Melnikov-Based Dynamical Analysis of Microcantilevers in Scanning Probe Microscopy
We study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation. The interaction between the sample and the cantilever is modeled by a Lennard--Jones potential whi...
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| Veröffentlicht in: | Nonlinear dynamics 1999-11, Vol.20 (3), p.197-220 |
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| creator | Ashhab, M Salapaka, M V Dahleh, M Mezić, I |
| description | We study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation. The interaction between the sample and the cantilever is modeled by a Lennard--Jones potential which consists of a short-range repulsive potential and a long-range van der Waals (vdW) attractive potential. We analyze the dynamics of the cantilever sample system when the cantilever is subjected to a sinusoidal forcing. Using the Melnikov method, the region in the space of physical parameters where chaotic motion is present is determined. In addition, using a proportional and derivative controller, we compute the Melnikov function in terms of the parameters of the controller. Using this relation, controllers can be designed to selectively change the regime of dynamical interaction. |
| doi_str_mv | 10.1023/A:1008342408448 |
| format | Article |
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We model the microcantilever by a single mode approximation. The interaction between the sample and the cantilever is modeled by a Lennard--Jones potential which consists of a short-range repulsive potential and a long-range van der Waals (vdW) attractive potential. We analyze the dynamics of the cantilever sample system when the cantilever is subjected to a sinusoidal forcing. Using the Melnikov method, the region in the space of physical parameters where chaotic motion is present is determined. In addition, using a proportional and derivative controller, we compute the Melnikov function in terms of the parameters of the controller. Using this relation, controllers can be designed to selectively change the regime of dynamical interaction.</description><identifier>ISSN: 0924-090X</identifier><identifier>EISSN: 1573-269X</identifier><identifier>DOI: 10.1023/A:1008342408448</identifier><language>eng</language><publisher>Dordrecht: Springer Nature B.V</publisher><subject>Atomic force microscopes ; Atomic force microscopy ; Controllers ; Mathematical models ; Microscopes ; Parameters ; Physical properties ; Scanning probe microscopy</subject><ispartof>Nonlinear dynamics, 1999-11, Vol.20 (3), p.197-220</ispartof><rights>Nonlinear Dynamics is a copyright of Springer, (1999). 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| ispartof | Nonlinear dynamics, 1999-11, Vol.20 (3), p.197-220 |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Atomic force microscopes Atomic force microscopy Controllers Mathematical models Microscopes Parameters Physical properties Scanning probe microscopy |
| title | Melnikov-Based Dynamical Analysis of Microcantilevers in Scanning Probe Microscopy |
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