2): 203-208.

Abstract(2856) PDF(606)

Abstract:
A new modification of false position method for solving nonlinear equations is presented by applying homotopy analysis method(HAM).Some numerical illustrations are given to show the efficiency of algorithm.

Entropy Generation Analysis of Thermally Developing Forced Convection in a Fluid-Saturated Porous Medium

K. Hooman, A. Ejlali, F. Hooman

2008, 29(2): 209-216.

Abstract(2680) PDF(632)

Abstract:
Entropy generation for thermally developing forced convection in a porous medium bounded by two isothermal parallel plates was investigated analytically on the basis of the Darcy flow model where the viscous dissipation effects had also been taken into account.A parametric study showed that decreasing the group parameter and the P clet number increases the entropy generation while for the Brinkman number the converse is true.Heatline visualization technique is applied with an emphasis on Br is less than 0 case where there is somewhere that heat transfer changes direction at some streamwise location to the wall instead of its original direction,i.e.from the wall.

Some Properties on the Far-Field Pattern of Scattering by a Penetrable Obstacle in an Ocean Waveguide

PAN Wen-feng, YOU Yun-xiang, MIAO Guo-ping, LI Zhuo-qiu

2008, 29(2): 217-227.

Abstract(2415) PDF(557)

Abstract:
The properties of propagation far-field patterns corresponding to the scattering of time harmonic acoustic waves by a bounded penetrable obstacle in an ocean waveguide were concerned with.The sets of solutions to the transmission problem were constructed such that the restriction of these solutions to the boundary of the penetrable obstacle is dense in a Hilbert space.Then conditions under which a set of propagation far-field patterns is complete in a Hilbert space were determined.These properties are important in investigating inverse transmission problems in an ocean waveguide.

Bifurcation of Non-Negative Solutions for an Elliptic System

YANG Ming, SHI Pei-hu

2008, 29(2): 228-234.

Abstract(2585) PDF(638)

Abstract:
A nonlinear elliptic system coming from the predator-prey model with diffusion is considered.Predator growth-rate was treated as bifurcation parameter.The range of parameter was found for which there exists nontrivial solution via the theory of bifurcation from infinity,local bifurcation and global bifurcation.

Asymptotic Behaviour of Solution for Fourth Order Wave Equation With Dispersive and Dissipative Terms

XU Run-zhang, ZHAO Xi-ren, SHEN Ji-hong

2008, 29(2): 235-238.

Abstract(3186) PDF(766)

Abstract:
The initial boundary value problem of fourth order wave equation with dispersive and dissipative terms is studied.By using multiplier method,it was proven that the global strong solution of the problem decays to zero exponentially as the time approaches infinite,under a very simple and mild assumption regarding the nonlinear term.

Study on the Behavior of Near-Field Dilution of Thermal Buoyant Jet Discharged Horizontally in Compound Open-Channel

HUAI Wen-xin, XIAO Qing-hua, ZENG Yu-hong, YANG Zhong-hua, QIAN Zhong-dong

2008, 29(2): 239-246.

Abstract(2642) PDF(623)

Abstract:
The RNG k-epsilon model with consideration of the buoyancy effect,which was solved by using the hybrid finite analytic method,was used to simulate the mixture of the horiz ontal round thermal buoyant jet in compound open channel flow.The mixing features near the spout and flowing characteristic of the secondary currents were studied by numerical simulation.Meanwhile,1) the distribution of the measured isovels for stream-wise velocity,2) secondary currents,3) the distribution of the measured isovels for temperature of typical cross-section near the spout,were obtained by using the three-dimensional Micro ADV and the temperature measuring device.Compared with experimental data,the RNG k-epsilon model based on buoyancy effect can preferably simulate the jet which performs the bifurcation phenomenon,jet reattachment(Conada effect) and beach secondary currents phenomenon with the effect of ambient flow,buoyancy,and secondary currents of compound section and so on.

Applications of a New Affine Invariant for Polytopes

YANG Liu, HE Bin-wu

2008, 29(2): 247-252.

Abstract(2492) PDF(641)

Abstract:
Using the technique of combination extremum,it was obtained that the analytic expression of the affineinvariant functional,by Lutwak,Yang and Zhang recently introduced,defined on a specific subclass of origin-symmetric convex polytopes in n-dimensional Euclidean space,and an application of it to Minkowski problem for origin-symmetric convex polytopes was given.