Feedback control in flashing ratchets

Craig, Erin M.; Kuwada, Nathan J.; López, Benjamín; Linke, Heiner

doi:10.1002/andp.200710276

Cited by 34 publications

(75 citation statements)

References 38 publications

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“…This is different from earlier studies based on the Langevin equation (see, e.g., [10,19,30]), where the feedback is applied directly to the position of one particle, χ i (t), or to the average of N particle positions…”

Section: Transport Mechanismmentioning

confidence: 68%

“…(4) on sees that the feedback force changes its sign whenever the delayed mean particle positionz(t−τ D ) becomes smaller or larger than z 0 ; we therefore call z 0 the "switching" position. Our ansatz is partially motivated by an earlier (Langevin equation based) study of Craig et al [19] on feedback control of a flashing ratchet via the so-called "maximum-displacement strategy". In that study, the fixed position z 0 was identified with the mean particle position of the uncontrolled system [i.e., F fc (t) = 0] at t → ∞, that is, the equilibrium positionz eq = dzzρ eq (z), where…”

Section: Definition Of the Modelmentioning

confidence: 99%

“…(16), that is, γχ(t) = −V (χ) + F fc (z(t − τ D )) + 2γk B T ξ(t) . (19) From Eq. (19), we can derive the FPE in the standard way, i.e., by using the Kramers-Moyal (KM) expansion [33].…”

Section: Appendixmentioning

confidence: 99%

See 2 more Smart Citations

Delay-induced transport in a rocking ratchet under feedback control

2014

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Based on the Fokker-Planck equation we investigate the transport of an overdamped colloidal particle in a static, asymmetric periodic potential supplemented by a time-dependent, delayed feedback force, F fc . For a given time t, F fc depends on the status of the system at a previous time t − τD, with τD being a delay time, specifically on the delayed mean particle displacement (relative to some "switching position"). For non-zero delay times F fc (t) develops nearly regular oscillations generating a net current in the system. Depending on the switching position, this current is nearly as large or even larger than that in a conventional open-loop rocking ratchet. We also investigate thermodynamic properties of the delayed non-equilibrium system and we suggest an underlying Langevin equation which reproduces the Fokker-Planck results.

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Section: Transport Mechanismmentioning

confidence: 68%

Section: Definition Of the Modelmentioning

confidence: 99%

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Delay-induced transport in a rocking ratchet under feedback control

2014

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“…(5) We have focused here on proving an upper bound for the particle flux because this quantity can readily be measured in experimental realizations of feedback ratchets [17]. In a recent paper [19], written after the present one, an analogous upper bound was derived for the power output of a feedback ratchet, based on the results and techniques presented here.…”

Section: Discussionmentioning

confidence: 94%

“…Using the results presented here, they obtain that no more than 95% of the maximum gain achieved by the feedback strategy can be observed for that real system. The experimental realization of this system is currently under way [17]. (4) In general, the flux generated by the open-loop ratchet is much smaller than the flux generated by the feedback ratchet [6].…”

Section: Discussionmentioning

confidence: 99%

Information and flux in a feedback controlled Brownian ratchet

Cao

Feito

Touchette

2009

Physica A: Statistical Mechanics and its Applications

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We study a feedback control version of the flashing Brownian ratchet, in which the application of the flashing potential depends on the state of the particles to be controlled. Taking the view that the ratchet acts as a Maxwell's demon, we study the relationship that exists between the performance of the demon as a rectifier of random motion and the amount of information gathered by the demon through measurements. In the context of a simple measurement model, we derive analytic expressions for the flux induced by the feedback ratchet when acting on one particle and a few particles, and compare these results with those obtained with its open-loop version, which operates without information. Our main finding is that the flux in the feedback case has an upper bound proportional to the square-root of the information. Our results provide a quantitative analysis of the value of information in feedback ratchets, as well as an effective description of imperfect or noisy feedback ratchets that are relevant for experimental applications.

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Feedback Control of Colloidal Transport

Gernert

Loos

Lichtner

et al. 2016

Understanding Complex Systems

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We review recent work on feedback control of one-dimensional colloidal systems, both with instantaneous feedback and with time delay. The feedback schemes are based on measurement of the average particle position, a natural control target for an ensemble of colloidal particles, and the systems are investigated via the Fokker-Planck equation for overdamped Brownian particles. Topics include the reversal of current and the emergence of current oscillations, transport in ratchet systems, and the enhancement of mobility by a co-moving trap. Beyond the commonly considered case of non-interacting systems, we also discuss the treatment of colloidal interactions via (dynamical) density functional theory and provide new results for systems with attractive interactions.

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Feedback control in flashing ratchets

Cited by 34 publications

References 38 publications

Delay-induced transport in a rocking ratchet under feedback control

Delay-induced transport in a rocking ratchet under feedback control

Information and flux in a feedback controlled Brownian ratchet

Feedback Control of Colloidal Transport

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