论文标题
最大的Lyapunov指数作为检测粒子位置相对变化的工具
The largest Lyapunov exponent as a tool for detecting relative changes in the particle positions
论文作者
论文摘要
通过分析响应函数，对于两个相邻粒子的最大的Lyapunov指数和Poincaré部分，可以检查具有非对称变形底物电位的驱动Frenkel-Kontorova模型的动力学。获得的结果表明，最大的Lyapunov指数除了用于研究积分数量外，还可用于检测两个阻尼的Frenkel-Kontorova模型的链构型中的微差异，并具有惯性术语及其严格中型限制的极限。颗粒的相对位置的略有变化是通过固定机制中最大的Lyapunov指数的跳跃进行注册的。这种跳跃的发生高度取决于相应结构的类型和底物电位的变形。获得的结果还表明，启动链的集体运动所需的最小力并不取决于固定机制中Lyapunov指数跳跃的数量。这些跳跃也注册在滑动方案中，这是步骤中最大的Lyapunov指数更复杂的结构的结果。
Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step.
