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.show moreshow less

Download full text files

  • SHA-1: f5e1a4e6d22b7af3122ab87caa5078e85c44f8de

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics
Metadaten
Author:Igor GoychukORCiD, Vasyl O. KharchenkoORCiD
URN:urn:nbn:de:kobv:517-opus4-416138
DOI:https://doi.org/10.1051/mmnp/20138210
ISSN:1866-8372
Parent Title (English):Mathematical Modelling of Natural Phenomena
Subtitle (English):origin, optimization and efficiency
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (622)
Document Type:Postprint
Language:English
Date of first Publication:2019/02/19
Year of Completion: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
Pagenumber:15
Source:Mathematical Modelling of Natural Phenomena 8 (2013), pp. 144-158 DOI: 10.1051/mmnp/20138210
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Peer Review:Referiert
Publication Way:Open Access
Grantor:Cambridge University Press (CUP)
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht