Browsing by Author "Trakhtenberg, L. I."

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Drift of particles caused by fluctuations of their sizes
(2017-03-01)
Zitserman, V. Yu.
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Makhnovskii, Yu. A.
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Trakhtenberg, L. I.
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Yang, D-Y.
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Lin, S. H.
Externally stimulated fluctuations of the size of a particle in an asymmetric environment result in its directional motion. This is demonstrated by considering the particle drift in a periodic symmetric channel, which arises due to fluctuations of the particle size. The emergence of the drift is caused by the time variation of the particle entropy, whereas fluctuations of the diffusion coefficient accompanying fluctuations of the size enhance the drift. The effect of the geometry of the channel and the amplitude and frequency of fluctuations on the drift velocity is studied by the Brownian dynamics method. A coarse-grained analytical description of the process is proposed whose predictions are in satisfactory agreement with the results of simulation.
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.
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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.
;
Lin, S. H.
;
Trakhtenberg, L. I.
;
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.