Phaseplane dynamics of an atomic force microscope cantilever.by danber Tags: afm, nonlinear dynamics, phaseplane 

#1
Aug113, 09:49 AM

P: 2

Hello,
A sinusoidally driven and undisturbed cantilever of an atomic force microscope (AFM) oscillates ideally in a sinusoidal fashion but the motion of the cantilever (timedomain trajectory) can become more complicated when it is disturbed by the interatomic forces as the cantilever taps on the sample surface. The cantilever dynamics can be better understood in the phaseplane. An undisturbed cantilever shows elliptical trajectories in the phaseplane around a center. On the other hand, a disturbed cantilever can show nonlinear effects like perioddoubling, bifurcation and chaos. I'd like to know what can be said about the phaseplane trajectory in terms of the attractor, basin of attraction or the possibility of chaos as shown in the attachement containing my experimental data? In the beginning the phaseplane trajectories circle around a center and as the signal size increases, these trajectories also grow in size and the center transforms into a set of two centers. Thanks. 



#2
Aug213, 09:28 AM

Sci Advisor
P: 5,468




#3
Aug213, 01:28 PM

P: 2

Thanks.
I already know the papers by Raman and Jamitzky but they've done experiments aimed at observing chaos in AFM and I've a different experiment where I'm not forcing the cantilever motion to be chaotic but observing breakdown of the cantilever trajectory in timedomain and the phaseplane trajectory shows a specific attractor which doesn't seem to be a chaotic one but still is markedly different from that of a harmonic oscillator. I think time series analysis of the given experimental data can be helpful but my question was how to understand the attractor from a purly dynamical point of view? 


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