Manipulation and controlled amplification of Brownian motion of microcantilever sensors

Mehta, Adosh; Cherian, Suman; Hedden, D. L.; Thundat, Thomas

doi:10.1063/1.1355001

Cited by 76 publications

(51 citation statements)

References 9 publications

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“…Figure 1 shows a schematic of such a device and typical parameters values. For experiments in air, Brownian motion due to collisions with air molecules is the main noise source in masssensing applications [18,29]. The transfer of kinetic energy between an air molecule and the oscillator due to a collision at time t k can be modeled by a state-impulse of the following form:…”

Section: Mems Oscillatormentioning

confidence: 99%

Lyapunov conditions for input-to-state stability of impulsive systems

2008

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This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for impulsive systems, i.e., dynamical systems that evolve according to ordinary differential equations most of the time, but occasionally exhibit discontinuities (or impulses). We provide a set of Lyapunov-based sufficient conditions for establishing these ISS properties. When the continuous dynamics are ISS but the discrete dynamics that govern the impulses are not, the impulses should not occur too frequently, which is formalized in terms of an average dwell-time (ADT) condition. Conversely, when the impulse dynamics are ISS but the continuous dynamics are not, there must not be overly long intervals between impulses, which is formalized in terms of a novel reverse ADT condition. We also investigate the cases where (i) both the continuous and discrete dynamics are ISS and (ii) one of these is ISS and the other only marginally stable for the zero input, while sharing a common Lyapunov function. In the former case we obtain a stronger notion of ISS, for which a necessary and sufficient Lyapunov characterization is available. The use of the tools developed herein is illustrated through examples from a Micro-Electro-Mechanical System (MEMS) oscillator and a problem of remote estimation over a communication network.

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Section: Mems Oscillatormentioning

confidence: 99%

Lyapunov conditions for input-to-state stability of impulsive systems

2008

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“…It has been shown previously that this method of excitation results in high-Q factors and hence better accuracy in real-time, fast data collection [10]. In contrast to the case where the cantilever is driven using an external signal generator source, this method is quicker since the cantilever is "self-tuning" and no external tuning of drive frequency is necessary.…”

Section: Experimental Methodsmentioning

confidence: 99%

Chemical Sensing With Resistive Microcantilevers

et al. 2002

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MEMS-based microcantilevers have been proposed for a variety of biological and chemical sensing applications. Measuring the magnitude of microcantilever deflection due to adsorption-induced bending, and following the variation in the resonant frequency of the microcantilevers due to the adsorbed mass are two techniques commonly employed for sensing analytes. Apart from possessing a high level of sensitivity to small changes in mass, microcantilevers are also very sensitive to small changes in temperature and hence the flow of heat. One way of achieving high sensitivity in thermal measurements is by using a bimaterial microcantilever and measuring its deflection as a result of thermal fluctuations. Commercially available piezoresistive microcantilevers are an example of bimaterial cantilevers and in this study, we propose the use of such cantilevers for sensing explosives. We show that sensing can be accomplished by following the differences in the thermal response of the cantilevers introduced by the presence of explosives adsorbed from the vapor phase onto the surface of the cantilever. We discuss the issues involved in determining the sensitivity of detection and selectivity of detection.

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“…Thermomechanical noise can be measured using custom-built laser interferometers [10]- [13], position sensitive photodetectors (in the configuration commonly employed in atomic force microscopes) [14]- [19], and laser Doppler vibrometers [20]- [24]. Laser Doppler vibrometry (LDV)…”

Section: The Link Between Thermomechanical Noise and Damping Is Estabmentioning

confidence: 99%