In this work we examine several noise-induced phenomena that are found in nano- and micro-electromechanical systems. Our aim is to exploit these phenomena, where possible, for system identification and sensing applications. The exception being our discussion of nonlinear oscillators, where our goal is to remove the effect of noise as much as possible. In general, however, our viewpoint is one of embracing the noise and nonlinearity that are an inevitable part of miniaturization and seek new modes of micro- and nano-system operation applicable where noise and nonlinearity are fundamentally unavoidable.In this work we discuss three different, but related, topics. First, we discuss the dynamics of a system subject to a parameter sweep through a bifurcation in the pres- ence of noise. We develop approximate distributions for the time at which a system swept through a subcritical pitchfork or a saddle-node bifurcation will leave the local region of phase space, leading to a sudden jump in response amplitude. These distri- butions are developed in the limit of "fast" sweeping, where the sweep rate is large compared to the noise strength, which is relevant to most MEMS applications. We then present the results of sweeping experiments performed on a MEMS resonator and show the value of our analytic predictions. Our primary conclusion is that de- layed bifurcation is prominent in MEMS devices, and we provide predictive tools for predicting the resulting distribution of jump events.Next, we consider a novel dynamical bridge sensing paradigm. This sensing methodology employs a vibrating bistable system arranged, by tuning of parameters, such that the rate of noise-activated escape out of the two stable basins of attraction are identical. The ratio of occupation probabilities can become extremely sensitive atthis point when the noise is weak. We calculate the sensitivity and detection time of the balanced dynamical bridge for use as a general use detector and we develop the conditions required and demonstrate its application as a detector of non-Gaussian noise. We illustrate the measurement of the parameters of a shot-noise process using a one-dimensional bridge model.Finally, we discuss phase noise in oscillators employing nonlinear frequency selec- tive elements. We employ the method of averaging to develop an expression for the spectrum of fractional frequency fluctuations in an oscillator. The expression for the spectrum of frequency fluctuations is quite general, although it neglects dynamics in the feedback elements of the oscillator. The expression contains elements of the noise model and the nominal limit cycle shape of the oscillator. We demonstrate the utility of the results by exploring the parameter space of a prototypical oscillator modeled by a biased Duffing equation. We find that one can reduce the phase diffusion con- stant of the oscillator by tuning the system to a zero-dispersion point of the resonator element, thus eliminating the action-angle coupling at zero-dispersion points of the resonator frequency can lower the phase diffusion constant.
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