The interaction of nonlinear waves in two-dimensional dust crystals

This paper investigates the collision between two nonlinear waves with different propagation directions in two-dimensional dust crystals. Using the extended Poincaré--Lighthill-Kuo perturbation method, two Korteweg--de Vries equations for nonlinear waves in both the ξ and eta directions are obtained, respectively, and the analytical phase shifts and trajectories after the collision of two nonlinear waves are derived. Finally, the effects of parameters of the lattice constant a, the arbitrary constant u_0η, the forces f(r), and the colliding angle θ on the phase shifts of both colliding nonlinear waves are examined.     

Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov－Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.     

玻色-费米混合气体的非线性Landau-Zener隧穿

在有相互作用的非线性两模系统中, 通过对相互作用参数的调节, 研究了该系统中玻色-费米混合气体的Landau-Zener隧穿现象. 研究发现, 其中某一组分的自相互作用会影响另一组分粒子的隧穿, 使得隧穿出现临界现象. 关键词： 玻色-费米混合气体 Landau-Zener隧穿 量子绝热隧穿     

Rosen--Zener Transition in a Nonlinear System for Two-Component Bose--Einstein Condensates in Optical Lattices

We study the Rosen-Zener transition （RZT） in a nonlinear system for two-component Bose-Einstein condensates in optical lattices. It is found that the percentage of the components could affect the quantum transition dramatically. For the component with large percentage it is equivalent that the effect of the nonlinearity is stronger, whereas for the component with small percentage the effect is weaker. We also find that the nonlinearity c11 can affect the quantum transition dramatically. This is similar to that reported from Ref. [14]. Compared with one-component systems, however, the effect of the nonlinearity is decreased due to the two components of the BEGs in optical lattices. Furthermore, the effect of the coupling nonlinearity between two components c12 is studied. The component with large percentage is more affected by the nonlinearity than that with small-percentage component.     

修正cKdV方程组的孤立波结构及其稳定性

利用函数展开法求解修正耦合KdV(Coupled KdV,cKdV)方程组,得到几类孤立波解,包括扭结型-钟型、双扭结型、双钟型以及双扭结-双钟型结构的单孤子解.在不同的极限情况下,这些解分别退化为修正cKdV方程的扭结状或钟状孤波解.对孤立波的稳定性进行了数值研究,结果表明:修正cKdV方程既存在稳定的孤立波解,也存在不稳定的孤立波解.     

一类非线性弹性杆波动方程的求解

对计入横向惯性效应后的非线性弹性杆纵向波动方程进行了分析,得到了一类非线性波动方程,并用完全近似方法求出了该方程的近似解析解．     

非线性弹性杆波动方程的摄动分析

针对计入横向惯性效应后的非线性弹性杆纵向波动方程进行了分析．在小振幅、长波长的一般情况下,根据远方场简单波理论,采用约化摄动法,得到了NLS方程,并讨论了存在NLS孤子的条件．     

织构化表面NbSe2涂层的真空载流摩擦学行为

针对航天器滑动电接触部件特殊的真空载流服役要求,利用建立的真空载流摩擦试验平台,探索铜基材织构化表面喷涂NbSe₂涂层作为空间新型导电润滑材料的可能性. 研究条状和网状不同织构以及各自在不同织构密度条件下喷涂NbSe₂涂层的真空载流摩擦学性能和影响作用规律;对比现役电镀金涂层,探讨其在真空载流条件下摩擦学和电接触行为优势. 结果表明:网格状较条状织构表面喷涂NbSe₂涂层的载流摩擦学性能更好,而且随织构密度的增加,减摩耐磨性能得到提高. 织构间距为200 μm的网格状织构表面喷涂的NbSe₂涂层展现出最佳的真空载流摩擦学性能. 相较于现役的金电镀层,其在真空载流摩擦条件下展现出更加优异的摩擦学和电接触性能,摩擦系数由0.25降至0.05,接触电压与现役材料处于同一量级,电噪音波动明显改善,由0.09V降至0.04V.      

PERTURBATION ANALYSIS FOR WAVE EQUATION OF NONLINEAR ELASTIC ROD

The longitudinal oscillation of a nonlinear elastic rod with lateral inertia was studied. Based on the far field and simple wave theory, a nonlinear Schrodinger (NLS) equation was established under the assumption of small amplitude and long wavelength. It is found that there are NLS envelop solitons in this system. Finally the soliton solution of the NLS equation was presented.     

组合KdV方程的双扭结孤立波及其稳定性研究

利用扩展的双曲函数法得到了combined KdV-mKdV (cKdV)方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为cKdV方程的扭结状或钟状孤波解.理论分析表明,cKdV方程既有传播型孤立波解,也有非传播型孤立波解.文中对双扭结型孤立波解的稳定性进行了数值研究,结果表明,cKdV方程既存在稳定的双扭结型孤立波,也存在不稳定的双扭结型孤立波. 关键词： cKdV方程 双扭结单孤子 稳定性