Stochastic resonance in a bistable piecewise potential: analytical solution

Berdichevsky, V.; Gitterman, Moshe

doi:10.1088/0305-4470/29/18/001

Cited by 28 publications

(12 citation statements)

References 9 publications

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“…In contrast to the OS, the presence of a peak around os ¼ 0:4 AE 0:05 Hz is apparent for the SNR. This value is close to that predicted by the matching condition, SR ¼ k c =2, which states that the SNR is maximum when the average hopping time of the hairpin (1=k c ¼ 1:56 s) is equal to half the period of the forcing oscillation (1=2 os ¼ 1:25 s) [12,[20][21][22]. This shows that SR in single-molecule hopping experiments approximately fulfills the matching condition as has been observed in other bistable systems.…”

Section: Sr Experimentssupporting

confidence: 87%

Single-Molecule Stochastic Resonance

et al. 2012

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Stochastic resonance (SR) is a well-known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic (random or probabilistic) noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively transitions from folded to unfolded configurations under the action of an oscillating mechanical force applied with optical tweezers. By varying the frequency of the force oscillation, we investigate the folding and unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measure several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that a good quantifier of the SR is the signal-to-noise ratio (SNR) of the spectral density of measured fluctuations in molecular extension of the DNA hairpins. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance-matching condition. Finally, we carry out experiments on short hairpins that show how SR might be useful for enhancing the detection of conformational molecular transitions of low SNR.

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Section: Sr Experimentssupporting

confidence: 87%

Single-Molecule Stochastic Resonance

et al. 2012

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“…20 For the classical case, in particular for systems in which a classical particle interacts with a time-dependent potential, different formalisms were developed, including treatments of the problem of a time-modulated barrier 5,21,22 and of a classical particle in a time-dependent oscillating well. 23,24 Consideration of the dynamics of these problems in the presence of noise has recently led to exact descriptions of diffusion within static single and double-square well potentials, 25,26 the introduction of an external field for twolevel systems in a classical potential, 27 a general solution of the problem of activated escape in periodically driven systems, 28 analytic solutions for the problem of a piecewise bistable potential in the limit of weak external perturbation, 29 calculation of the escape flux from a multiwell metastable potential at times preceding the formation of quasiequilibrium, 30 activation over a randomly fluctuating barrier, 31,32 and diffusion across a randomly fluctuating barrier. 33 In this paper we revisit the problem of a classical particle interacting with an infinitely deep potential well containing a periodically oscillating square well, with the aim of describing some of its scaling properties.…”

Section: Introductionmentioning

confidence: 99%

Scaling properties for a classical particle in a time-dependent potential well

Leonel

McClintock

2005

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Some scaling properties for a classical particle interacting with a time-dependent square-well potential are studied. The corresponding dynamics is obtained by use of a two-dimensional nonlinear area-preserving map. We describe dynamics within the chaotic sea by use of a scaling function for the variance of the average energy, thereby demonstrating that the critical exponents are connected by an analytic relationship. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1941067͔Scaling arguments are used to characterize the chaotic sea in the low energy domain for the problem of a classical particle confined to an infinitely deep potential box containing an oscillating square well. The system is described by three relevant control parameters via the formalism of an area-preserving map. We thus concentrate on analyzing the variance of the average energy, which we refer to as the roughness. We do so as a function of two relevant control parameters, namely: (i) the oscillating frequency; and (ii) the depth of the oscillating potential. As the map is iterated, the roughness grows to start with. For a sufficient number of iterations, however, the rate of growth decreases and a regime of saturation is entered. The changeover from growth to saturation is characterized by a crossover iteration number. Both the roughness saturation value and the crossover iteration number can be described in terms of critical exponents, and we show that the exponents differ depending on which control parameter is considered. The scaling arguments are proved by a convincing collapse of different roughness curves into a single universal plot.

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“…Recent results include exact solutions for the problem of diffusion within static single and double square wells [12,13], an introduction of external fields for a two-level system in a classical potential [14], a general solution of the problem of activated escape in periodically driven systems [15], analytical solutions for the problem of a piecewise bistable potential in the limit of low external perturbation [16], the escape flux from a multi-well metastable potential preceding the formation of quasi-equilibrium [17], activation over a randomly fluctuating barrier [18,19], diffusion across a randomly fluctuating barrier [20] and diffusion of a particle in a piecewise potential in the presence of small fluctuations of the barriers [21]. The main result of [21] is that the flux of particles through the barrier may either increase or decrease, a result that is independent of the frequency of the oscillations.…”

Section: Introductionmentioning

confidence: 99%

Dynamical properties of a particle in a time-dependent double-well potential

Leonel¹,

McClintock²

2004

J. Phys. A: Math. Gen.

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Some chaotic properties of a classical particle interacting with a time-dependent double-square-well potential are studied. The dynamics of the system is characterized using a two-dimensional nonlinear area-preserving map. Scaling arguments are used to study the chaotic sea in the low-energy domain. It is shown that the distributions of successive reflections and of corresponding successive reflection times obey power laws with the same exponent. If one or both wells move randomly, the particle experiences the phenomenon of Fermi acceleration in the sense that it has unlimited energy growth.

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Stochastic resonance in a bistable piecewise potential: analytical solution

Cited by 28 publications

References 9 publications

Single-Molecule Stochastic Resonance

Single-Molecule Stochastic Resonance

Scaling properties for a classical particle in a time-dependent potential well

Dynamical properties of a particle in a time-dependent double-well potential

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