Rocking subdiffusive ratchets
- We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-inversion symmetry and driven by a time-periodic field. The anomalous transport becomes optimal for a subthreshold driving when the driving period matches a characteristic time scale of interwell transitions. It can also be optimized by varying temperature, amplitude of periodic potential and driving strength. The useful work done against a load shows a parabolic dependence on the load strength. It grows sublinearly with time and the correspondingWe study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-inversion symmetry and driven by a time-periodic field. The anomalous transport becomes optimal for a subthreshold driving when the driving period matches a characteristic time scale of interwell transitions. It can also be optimized by varying temperature, amplitude of periodic potential and driving strength. The useful work done against a load shows a parabolic dependence on the load strength. It grows sublinearly with time and the corresponding thermodynamic efficiency decays algebraically in time because the energy supplied by the driving field scales with time linearly. However, it compares well with the efficiency of normal diffusion rocking ratchets on an appreciably long time scale.…
Author details: | Igor GoychukORCiD, Vasyl O. KharchenkoORCiD |
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URN: | urn:nbn:de:kobv:517-opus4-416138 |
DOI: | https://doi.org/10.1051/mmnp/20138210 |
ISSN: | 1866-8372 |
Title of parent work (English): | Mathematical Modelling of Natural Phenomena |
Subtitle (English): | origin, optimization and efficiency |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (622) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2019/02/19 |
Publication year: | 2013 |
Publishing institution: | Universität Potsdam |
Release date: | 2019/02/19 |
Tag: | anomalous Brownian motion; generalized Langevin equation; memory effects; ratchet transport; stochastic; viscoelasticity |
Issue: | 622 |
Number of pages: | 15 |
Source: | Mathematical Modelling of Natural Phenomena 8 (2013), pp. 144-158 DOI: 10.1051/mmnp/20138210 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access |
Grantor: | Cambridge University Press (CUP) |
License (German): | Keine öffentliche Lizenz: Unter Urheberrechtsschutz |