Modulational Instability of Dust Ion Acoustic Waves in a Collisional Dusty Plasma

The modulational instability of dust ion accoustic waves in a dust plasma with ion-dust collision effects is studied.Using the perturbation method,a modified nonlinear Schroedinger equation contains a damping term that comes from the effect of the ion-dust collision is derived.It is found that the inclusion of the ion-dust collision would modify the modulational instability of the wave packet and could not admit any stationary envelope solitary waves.     

Single mode rate equations for two sections self—pulsating DFB laser

We Propose a set of single mode rate equations for multi-section distributed feedback(DFB) lasers. On the basis of the rate equations, the self-pulsation in the two-section DFB lasers with asymmetrical injection current was explained. It was found that the dynamic distribution of the power in two sections play key role in the self-pulsation running.     

A theoretical study about the chirped pulse amplification laser

Starting from the Maxwell‘s equation,and using the resonant-dipole equation together with the multilevel rate equations which take the effects of energy relaxation into consideration,we have derived a more realistic numerical model of the chirped pulse amplification for an ultra-broad band width laser amplifier.Numerical simulations of this model show that both the intensity profile and the energy fluence of the amplified chirped pulse are closely connected with the two relaxation effects:the relaxation of the thermalization among the components of the laser multiplets and the depletion of the lower laser level.The results are valuable for the design of ultra-broad bandwidth chirped pulse amplification lasers.     

Quantization of the space－time with topological defect

We present the classical solution of Lagrange equations for the black hole with a global monopole or with a cosmic string. Then we obtain the wavefunction of the space－time by solving the Wheeler－De Witt equation. De Broglie－Bohm interpretation applied to the wavefunction gives the quantum solution of the space－time. In the end, the quantum effect on Hawking radiation is studied.     

The effects of dust temperature and the dust charge variation in a dusty plasma with vortex—like ion distribution

By considering both the dust temperature and the dust charge variation in dusty plasma with vortex-like ion distribution, we obtained a modified Korteweg－de Vries equation. It indicates that the effect of dust charge variation can cause the one-dimensional soliton amplitude to become larger, and the dust temperature can cause the soliton amplitude to become larger as well. Moreover, as the dust temperature increases, the soliton amplitude will increase.     

AN UNCONDITIONALLY STABLE HYBRID FE-FD SCHEME FOR SOLVING A 3-D HEAT TRANSPORT EQUATION IN A CYLINDRICAL THIN FILM WITH SUB-MICROSCALE THICKNESS

Heat transport at the microscale is of vital importance in microtechnology applications.The heat transport equation is different from the traditional heat transport equation since a second order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect to space and time are introduced. In this study,we develop a hybrid finite element-finite difference (FE-FD) scheme with two levels in time for the three dimensional heat transport equation in a cylindrical thin film with submicroscale thickness. It is shown that the scheme is unconditionally stable. The scheme is then employed to obtain the temperature rise in a sub-microscale cylindrical gold film. The method can be applied to obtain the temperature rise in any thin films with sub-microscale thickness, where the geometry in the planar direction is arbitrary.     

SYMMETRIC POINT STRUCTURE OF SUPERCONVERGENCE FOR CUBIC TRIANGULAR ELEMENTS -A CONSULTATION WITH ZHU

Superconvergence structures for rectangular and triangular finite elements are summarized. Two debatable issues in Zhu‘‘s paper [18] are discussed. A superclose polynomial to cubic triangular finite element is constructed by area coordinate.     

Congratulations to Academician Zhou Yulin on His 80th Birthday

Editorial Committee of Journal of Computational Mathematics Editorial Committee of Mathematica Numerica Sinica Editorial Committee of Journal on Numerical Methods and Computer ApplicationsEditorial Committee of Chinese Journal of Numerical Mathematics and Applications     

AD GALERKIN ANALYSIS FOR NONLINEAR PSEUDO—HYPERBOLIC EQUATIONS

AD(Alternating direction)Galerkin schemes for d-dimensional nonlinear pseudo-hyperbolic equations are studied.By using patch approximation technique,AD procedure is realized,and calculation,work is simplified.By using Galerkin approach,highly computational accuracy is kept.By using various priori estimate techniques for differential equations,difficulty coming form non-linearity is treated,and optimal H^1 and L^2 convergence prop-erties are demonstrated.Moreover,although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment,yet the schemes formulated in this paper have second order accuracy in it.This implies an essential advancement in AD Galerkin aualysis.     

Comment on “A Hierarchy of Integrable Nonlinear Lattice Equations and New Integrable Symplectic Map”

Comment on a recent paper on Commun. Theor. Phys. (Beijing, China) 38 (2002) pp. 523-528.