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Controlling directed ratchet transport of driven overdamped Brownian particles subjected to a vibrating periodic potential: ratchet universality versus harmonic-mixing perturbation theory

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Abstract

We study directed ratchet transport of a harmonically driven overdamped Brownian particle subjected to a harmonically shaken periodic potential. The existence of a frequency-dependent optimal value of the relative amplitude of the two harmonic excitations involved is theoretically predicted from the criticality scenario giving rise to ratchet universality and numerically confirmed by extensive numerical experiments. The robustness of the ratchet universality scenario is also demonstrated when the external harmonic excitation is replaced by a bounded chaotic excitation having the same underlying main frequency in its Fourier spectrum. We remark that our findings are in sharp contrast with the predictions from the standard harmonic-mixing perturbation theory.

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Acknowledgements

R.C. acknowledges financial support from the Junta de Extremadura (JEx, Spain) through Project No. GR18081 cofinanced by FEDER funds. P.J.M. acknowledges financial support from the Ministerio de Economía y Competitividad (MINECO, Spain) through project FIS2017-87519 cofinanced by FEDER funds and from the Gobierno de Aragón (DGA, Spain) through Grant E36_17R to the FENOL group.

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Authors and Affiliations

  1. Departamento de Física Aplicada, E. I. I., Universidad de Extremadura, Apartado Postal 382, 06006, Badajoz, Spain

    Ricardo Chacón

  2. Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006, Badajoz, Spain

    Ricardo Chacón

  3. Departamento de Física Aplicada, E.I.N.A., Universidad de Zaragoza, 50018, Zaragoza, Spain

    Pedro J. Martínez

  4. Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009, Zaragoza, Spain

    Pedro J. Martínez

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  1. Ricardo Chacón
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  2. Pedro J. Martínez
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Correspondence to Ricardo Chacón.

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Chacón, R., Martínez, P.J. Controlling directed ratchet transport of driven overdamped Brownian particles subjected to a vibrating periodic potential: ratchet universality versus harmonic-mixing perturbation theory. Nonlinear Dyn 104, 2411–2416 (2021). https://doi.org/10.1007/s11071-021-06432-0

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