非线性Schrodinger方程的Jacobi椭圆函数包络解

通过函数变换和扩展Jacobi椭圆函数展开法,利用吴消元法,借助符号运算软件Maple,得到非线性Schringer方程丰富的包络形式精确解,特别是由两个Jacobi椭圆函数表示的精确解.当模数m→1或m→0时,一部分解退化为双曲函数或三角函数表示的解,F-展开法和扩展的F-展开法得到的精确解是本文结果的特例.     

Thermal fields in laser–multi-layer structures interaction

In the present paper, we are dealing with the thermal fields for laser–periodic multilayer structures interaction. Our point of view is originally that we consider any order transverse laser beams, like heating sources. We consider that the laser beam acts in IR (Nd:YAG or CO₂ laser beam) and it is in one transverse mode or in only a few decoupled modes. In order to solve this problem, we will use the Green function method. Specific results are presented for a laser beam (Nd:YAG laser) operating in the mode TEM₀₁ and a two-layer structure.     

2-Soliton-Solution of the Novikov-Veselov Equation

Based on a superposition method recently proposed to obtain 1-solitary wave solutions of the KdV-Burgers equation (Yuanxi and Jiashi, 2005, International Journal of Theoretical Physics 44, 293–301), we show that this method can also be used to find a 2-solitary wave solution of the Novikov-Veselov equation. Thus, it seems that the method of Yuanxi and Jiashi in general is not restricted to constructing 1-solitary wave solutions of nonlinear wave and evolution equations (NLWEEs).     

Nucleation of atmospheric aerosol particles

A significant fraction of the total number of particles present in the atmosphere is formed originally by nucleation from the gas phase. Binary nucleation of sulphuric acid and water, ternary nucleation of sulphuric acid, water and ammonia and ion-induced nucleation are thought to be the most important aerosol nucleation processes in the atmosphere. Within the last two decades, instrumentation to observe and characterize nucleation has improved greatly and numerous observations of nucleation have been made including quantification of the nucleation rate, characterization of the growth process and first chemical characterizations of the freshly formed particles. Nucleation has been observed at many different places in the atmosphere: in the boundary layer, in the free troposphere, in remote locations, in coastal areas, in boreal forests as well as urban areas and pollution plumes. In most cases gaseous sulphuric acid is assumed to be the key precursor gas. After nucleation, other supersaturated substances, especially low vapour pressure organics often take part in the subsequent aerosol growth. Iodine oxides seem to be responsible for nucleation observed in some coastal areas.Recent advances in modelling allow for a kinetic treatment of the nucleation process based on measured thermochemical data for the cluster formation. Considerable improvement over the classical nucleation treatment is expected from this approach.A detailed understanding of atmospheric aerosol nucleation processes is needed as the freshly formed particles directly influence the number concentration and size distribution of the atmospheric aerosol. The formation of clouds and precipitation is affected and influences on climate are anticipated. Anthropogenic emissions influence atmospheric aerosol nucleation processes considerably.Despite the comprehensive research efforts, substantial inconsistencies remain and conflicting results of laboratory studies, model studies as well as atmospheric observations persist. Several key questions about the predictability of atmospheric nucleation in general, about the substances, that take part in nucleation and subsequent growth and about the size and composition of the critical cluster, have not been resolved so far. To cite this article: J. Curtius, C. R. Physique 7 (2006).     

Finite element acoustic simulation based shape optimization of a muffler

This paper describes a methodology which combines finite element analysis and Zoutendijk’s feasible directions method for mufflers shape design. The main goal is to obtain the dimensions of the acoustic muffler with the transmission loss (TL), being maximized in the frequency range of interest. The improved four parameters method is used for TL evaluations and the Helmholtz’s equation is solved numerically with the finite element method (FEM). The quadratic triangular finite element meshes are adequately constructed to control the pollution error and the optimization problem is solved using the Zoutendijk’s feasible directions method due to robustness and efficiency for problems with nonlinear constraints. Numeric experiments performed with circular expansion chambers with extended inlet and outlet show results for constrained and unconstrained shape optimization.     

（Anti-）de Sitter Black Hole Entropy and Generalized Uncertainty Principle

We generalize the method that is used to study corrections to Cardy-Verlinde formula due to generalized uncertainty principle and discuss corrections to Cardy-Verlinde formula due to generalized uncertainty principle in （anti）- de Sitter space. Because in de Sitter black hole spacetime the radiation temperature of the black hole horizon is different from the one of the cosmological horizon, this spacetime is a thermodynamical non-equilibrium spacetime.     

Localization of s-Wave and Quantum Effective Potential of a Quasi-free Particle with Position-Dependent Mass

The properties of the 8-wave for a quasl-free partide with position-dependent mass （PDM） have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the free quantum particle around the origin only occurs in two dimensions, the quasi-free particle with PDM can experience attractive forces in D dimensions except D = 1 when its mass function satisfies some conditions. The effective mass of a particle varying with its position can induce effective interaction, which may be attractive in some cases. The analytical expressions of the eigenfunctions and the corresponding probability densities for the 8-waves of the two- and three-dimensional systems with a special PDM are given, and the existences of localization around the origin for these systems are shown.     

Cylindrical KP-Burgers Equation for Two-Temperature Ions in Dusty Plasma with Dissipative Effects and Transverse Perturbations

In this paper, the cylindrical KP-Burgers equation with variable coefficient for two-temperature ions in unmagnified dusty plasma with dissipative effects and transverse perturbations in cylindrical geometry is derived by using the standard reductive perturbation technique. With the help of variable-coefficient generalized projected Ricatti equation expansion method, the cylindrical KP-Burgers equation is solved and shock wave solution is obtained. The effects of some important parameters to the shock wave solution are illustrated from the wave evolution figures. The effects caused by dissipation and transverse perturbations are also discussed.     

A (2+1)-dimensional KdV equation and mKdV equation: Symmetries,group invariant solutions and conservation laws

In this paper, we analyse the (2+1)-dimensional KdV and mKdV equations. Firtly, on the basis of the extended Lax pair, we derive these equations. Thereafter, the symmetry generators are determined followed by the application of the mCK method. Finally, conservation laws (including higher order) are studied.