In an effort to aid in the understanding of the nonlinear dynamics of the trajectories followed by an Atomic Force Microscope (AFM), I have written an interactive java applet simulator using a simple inelastic billiard model developed by Predrag Cvitanović and Rytis Paškauskas. We study the trajectories followed by the tip of the AFM as a function of its physical parameters and initial conditions.
The model represents the AFM as the addition of two harmonic oscillators vibrating independently in the vertical and horizontal planes. The moving surface imaged by the AFM is modeled as a time-periodic sinusoid. The attractors in this system can be strange attractors (recurrent and aperiodic), stable periodic trajectories, and attracting or 2-tori. Once we have an idea of the nature of these attractors, we iterate points in their phase space vicinity to estimate their basins of attraction. We also study the basic topology of the various attractors produced in this system.
The simulator is useful in developing intuition about the long term behaviors of different AFM setups, and might also be helpful in developing new techniques for imaging clean periodic surfaces by atomic force friction microscopy. The program is open source [download].
|Related AFM projects|
|William Mather||A billiard calculation of the dynamical friction of an Atomic Force Microscope|
|Tyson Shepard||Modeling atomic dynamical friction by an inelastic impact oscillator|
|Elisa Riedo||PicoForce Lab|