Browsing by Author "Shapochkina, I. V."

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Adiabatically slow and adiabatically fast driven ratchets
(2012-04-12)
Rozenbaum, V. M.
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Makhnovskii, Yu. A.
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Shapochkina, I. V.
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Sheu, S. -Y.
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Yang, D. -Y.
We revisit two known models of deterministically driven ratchets, which exhibit high energetic efficiency, with the goal to uncover similarities and differences in the principles of their operation. Both the models rely on adiabaticity of the potential change process, however, the adiabaticity that we deal with in the two cases is of different types, slow and fast. It is shown that in the former (latter) case the drift velocity is an even (odd) functional of the potential, with the notable consequence that for the adiabatically slow driven ratchet the necessary symmetry breaking occurs only due to time-dependent parametric perturbations, while the spatial asymmetry of the potential is a mandatory condition for the adiabatically fast driven ratchet to operate. To treat energetic characteristics, the models are restated in terms of traveling potential ratchets. With such an approach, we find that in these cases (i) the conditions of high energetic efficiency to be reached are similar, and (ii) the symmetry properties of the kinetic coefficients are different. Based on our results, a strategy for designing efficient Brownian motors is suggested.
High-temperature ratchets driven by deterministic and stochastic fluctuations
(2019-01-03)
Rozenbaum, V. M.
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Shapochkina, I. V.
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Teranishi, Y.
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Trakhtenberg, L. I.
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物理研究所
We consider the overdamped dynamics of a Brownian particle in an arbitrary spatial periodic and time-dependent potential on the basis of an exact solution for the probability density in the form of a power series in the inverse friction coefficient. The expression for the average velocity of a Brownian ratchet is simplified in the high-temperature consideration when only the first terms of the series can be used. For the potential of an additive-multiplicative form (a sum of a time-independent contribution and a time-dependent multiplicative perturbation), general explicit expressions are obtained which allow comparative analysis of frequency dependencies of the average velocity, implying deterministic and stochastic potential energy fluctuations. For qualitative and quantitative analysis of these dependences, we choose illustrative examples for spatial harmonic fluctuations: with deterministic time dependences of a relaxation type and stochastic time dependences describing Markovian dichotomous and harmonic noise processes. We explore the influence of fluctuation types on the ratchet effect and demonstrate its enhancement in the case of harmonic noise.
Relaxation high-temperature ratchets
(2019-01-15)
Shapochkina, I. V.
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Rozenbaum, V. M.
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Sheu, S. -Y.
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Yang, D. -Y.
;
Lin, S. H.
We consider the overdamped motion of a Brownian particle in an asymmetric spatially periodic potential which fluctuates periodically in time, under assumption of finite duration of the relaxation response of the system on deterministic dichotomous fluctuations. It is assumed that the period of these fluctuations is much larger than the characteristic diffusion time and the potential barrier height is small as compared to the thermal energy (an adiabatic high-temperature flashing ratchet). We derive an analytical expression for the average particle velocity, which is concretized for a saw-tooth potential profile. It is revealed the different, linear and quadratic, asymptotic behavior of the average velocity as a function of the relaxation time for extremely and not extremely asymmetric potential profiles, respectively. The result is interpreted in terms of the self-similar representation. (C) 2018 Elsevier B.V. All rights reserved.
Symmetry of Pulsating Ratchets
(2018-04-01)
Rozenbaum, V. M.
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Shapochkina, I. V.
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Teranishi, Y.
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Trakhtenberg, L. I.
;
物理研究所
Using an exact expression for the average velocity of inertialess motion of pulsating ratchets, a simple proof is given for the recently discovered hidden space-time symmetry of Cubero-Renzoni (D. Cubero, F. Renzoni, 2016). The conditions are revealed for the absence of the ratchet effect in systems with potential energies described by products of periodic functions of coordinate and time possessing the symmetry of the main types. In particular, it is shown that the ratchet effect is absent for the time dependence of the universal symmetry type (which combines three standard symmetries), and this restriction is removed when inertia is taken into account, unless the coordinate dependence of the potential energy is related to symmetric or antisymmetric functions.
Theory of slightly fluctuating ratchets
(2017-04-01)
Rozenbaum, V. M.
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Shapochkina, I. V.
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Lin, S. H.
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Trakhtenberg, L. I.
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應用化學系
We consider a Brownian particle moving in a slightly fluctuating potential. Using the perturbation theory on small potential fluctuations, we derive a general analytical expression for the average particle velocity valid for both flashing and rocking ratchets with arbitrary, stochastic or deterministic, time dependence of potential energy fluctuations. The result is determined by the Green's function for diffusion in the time-independent part of the potential and by the features of correlations in the fluctuating part of the potential. The generality of the result allows describing complex ratchet systems with competing characteristic times; these systems are exemplified by the model of a Brownian photomotor with relaxation processes of finite duration.