Leibniz Supercomputing Centre, Garching, Germany.
Ultramicroscopy. 2010 May;110(6):618-21. doi: 10.1016/j.ultramic.2010.02.021. Epub 2010 Feb 23.
From a mathematical point of view, the atomic force microscope (AFM) belongs to a special class of continuous time dynamical systems with intermittent impact collisions. Discontinuities of the velocity result from the collisions of the tip with the surface. Transition to chaos in non-linear systems can occur via the following four routes: bifurcation cascade, crisis, quasi-periodicity, and intermittency. For the AFM period doubling and period-adding cascades are well established. Other routes into chaos, however, also may play an important role. Time series data of a dynamic AFM experiment indicates a chaotic mode that is related to the intermittency route into chaos. The observed intermittency is characterized as a type III intermittency. Understanding the dynamics of the system will help improve the overall system performance by keeping the operation parameters of dynamic AFM in a range, where chaos can be avoided or at least controlled.
从数学的角度来看，原子力显微镜（AFM）属于具有间歇冲击碰撞的连续时间动力系统的特殊类别。由于尖端与表面的碰撞，速度会出现不连续。非线性系统中的混沌可以通过以下四种途径发生：分岔级联、危机、准周期性和间歇性。对于 AFM，倍周期分岔和倍周期添加级联已经得到很好的确立。然而，进入混沌的其他途径也可能起着重要的作用。动态 AFM 实验的时间序列数据表明，与间歇进入混沌的途径有关的混沌模式。所观察到的间歇特征是 III 型间歇。理解系统的动力学将有助于通过将动态 AFM 的操作参数保持在可以避免或至少控制混沌的范围内，从而提高整体系统性能。
