Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes

[+] Author and Article Information
M. Basso

Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S. Marta 3, 50139 Firenze, Italybasso@dsi.unifi.it

L. Giarré

Dipartimento di Ingegneria Automatica e Informatica, Università di Palermo, Viale delle Scienze, 90128-Palermo, Italygiarre@ias.unipa.it

M. Dahleh, I. Mezić

Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106mezic@engineering.ucsb.edu

J. Dyn. Sys., Meas., Control 122(1), 240-245 (Jan 30, 1998) (6 pages) doi:10.1115/1.482465 History: Received January 30, 1998
Copyright © 2000 by ASME
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A schematic of the atomic force microscope
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Phase portrait for the unperturbed system
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Trajectories in the phase plane: (a) Γ=10; (b) Γ=11; (c) Γ=16.2; (d) Γ=20
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Bifurcation diagram of the AFM model
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Sensitive dependence on initial conditions: position error for i.c. differing by 0.1%
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Power spectral densities of the tip position ξ1; (a) Γ=10; (b) Γ=11; (c) Γ=16.2; (d) Γ=20. To compute the spectra, an FFT algorithm has been used on a window of 4096 data points collected at a sampling rate of 50 rad/s.
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Poincaré map of the AFM model (10,000 points), Γ=20,θ̃=0
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Period doubling bifurcation curve in the (Γ, α) plane: the region of chaotic attractors lies in a subset of the right side of the curve. The dashed line separates the region of validity for the Melnikov theory.
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Poincaré map of the AFM model (10,000 points), Γ=20,α=0.8,θ̃=0




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