Math. Model. Nat. Phenom.
Volume 8, Number 2, 2013Anomalous diffusion
|144 - 158
|24 April 2013
Rocking Subdiffusive Ratchets: Origin, Optimization and Efficiency
1 Institute of Physics, University of
Augsburg, Universitätstr. 1, D-86135 Augsburg, Germany & Institute for Physics
and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476
2 Institute of Applied Physics, NAS of Ukraine, 58 Petropavlovskaya str., 40030 Sumy, Ukraine
⋆ Corresponding author. E-mail:
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 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.
Mathematics Subject Classification: 82C31 / 82C70 / 82C80 / 60H10
Key words: anomalous Brownian motion / generalized Langevin equation / memory effects / viscoelasticity / ratchet transport / stochastic thermodynamics
© EDP Sciences, 2013
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