Application of higher-order KdV--mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.     

Exact solutions of （3＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system.     

从稀土废料中回收稀土的研究进展

中国每年都会产生不同种类的稀土废料,这些废料中包含大量的稀土、铁、铝等有价金属,对稀土废料进行综合回收利用是解决中国稀土资源短缺的有效途径。对废旧稀土荧光粉、钕铁硼废料、稀土熔盐电解渣以及其他稀土废料的综合回收处理方法进行了综述,分析了它们的优势与共性,以期在实际处理过程中提供技术支持和帮助。     

Enhanced electron positron pair creation by the frequency chirped laser pulse

Based on the quantum Vlasov equation, the effect of frequency chirp on electron-positron pair production is investigated. The cycle parameter, which characterizes the laser field cycle degree within the pulse, is also considered. In both supercycle and subcycle laser pulses the frequency chirp can greatly enhance the momentum distribution function of created pairs and the pair number density. The pair number density created by a supercycle laser pulse is larger than that by a subcycle pulse under the same laser frequency and chirping. There exists an optimal cycle parameter corresponding to the maximum value of the created pair number density for different chirp rates. It is found that the pair number density is sensitive/insensitive to chirping rate when the cycle parameter lies below/above the optimal one.     

氢原子电子云密度分布分析

通过数值计算形象地分析了氢原子中电子概率密度的分布情况,对此做了一些有别于传统认识的讨论,并由此引出了对粒子运动和波函数概率解释的认识。     

岛屿地形对极地低压和热带气旋发展的线性理论模型和观测资料分析

基于轴对称和热成风平衡系统,研究了柱坐标系中的线性涡旋动力学方程组的初值问题,分析了岛屿地形对极地低压和热带气旋类涡旋的影响,同时分析了感热和潜热,摩擦和地形在极地低压和热带气旋类涡旋的强度和结构演变中的作用.通过对地形影响下的流体运动的径向和法向速度,以及垂直速度和流体运动的不稳定增长率的分析指出,流动和地形的相互作用对极地低压和热带气旋类系统的强度和结构演变起着非常重要的作用. 在岛屿山脉地形的迎风坡上,地形强迫的径向入流气流和垂直上升运动有利于极地低压和热带气旋类涡旋的加强和发展,有利于加强流体的不稳定增长率.但是,在山脉地形的背风侧,地形强迫的径向入流气流和垂直下沉运动,有利于极地低压和热带气旋类涡旋的减弱和消亡,有利于减弱流体的不稳定增长率.同时,基于气象观测资料分析了2003年12月19日发生在日本海上的一次极地低压生消和演变过程,所得到的观测事实和理论分析具有较好的一致性,并在此基础上讨论了极地低压和台风涡旋,斜压背风涡旋和斜压锢囚涡旋的生消机制和演变特征的异同.     

A class of coupled nonlinear Schrödinger equations: Painlevé property,exact solutions,and application to atmospheric gravity waves

The Painleve integrability and exact solutions to a coupled nonlinear Schrodinger （CNLS） equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painleve test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.     

Electron-Positron Pair Production in a Strong Laser Field Enhanced by an Assisted High Frequency Weak Field

Electron-positron pair production in a strong laser field enhanced by an assisted high frequency weak field is investigated by solving the quantum Vlasov equation.The average and residual pair number densities are obtained for sinusoid electric field and it is found that the high frequency assisted weak field will enhance pair production significantly.There exists an optimal frequency of assisted field that makes the pair production number density get a maximum one,which is a few orders of higher than that without assisted field.We also discuss the other possible assisted fields.     

Topographic effects on polar low and tropical cyclone development in simple theoretical model

The polar low and tropical cyclone type vortices over topography are assumed to be the axisymmetrical and thermal-wind balanced systems, which are solved as an initial value problem of a linearized vortex equation set in cylindrical coordinates. The roles of the sensible and latent heating, friction, and topography in the structure and intensification of the polar low and tropical cyclone type vortices are analyzed. The radial velocity, vertical velocity, azimuthal velocity, and the unstable growth rate including the topography effects are obtained. It is shown that the interaction between the flow and the topography plays a significant role in the structure and intensification of the polar low and tropical cyclone system. The analysis of the topography term indicates that, in the up-slope side of the mountain, the radial inflow and the vertical ascent forced by the mountain can intensify the polar low and tropical cyclone type vortex and increase the unstable growth rate. However, in the lee side of the mountain, the radial inflow and the vertical descent forced by the mountain can weaken the polar low and tropical cyclone type vortex and decrease the unstable growth rate of the polar low and tropical cyclone system. In addition, the evolutionary process and the spatial structure of the polar low observed over the Japan Sea on 19 December 2003 are investigated with the observational data to verify this theoretical result.     

强场下真空中粒子对产生的研究进展

随着激光技术的飞快发展,激光强度不断提高,超强外场下真空中正负电子对产生的过程,即能量向质量转化过程,已经成为一个研究热点。主要综述了近几年量子Vlasov方程方法和计算量子场论(数值求解Dirac方程)方法在研究强场下真空中正负电子对产生方面的进展,分别介绍了空间均匀场和空间不均匀场下的粒子对产生的情况。第一种情况主要介绍双脉冲结构振荡电场中电子-正电子对的产生、强双频振荡电场中非微扰电子-正电子对的产生、频率调制的激光场中电子-正电子对的产生和Dirac真空对啁啾外场的快速分辨。第二种情况主要介绍优化空间局域电场提高粒子对的产生率、多个势阱-垒结构的振荡场对粒子对产生的增强、振荡 Sauter 电势中正负电子对产生的问题、操纵Dirac真空以控制其在场诱导下的衰变、作为信息传输介质的Dirac真空还有正负电子对产生中的相干和非相干啁啾机制的转变。