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Roy-Layinde TO, Vincent UE, Abolade SA, Popoola OO, Laoye JA, McClintock PVE. Vibrational resonances in driven oscillators with position-dependent mass. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200227. [PMID: 33455553 DOI: 10.1098/rsta.2020.0227] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/25/2020] [Indexed: 05/22/2023]
Abstract
The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM). We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework for determining the response amplitude of PDM systems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximize the efficiency of devices being operated in VR modes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
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Affiliation(s)
- T O Roy-Layinde
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
| | - U E Vincent
- Department of Physical Sciences, Redeemer's University, P.M.B. 230 Ede, Nigeria
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
| | - S A Abolade
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - O O Popoola
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - J A Laoye
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
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Huang L, Soskin SM, Khovanov IA, Mannella R, Ninios K, Chan HB. Frequency stabilization and noise-induced spectral narrowing in resonators with zero dispersion. Nat Commun 2019; 10:3930. [PMID: 31477718 PMCID: PMC6718662 DOI: 10.1038/s41467-019-11946-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2019] [Accepted: 08/02/2019] [Indexed: 11/17/2022] Open
Abstract
Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors including thermal noise, frequency noise of the resonator and noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the eigenfrequency on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large amplitudes. The spectral peak undergoes narrowing when the noise intensity is increased. With the resonator serving as the frequency-selecting element in a feedback loop, the phase noise at the extremum amplitude is ~3 times smaller than the minimal noise in the conventional nonlinear regime.
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Affiliation(s)
- L Huang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
- William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - S M Soskin
- Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, 03028, Kiev, Ukraine
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - I A Khovanov
- School of Engineering, University of Warwick, Coventry, CV4 7AL, UK
| | - R Mannella
- Dipartimento di Fisica, Universita di Pisa, 56127, Pisa, Italy
| | - K Ninios
- Department of Physics, University of Florida, Gainesville, FL, 32611, USA
| | - H B Chan
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China.
- William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China.
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Roy-Layinde TO, Laoye JA, Popoola OO, Vincent UE, McClintock PVE. Vibrational resonance in an inhomogeneous medium with periodic dissipation. Phys Rev E 2017; 96:032209. [PMID: 29346993 DOI: 10.1103/physreve.96.032209] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2017] [Indexed: 06/07/2023]
Abstract
The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.
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Affiliation(s)
- T O Roy-Layinde
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - J A Laoye
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
| | - O O Popoola
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - U E Vincent
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
- Department of Physical Sciences, Redeemer's University, Ede, Nigeria
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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Samanta HS, Bhattacharjee JK, Bhattacharyay A, Chakraborty S. On noise induced Poincaré-Andronov-Hopf bifurcation. CHAOS (WOODBURY, N.Y.) 2014; 24:043122. [PMID: 25554042 DOI: 10.1063/1.4900775] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
It has been numerically seen that noise introduces stable well-defined oscillatory state in a system with unstable limit cycles resulting from subcritical Poincaré-Andronov-Hopf (or simply Hopf) bifurcation. This phenomenon is analogous to the well known stochastic resonance in the sense that it effectively converts noise into useful energy. Herein, we clearly explain how noise induced imperfection in the bifurcation is a generic reason for such a phenomenon to occur and provide explicit analytical calculations in order to explain the typical square-root dependence of the oscillations' amplitude on the noise level below a certain threshold value. Also, we argue that the noise can bring forth oscillations in average sense even in the absence of a limit cycle. Thus, we bring forward the inherent general mechanism of the noise induced Hopf bifurcation naturally realisable across disciplines.
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Affiliation(s)
- Himadri S Samanta
- Biophysics Program, Institute For Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | | | | | - Sagar Chakraborty
- Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
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Yamgoué SB, Morfu S, Marquié P. Noise effects on gap wave propagation in a nonlinear discrete LC transmission line. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:036211. [PMID: 17500773 DOI: 10.1103/physreve.75.036211] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2006] [Revised: 11/28/2006] [Indexed: 05/15/2023]
Abstract
We report here the results of numerical investigation of noise effects on the propagation in a nonlinear waveguide modeled by a discrete electrical line. Considering a periodic signal of frequency exceeding the natural cutoff frequency of this system, we show that noise can be used to trigger soliton generation in the medium. Besides the classical stochastic resonance signature exhibited by each oscillator of the network, our simulation results reveal in particular that the signal-to-noise ratio remains almost constant in the whole network for an appropriate amount of noise. This interesting feature insures for the generated solitons a quality preserved propagation along the network.
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Affiliation(s)
- Serge Bruno Yamgoué
- Laboratoire d'Electronique, Informatique et Image, UMR CNRS 5158, Dijon, UFR Sciences et Techniques, Université de Bourgogne 9, allée Alain Savary, BP 47870, 21078 Dijon Cedex, France.
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Guo F, Zhou YR, Jiang SQ, Gu TX. Stochastic resonance in a mono-stable system with multiplicative and additive noise. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/45/002] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Soskin SM, McClintock PVE. Comment on "monostable array-enhanced stochastic resonance". PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:013101. [PMID: 12241403 DOI: 10.1103/physreve.66.013101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2001] [Indexed: 11/07/2022]
Abstract
Lindner et al. [Phys. Rev. E 63, 051107 (2001)] have reported multiple stochastic resonances (SRs) in an array of underdamped monostable nonlinear oscillators. This is in contrast to the single SR observed earlier in a similar but isolated oscillator. Though the idea that such an effect might occur is intuitively reasonable, the notation and the interpretation of some of the major results seem confusing. These issues are identified and some of them are clarified. In addition, comments are made on two possible extensions of the central idea of Lindner et al.: one of these promises to provide much more striking manifestations of multiple SR in arrays; the other significantly widens the range of systems in which multiple SRs may be observed.
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Affiliation(s)
- S M Soskin
- Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine
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Lindner JF, Breen BJ, Wills ME, Bulsara AR, Ditto WL. Monostable array-enhanced stochastic resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:051107. [PMID: 11414887 DOI: 10.1103/physreve.63.051107] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2000] [Revised: 01/17/2001] [Indexed: 05/23/2023]
Abstract
We present a simple nonlinear system that exhibits multiple distinct stochastic resonances. By adjusting the noise and coupling of an array of underdamped, monostable oscillators, we modify the array's natural frequencies so that the spectral response of a typical oscillator in an array of N oscillators exhibits N-1 different stochastic resonances. Such families of resonances may elucidate and facilitate a variety of noise-mediated cooperative phenomena, such as noise-enhanced propagation, in a broad class of similar nonlinear systems.
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Affiliation(s)
- J F Lindner
- Department of Physics, The College of Wooster, Wooster, Ohio 44691-2363, USA
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Alfonsi L, Gammaitoni L, Santucci S, Bulsara AR. Intrawell stochastic resonance versus interwell stochastic resonance in underdamped bistable systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:299-302. [PMID: 11088463 DOI: 10.1103/physreve.62.299] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2000] [Indexed: 05/23/2023]
Abstract
We show that, for periodically driven noisy underdamped bistable systems, an intrawell stochastic resonance can exist, together with the conventional interwell stochastic resonance, resulting in a double maximum in the power spectral amplitude at the forcing frequency as a function of the noise intensity. The locations of the maxima correspond to matchings of deterministic and stochastic time scales in the system. In this paper we present experimental evidence of these phenomena and a phemonological nonadiabatic description in terms of a noise-controlled nonlinear dynamic resonance.
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Affiliation(s)
- L Alfonsi
- Dipartimento di Fisica, Universita di Perugia, I-06100 Perugia, Italy
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Luchinsky D, Mannella R, McClintock P, Stocks N. Stochastic resonance in electrical circuits. II. Nonconventional stochastic resonance. ACTA ACUST UNITED AC 1999. [DOI: 10.1109/82.793711] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Luchinsky D, Mannella R, McClintock P, Stocks N. Stochastic resonance in electrical circuits. I. Conventional stochastic resonance. ACTA ACUST UNITED AC 1999. [DOI: 10.1109/82.793710] [Citation(s) in RCA: 61] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Dykman MI, Luchinsky DG, Mannella R, McClintock PV, Soskin SM, Stein ND. Resonant subharmonic absorption and second-harmonic generation by a fluctuating nonlinear oscillator. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:2366-2377. [PMID: 9965341 DOI: 10.1103/physreve.54.2366] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Luchinsky DG, McClintock PV, Soskin SM, Mannella R. Zero-dispersion nonlinear resonance in dissipative systems. PHYSICAL REVIEW LETTERS 1996; 76:4453-4457. [PMID: 10061296 DOI: 10.1103/physrevlett.76.4453] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Soskin SM. Nonlinear resonance for the oscillator with a nonmonotonic dependence of eigenfrequency on energy. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:R44-R46. [PMID: 9962026 DOI: 10.1103/physreve.50.r44] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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McClintock PV, Soskin SM, Stein ND, Stocks NG. Universality of zero-dispersion peaks in the fluctuation spectra of underdamped nonlinear oscillators. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:147-156. [PMID: 9960576 DOI: 10.1103/physreve.48.147] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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