Signal Amplification by 1/<i>f</i> Noise in Silicon-Based Nanomechanical Resonators

Guerra, Diego; Dunn, Tyler; Mohanty, Pritiraj

doi:10.1021/nl9004546

Cited by 23 publications

(22 citation statements)

References 19 publications

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“…Noise provides a critical barrier for the development of sensitive electronic and mechanical devices, particularly at the nanoscale [2,3]. Increasingly, researchers are focusing on exploring innovative, non-traditional device design and control strategies that exploit the ambient noise [4][5][6][7][8][9][10][11]. In this regard, there are clear advantages to understanding how nature has managed to harness noise in a setting whose primary (apparent) function is to manage information.…”

Section: Introductionmentioning

confidence: 99%

“…all exhibit 1/f behavior. Guerra et al [7] demonstrated how stochastic resonance induced by 1/f noise can increase the sensitivity of nanomechanical resonators, allowing for the possibility of fashioning them into noisy but robust nanoscale computation devices. Neither the response nor the details of the underlying non-equilibrium behavior that makes neurons robust to natural (1/f ) noise is well understood.…”

Section: Introductionmentioning

confidence: 99%

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Neuron dynamics in the presence of1/fnoise

Sobie

Babul²,

Sousa³

2011

Phys. Rev. E

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Interest in understanding the interplay between noise and the response of a non-linear device cuts across disciplinary boundaries. It is as relevant for unmasking the dynamics of neurons in noisy environments as it is for designing reliable nanoscale logic circuit elements and sensors. Most studies of noise in non-linear devices are limited to either time-correlated noise with a Lorentzian spectrum (of which the white noise is a limiting case) or just white noise. We use analytical theory and numerical simulations to study the impact of the more ubiquitous "natural" noise with a 1/f frequency spectrum. Specifically, we study the impact of the 1/f noise on a leaky integrate and fire model of a neuron. The impact of noise is considered on two quantities of interest to neuron function: The spike count Fano factor and the speed of neuron response to a small step-like stimulus. For the perfect (non-leaky) integrate and fire model, we show that the Fano factor can be expressed as an integral over noise spectrum weighted by a (low pass) filter function given by F(t, f ) = sinc 2 (πf t). This result elucidates the connection between low frequency noise and disorder in neuron dynamics. Under 1/f noise, spike dynamics lacks a characteristic correlation time, inducing the leaky and non-leaky models to exhibit non-ergodic behavior and Fano factor increasing logarithmically as a function of time. We compare our results to experimental data of single neurons in vivo [M.C. Teich, C. Heneghan, S.B. Lowen, T. Ozaki, and E. Kaplan, Journal of the Optical Society of America A 14, 529 (1997)], and show how the 1/f noise model provides much better agreement than the usual approximations based on Lorentzian noise. The low frequency noise, however, complicates the case for information coding scheme based on interspike intervals by introducing variability in the neuron response time. On a positive note, the neuron response time to a step stimulus is, remarkably, nearly optimal in the presence of 1/f noise. An explanation of this effect elucidates how the brain can take advantage of noise to prime a subset of the neurons to respond almost instantly to sudden stimuli.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Neuron dynamics in the presence of1/fnoise

Sobie

Babul²,

Sousa³

2011

Phys. Rev. E

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“…using phase modulation and/or phase noise (i.e. phase random fluctuations of input signal) [15,23]. Most of them use amplitude noise to demonstrate amplitude stochastic resonance, or introduce noise in the form of the response of a stochastic oscillator [39].…”

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confidence: 99%

Phase Stochastic Resonance in a Forced Nanoelectromechanical Membrane

et al. 2017

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Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems.We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced nano-electromechanical membrane by evidencing the enhancement of a weak phase modulated signal thanks to the addition of phase noise. Based on a general forced Duffing oscillator model, we demonstrate experimentally and theoretically that phase noise acts multiplicatively inducing important physical consequences. These results may open interesting prospects for phase noise metrology or coherent signal transmission applications in nanomechanical oscillators. Moreover, our approach, due to its general character, may apply to various systems.Stochastic resonance whereby a small signal gets amplified resonantly by application of external noise has been introduced originally in paleoclimatology [1,19] to explain the recurrence of ice ages and has then been observed in many other areas including neurobiology [6,16] [3,33,34,42]. Implementation of stochastic resonances involves generally three ingredients : (i) the existence of metastable states separated by an activation energy, as in excitable or bistable nonlinear systems, (ii) a coherent excitation, whose amplitude is however too weak to induce deterministic hopping between the states, and (iii) stochastic processes inducing random jumps over the potential barrier. In the classical picture of a bistable system, this corresponds to the motion of a fictive particle in a double-well potential periodically modulated in amplitude by the signal and subjected to noise [21]. When an optimal level of noise is reached, the system's response power spectrum displays a peak in the signal to noise ratio, unveiling the stochastic resonance phenomenon. The resonance occurs as a 'bona-fide' resonance in a frequency band around a signal frequency approximately given by the time-matching condition [5,22], i.e. when the potential modulation period is twice the mean residence time of the noise-driven particle. Experimental works on stochastic resonance are almost exclusively using amplitude modulation going along with additive amplitude noise or multiplicative amplitude noise [10,20,37,44,45]. In this case, it corresponds to a pure one dimensional effect. Few studies take advantage of a bidimensional phase space by e.g. using phase modulation and/or phase noise (i.e. phase random fluctuations of input signal) [15,23]. Most of them use amplitude noise to demonstrate amplitude stochastic resonance, or introduce noise in the form of the response of a stochastic oscillator [39]. However in the latter scheme, neither the noise nor the modulation are controlled, thus preventing to unveil the specific roles of phase modulation and phase noise in stochastic resonance.In this Letter, stochastic resonance is implemented in a nonlinear nanomechanical oscillator forced close to its resonant frequency. It enables, in a bidimensionnal phase space, the implementation of phase...

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“…From the perspective of basic science, NEM systems represent a novel class of high-dimensional nonlinear dynamical systems. Recent years have witnessed a growing interest in exploring and understanding various nonlinear phenomena in NEM systems such as synchronization [15], signal amplification and stochastic resonance [16,17], extensive chaos [18], and multistability [19].…”

Section: Introductionmentioning

confidence: 99%

Regularization of chaos by noise in electrically driven nanowire systems

Hessari

Lai

et al. 2014

Phys. Rev. B

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The electrically driven nanowire systems are of great importance to nanoscience and engineering. Due to strong nonlinearity, chaos can arise, but in many applications it is desirable to suppress chaos. The intrinsically high-dimensional nature of the system prevents application of the conventional method of controlling chaos. Remarkably, we find that the phenomenon of coherence resonance, which has been well documented but for low-dimensional chaotic systems, can occur in the nanowire system that mathematically is described by two coupled nonlinear partial differential equations, subject to periodic driving and noise. Especially, we find that, when the nanowire is in either the weakly chaotic or the extensively chaotic regime, an optimal level of noise can significantly enhance the regularity of the oscillations. This result is robust because it holds regardless of whether noise is white or colored, and of whether the stochastic drivings in the two independent directions transverse to the nanowire are correlated or independent of each other. Noise can thus regularize chaotic oscillations through the mechanism of coherence resonance in the nanowire system. More generally, we posit that noise can provide a practical way to harness chaos in nanoscale systems.

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Signal Amplification by 1/f Noise in Silicon-Based Nanomechanical Resonators

Cited by 23 publications

References 19 publications

Neuron dynamics in the presence of1/fnoise

Neuron dynamics in the presence of1/fnoise

Phase Stochastic Resonance in a Forced Nanoelectromechanical Membrane

Regularization of chaos by noise in electrically driven nanowire systems

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