The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation
The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation
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流体中微米级和纳米级弹性悬臂梁的随机动力学：耗散引起的波动
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
M. Cross
中科院分区：
文献类型：
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作者：
M. Paul;M. Clark;M. Cross
定量了微米级和纳米级悬臂梁在粘性流体中的随机动力学。给出了布朗噪声驱动下细长悬臂梁的分析结果。噪声力的谱密度不假定为白色，并且噪声力的频率依赖性由涨落耗散定理确定。分析结果对原子力显微镜中常用的微米级悬臂梁是有用的。发展了一种适用于任意几何形状的悬臂梁以及多个随机运动通过流体耦合的悬臂梁阵列的通用热力学方法。结果表明，涨落耗散定理允许用直接的确定性方法计算随机量。利用热力学方法和确定性有限元数值模拟方法，量化了单个微米级悬臂梁的自相关谱和噪声谱，以及两个实验激励的纳米级悬臂梁阵列的相互关联和噪声谱作为悬臂梁间距的函数。结果被用来量化使用两个紧密间隔的纳米悬臂的相关测量可能的降噪。
The stochastic dynamics of micron and nanoscale cantilevers immersed in a viscous fluid are quantified. Analytical results are presented for long slender cantilevers driven by Brownian noise. The spectral density of the noise force is not assumed to be white and the frequency dependence of the noise force is determined from the fluctuation-dissipation theorem. The analytical results are shown to be useful for the micron scale cantilevers that are commonly used in atomic force microscopy. A general thermodynamic approach is developed that is valid for cantilevers of arbitrary geometry as well as for arrays of multiple cantilevers whose stochastic motion is coupled through the fluid. It is shown that the fluctuation-dissipation theorem permits the calculation of stochastic quantities via straightforward deterministic methods. The thermodynamic approach is used with deterministic finite element numerical simulations to quantify the auto-correlation and noise spectrum of cantilever fluctuations for a single micron scale cantilever and the cross-correlations and noise spectra of fluctuations for an array of two experimentally motivated nanoscale cantilevers as a function of cantilever separation. The results are used to quantify the noise reduction possible using correlated measurements with two closely spaced nanoscale cantilevers.