Fluctuation and dissipation of a stochastic micro-oscillator under delayed feedback

Abstract

We investigate the dynamics of a microcantilever subjected to the combined forcing from Brownian motion and delayed self-feedback. Specifically, the excitation of the fundamental mode of the cantilever by thermomechanical agitation is utilized as delayed external forcing and the resulting dynamical response is studied as a function of the delay and the coupling strength. A fluctuation-dissipation theorem is derived from the delay Langevin-like equation and its validity is discussed. The relaxation time scale associated with the adsorption processes is established and an experiment to determine the oscillator’s effective temperature is proposed.

Torsional and Lateral Resonant Modes of Cantilevers as Biosensors: Alternatives to Bending Modes

“…Analysis of mode shapes suggests that, although both anchor asymmetries enabled resonance-coupling to impedance changes, different types of modes are coupled in each case. We note that feedback control has been used as a technique for enhancing resonance in cantilever sensors; however, such a technique does not affect the nature of the modes as does the anchor asymmetry technique shown here. − Importantly, such modes have not yet been investigated for measuring surface-based molecular binding in the literature which is important for their use as biosensors.…”

An experimental investigation of analog delay generation for dynamic control of microsensors and atomic force microscopy

“…Using similar experimental results as presented, it may also be interesting to investigate the case where fluctuation and dissipation of the oscillator may be studied under delayed feedback. Such experiments may present unique opportunities in obtaining stochastic information such as those formulated by the fluctuation dissipation theorem [24].…”

Karhunen–Loève treatment to remove noise and facilitate data analysis in sensing, spectroscopy and other applications

“…In the absence of any external driving forces, S(t) represents the equilibrium state of u and the accumulative random uctuations in the entire system including the electronics noise and the Brownian oscillations of the cantilever at temperature T. Denoting the Fourier transform of the signal S(u), the uctuation-dissipation theorem states that S(u)S*(u) ¼ (2K B T/u)J(S(u)) (which for example can take the form of eqn (5) in ref. 30), where K B is the Boltzmann constant. Embedded in S(t) is the resonant oscillations of the cantilever due to stochastic excitation as shown in Fig.…”