Browsing by Author "Rozenbaum, V. M."

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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.
Reciprocating and Directed Motion on the Nanoscale: A Simple Kinetic Model
(2010-02-11)
Rozenbaum, V. M.
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Makhnovskii, Yu. A.
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Yang, D. -Y.
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Sheu, S. -Y.
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Lin, S. H.
We consider noise-induced reciprocating motion on the nanoscale and its rectification to directed motion using a simple model in which transitions between two fluctuating states occur through two reaction channels with fluctuating transition rates. The fluctuations of states and transition rates arise from equilibrium thermal and external nonthermal noise which is in either case position-dependent. The model is equivalent to a Brownian particle hopping in a periodic double-well potential which randomly switches between two profiles. With a nonequilibrium noise, a generalized driving force may be regarded as the sum of two forces: one resulting from energy fluctuations and the other from fluctuations of the spatial dependence of the transition rates. This suggests two mechanisms, energetic and informational, by which the motion occurs. The reciprocating motion results in directed motion if rectified by asymmetric fluctuations of potential barriers. The energy conversion efficiency is calculated and the conditions to maximize it are established.
Reciprocating nanoengine
(2006-08-01)
Makhnovskii, Yu. A.
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Rozenbaum, V. M.
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Yang, D. -Y.
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Lin, S. H.
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Tsong, T. Y.
Brownian motion in a confining potential fluctuating between two spatially separated potential profiles is considered as a model of an engine converting nonequilibrium fluctuations into reciprocating motion on the nanoscale. We present two exact solutions obtained for the parabolic and step potential, which reveal the temperature and frequency-modulation behavior of the engine. The confining potential determines the interplay of the independent internal (thermal) and external (discrete) noises: the noises are cooperated for any potential, except the parabolic one. The engine can operate as a molecular motor, being supplemented by a rectifying mechanism.
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 deterministic ratchets
(2019-08-13)
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 motion of a Brownian particle in an unbiased force field described by a periodic function of coordinate and time. A compact analytical representation has been obtained for the average particle velocity as a series in the inverse friction coefficient, from which follows a simple and clear proof of hidden symmetries of ratchets, reflecting the symmetry of summation indices of the applied force harmonics relative to their numbering from left to right and from right to left. We revealed the conditions under which (i) the ratchet effect is absent; (ii) the ratchet average velocity is an even or odd functional of the applied force, whose dependences on spatial and temporal variables are characterized by periodic functions of the main types of symmetries: shift, symmetric, and antisymmetric, and universal, which combines all three types. These conditions have been specified for forces with those dependences of a multiplicative (or additive-multiplicative) and additive structure describing two main ratchet types, pulsating and forced ratchets. We found the fundamental difference in dependences of the average velocity of pulsating and forced ratchets on parameters of spatial and temporal asymmetry of potential energy of a particle for systems in which the spatial and temporal dependence is described by a sawtooth potential and a deterministic dichotomous process, respectively. In particular, it is shown that a pulsating ratchet with a multiplicative structure of its potential energy cannot move directionally if the energy is of the universal symmetry type in time; this restriction is removed in the inertial regime, but only if the coordinate dependence of the energy does not belong to either symmetric or antisymmetric functions.
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.
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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.
Two-state Brownian motor driven by synchronously fluctuating unbiased forces
(2011-08-04)
Rozenbaum, V. M.
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Makhnovskii, Yu A.
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Sheu, S. -Y.
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Yang, D. -Y.
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Lin, S. H.
As a model of the Brownian motor, we consider a particle moving unidirectionally under the action of two synchronously fluctuating unbiased forces, transverse and longitudinal with respect to the particle track. The former force induces track-normal transitions of the particle between the attached and detached states (with and without a periodic potential, respectively), whereas the latter drives track-parallel motion in either state. Analytical expressions of the current and efficiency are derived for different regimes, with due account of the delayed response of the system to force fluctuations. For a sawtooth potential in the attached state, we reveal several motion regimes affording the maximum current or the maximum efficiency. A special emphasis is placed on the possibility of current reversal. As shown, the interplay between two phase-shifted harmonically varied forces as well as inherent and externally induced asymmetry can lead to the emergence of multiple current reversals, thus enabling the flexible controllability of the motion direction.