弹簧螺旋摆系统非线性振动的理论研究

运用牛顿第二运动定律对弹簧螺旋摆系统建立了模型方程,该方程为一组非线性微分方程,表明该系统具有复杂的非线性特征.理论分析表明,当系统固有的振动频率和摆动频率之比为2时,自由振动的弹簧螺旋摆系统存在内共振现象,数值求解结果证实了这一结论.并认为在一般情况下,弹簧螺旋摆系统的自由振动可能是准周期的.     

基底势函数的无序性对静摩擦力的影响

在二维Frenkel-Kontorova模型中, 为了更好地模拟真实的物理系统, 采用高斯波的平移叠加作为基底, 运用分子动力学模拟方法, 讨论了有相互作用的原子平面在公度、 不公度两种情况下, 原子在无序基底上运动的摩擦机理, 以及基底的无序对静摩擦力F_s 的影响.     

Application of the homotopy analysis method for the Gross-Pitaevskii equation with a harmonic trap

<正>The Homotopy analysis method(HAM) is adopted to find the approximate analytical solutions of the GrossPitaevskii equation,a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they fit very well with each other when the atomic interaction is weak.     

柱和球尘埃离子声孤波的绝热近似解

通过运用等价粒子理论，得到了尘埃声孤波中的KdV类型方程（包括KdV方程，柱KdV方程和球KdV方程）的绝热近似解。这种方法也可以运用到其它的非线性演化方程。     

同伦分析法在求解非线性演化方程中的应用

利用同伦分析法求解了(2+1)维改进的 Zakharov-Kuznetsov方程, 得到了它的近似周期解,该解与精确解符合很好. 结果表明，同伦分析法在求解高维非线性演化方程时, 仍然是一种行之有效的方法. 同时,还对该方法进行了一定的扩展， 经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解. 关键词： 同伦分析法 改进的 Zakharov-Kuznetsov方程 周期解     

耦合KdV方程的双峰孤立子及其稳定性

利用扩展双曲函数法求解了耦合KdV方程,得到了6类精确解,其中一类为具有双峰状结构的单孤子解.在不同的极限情况下,该解分别退化为耦合KdV方程的扭结状或钟状孤波解.文中对双峰孤立波的稳定性进行了数值研究,结果表明:耦合KdV方程的双峰孤立波在长波小振幅扰动和小振幅钟型孤立波扰动下,均稳定. 关键词： 耦合KdV方程 双峰孤立子 稳定性     

磁化尘埃等离子体中的冲击波及其横向扰动稳定性

利用双曲函数法得到ZKB方程的一组冲击波解,并对波在横向扰动下的动力学稳定性进行研究.对冲击波解进行线性稳定性分析,并构造高精度的有限差分格式求解所得本征值问题.结果表明：对于正耗散的情形,该冲击波在线性意义下稳定;对于负耗散情形,该冲击波在线性意义下不稳定.构造有限差分格式对受扰动的冲击波进行非线性动力学演化,结果表明：对于正耗散的情况,该冲击波是稳定的.     

Effect of multicomponent dust grains in a cold quantum dusty plasma

By employing the quantum hydrodynamic model for electron-ion-dust plasma,we derive a dispersion relation of the quantum dusty plasma.The effects of the dust size distribution on the dispersion relation in a cold quantum dusty plasma are studied.Both analytical and numerical results are given to compare the differences between the dusty plasma by considering the dust size distribution and the mono-sized dusty plasma.It is shown that many system parameters can significantly influence the dispersion relation of the quantum dusty plasma.     

Anisotropic character of atoms in a two-dimensional Frenkel–Kontorova model

The dynamics of a certain density of interacting atoms arranged on a two-dimensional square lattice, which is made to slide over a two-dimensional periodic substrate potential with also the quare lattice symmetry, in the presence of dissipation, by an externally applied driving force, is studied. By rotating the misfit angle θ, the dynamical behaviour displays two different tribological regimes: one is smooth, the other becomes intermittent. We comment both on the nature of the atomic dynamics in the locked-to-sliding transition, and on the dynamical states displayed during the atom motion at different values of the driving force. In tribological applications, we also investigate how the main model parameters such as the stiffness strength and the magnitude of the adhesive force affect the static friction of the system. In particular, our simulation indicates that the superlubricity will appear.     

三体作用下准一维玻色-爱因斯坦凝聚体中表面带隙孤子及其稳定性

数值研究了具有三体相互作用的均匀介质界面和半无限雅克比椭圆正弦势下准一维玻色-爱因斯坦凝聚体(Bose-Einstein condensate,BEC)中的表面带隙孤子及其稳定性.在平均场近似下,其动力学行为可用3次-5次Gross-Pitaevskii方程描述.首先用牛顿-共轭梯度法寻找表面带隙孤子,发现表面亮孤子仅当化学势小于0时才可于带隙内激发,但表面扭结孤子和气泡孤子既可存在于带隙中也可存在于能带中.然后采用线性稳定性分析和非线性动力学演化研究了孤子的稳定性,结果表明三体相互作用会明显影响表面亮孤子的稳定性,表面扭结孤子既有稳定的也有不稳定的,但表面气泡孤子均不稳定.