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Virtual Resonance and Frequency Difference Generation by van der Waals Interaction

“…By studying the pair (γ a , γ r ), determining the power law of Γ(t), the emergence of oscillations at ω − are shown in Fig. 2 exhibiting an optimization for (γ a , γ r )=(-2,-8) corresponding to the volume integrated Lennard-Jones potential [9,10]. The computed ω − oscillation amplitude shows a higher sensitivity to the long-range van der Waals power form than the short-range repulsive power form, which once turned on at γ r ≤ −8, exhibits little variation.…”

Controlling chaos in dynamic-mode atomic force microscope

“…is the tip-sample interaction force depending on the tip-sample distance Z. f (Z) is often described based on such as the Lennard-Jones potential [28,32] and DMT (Derjaguin-Muller-Toporov) theory [18].…”

“…The AM-AFM, in fact, exhibits various nonlinear phenomena including bistability [22,21], bifurcation [23,24], chaotic oscillations [25,26], which nonlinear scientists have focused on for half a century [27]. Actually, the existing techniques for analysis of nonlinear systems have been applied to some problems in the nonlinear cantilever dynamics [17,18,19,20,21,25,26,28,29,30] such as the application of Melnikov method [31,32]. It should be emphasized that the cantilever dynamics is directly connected to the resolution of images [26] and scanning rate of the AM-AFM [33].…”

Control of microcantilevers in dynamic force microscopy using time delayed feedback

“…20,21 As a result, a bistable behavior occurs in the proximity of sample surfaces. [25][26][27][28][29] The resulting oscillation modes possibly reduce the force sensitivity of AM-DFM due to undesirable subharmonics and wide spread frequency spectrum, which are neglected in the standard device configuration of the AM-DFM. 21 In addition, it was reported that the microcantilever exhibits subharmonic oscillation, period-doubling bifurcation, 23,24 and chaotic oscillations.…”

“…22 The involving jumping and hysteresis phenomena cause sudden and discontinuous transition of imaging characteristics. 25,26,30 In this article, we propose stabilization of the chaotic microcantilever oscillations using time delayed feedback control method. [25][26][27][28][29] The resulting oscillation modes possibly reduce the force sensitivity of AM-DFM due to undesirable subharmonics and wide spread frequency spectrum, which are neglected in the standard device configuration of the AM-DFM.…”