Exactly solvable model of a slightly fluctuating ratchet.

We consider the motion of a Brownian particle in a sawtooth potential dichotomously modulated by a spatially harmonic perturbation. An explicit expression for the Laplace transform of the Green function of an extremely asymmetric sawtooth potential is obtained. With this result, within the approximation of small potential-energy fluctuations, the integration of the relations for the average particle velocity is performed in elementary terms. The obtained analytical result, its high-temperature, low-frequency, and high-frequency asymptotics, as well as numerical calculations performed for a sawtooth potential of an arbitrary symmetry, indicate that in such a system, the frequency-temperature controlling the magnitude and direction of the ratchet velocity becomes possible. We clarify the mechanism of the appearance of additional regions of nonmonotonicity in the frequency dependence of the average velocity, which leads to the appearance of additional ratchet stopping points. This mechanism is a consequence of the competition between the sliding time along the steep slope of the highly asymmetric sawtooth potential and the correlation time of the dichotomous noise.

Symmetry of deterministic ratchets.

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.

High-temperature ratchets driven by deterministic and stochastic fluctuations.

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.

Adiabatically slow and adiabatically fast driven ratchets.

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.

Quasiequilibrium directed hopping in a time-dependent two-well periodic potential.

We consider the directed motion of a Brownian particle in a two-well periodic potential with time-varying barriers and wells described by arbitrary periodic functions of time, v(t) and u(t), alternating with the period τ. In the framework of the low-temperature kinetic approach, we obtain explicit formulas for the probabilities of finding the particle in potential wells, average velocity of directed motion, input energy P(in) and useful work P(out) against additionally introduced stationary load force f. These formulas are considerably simplified by the assumption of the quasiequilibrium regime of motion corresponding to small values of u(t) and f. It is shown that depending on the same or opposite parity of the functions v(t) and u(t) with respect to time reversal, the motion direction of a Brownian particle is retained or reversed under the reversal of the direction of movement along the (v-u) loop in the phase space of the functions v(t) and u(t), and the nondiagonal kinetic coefficients are mutually symmetric or antisymmetric. In the adiabatic limit τ→∞, the average velocity is proportional to τ(-1) in two cases: (i) the above loop has a nonzero area, (ii) the functions v(t) and u(t) are proportional to each other (zero loop area) and include intervals of fast changes with small durations τ(0) on the period τ of their variations. In both of these cases, the efficiency of energy conversion, η=P(out)/P(in), tends to unity at large variations of the barriers v(t). In the second case, the deviation of η from unity can be split into two contributions: The former decreases exponentially with increasing amplitude v(0) of v(t), while the latter is a small nonadiabatic correction proportional to v(0)(-3/2). It is the nonadiabatic correction that limits high efficiencies at large variations of barriers.

Two-state Brownian motor driven by synchronously fluctuating unbiased forces.

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.

Brownian motor with competing spatial and temporal asymmetry of potential energy.

A Brownian motor is considered which operates due to asymmetric dichotomic fluctuations of the spatially periodic asymmetric potential energy. As shown, the motion direction and stopping points of this motor are dictated by the competition between the spatial and temporal asymmetry of the potential energy (or solely by temporal asymmetry in the case that the potential energy sign fluctuates). For an asymmetric sawtooth potential, the Brownian-particle average velocity is calculated numerically as a function of certain parameters of the model, whereas the low-frequency and low-energy approximations allow the corresponding analytical relationships to be derived for an arbitrarily shaped potential profile. It is shown that temporal asymmetry is not necessary for stopping point occurrence provided that the potential profile fluctuates not only in amplitude but in shape as well. This inference is illustrated by photoinduced fluctuations of the potential energy for a number of substituted arylpyrene molecules on a substrate with symmetrically distributed charge density.

Reciprocating and directed motion on the nanoscale: a simple kinetic model.

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.

Brownian dipole rotator in alternating electric field.

The study addresses the azimuthal jumping motion of an adsorbed polar molecule in a periodic n -well potential under the action of an external alternating electric field. Starting from the perturbation theory of the Pauli equation with respect to the weak field intensity, explicit analytical expressions have been derived for the time dependence of the average dipole moment as well as the frequency dependences of polarizability and the average angular velocity, the three quantities exhibiting conspicuous stochastic resonance. As shown, unidirectional rotation can arise only provided simultaneous modulation of the minima and maxima of the potential by an external alternating field. For a symmetric potential of hindered rotation, the average angular velocity, if calculated by the second-order perturbation theory with respect to the field intensity, has a nonzero value only at n=2 , i.e., when two azimuthal wells specify a selected axis in the system. Particular consideration is given to the effect caused by the asymmetry of the two-well potential on the dielectric loss spectrum and other Brownian motion parameters. When the asymmetric potential in a system of dipole rotators arises from the average local fields induced by an orientational phase transition, the characteristics concerned show certain peculiarities which enable detection of the phase transition and determination of its parameters.

Reciprocating motion on the nanoscale.

This paper analyzes the confined motion of a Brownian particle fluctuating between two conformational states with different potential profiles and different position-dependent rate constants of the transitions, the fluctuations arising from both thermal (equilibrium) and external (nonequilibrium) noise. The model illustrates a mechanism to transduce, on the nanoscale, the energy of nonequilibrium fluctuations into mechanical energy of reciprocating motion. Expressions for the reciprocating velocity and the efficiency of energy conversion are derived. These expressions are treated in more detail in the slow-fluctuation (quasi-equilibrium) regime, by simple perturbation theory arguments, and in the fast fluctuation limit, in terms of the potential of mean force. A notable observation is that the generalized driving force of the reciprocating motion is caused by two sources: the energy contribution due to the difference between the potential profiles of the states and the entropic contribution due to the difference between the position-dependent rate constants. Two illustrative examples are presented, where one of the two sources can be ignored and an exact solution is allowed. Among other aspects, we also discuss the ways to construct a molecular motor based on the reciprocating engine.

Conventional and generalized efficiencies of flashing and rocking ratchets: analytical comparison of high-efficiency limits.

We consider two basic types of Brownian motors which generate directed motion in a periodic asymmetric piecewise-linear potential as a result of random half-period shifts of the potential relief (flashing ratchets) or due to a temporally asymmetric unbiased force applied to the system (rocking ratchets). Analytical relationships have been derived which enable the comparison of the upper limits for the conventional and generalized energy conversion efficiencies in these motors. As found, the increasing amplitude of a sawtooth potential (or the decreasing temperature) makes the conventional efficiency tend to the unity limit faster for a rocking ratchet (in the absence of temporal asymmetry) than for a flashing ratchet. The inverse is true for the generalized efficiency. The potential amplitude being the same, the generalized efficiency is always less than the conventional efficiency. A decreased asymmetry of the potential always results in the reduction of both efficiencies. The temporal asymmetry of an unbiased force has an opposite effect on the conventional and generalized efficiencies: the former rises and the latter drops as the positive signal component becomes shorter in time and larger in amplitude.

Two approaches toward a high-efficiency flashing ratchet.

For a flashing ratchet with periodic potentials fluctuating via random shifts of one-half period, a high efficiency is shown to result from two mechanisms. The previously reported one [Yu. A. Makhnovskii, Phys. Rev. E 69, 021102 (2004); V. M. Rozenbaum, JETP Lett. 79, 388 (2004)] is realized in the near-equilibrium region and implies, first, the presence of a high barrier V0 blocking the reverse movement of a Brownian particle and, second, identical, though energy-shifted, portions of the asymmetric flat potential profile on both half periods. We report another mechanism acting far from equilibrium, typical of strongly asymmetric potentials which are shaped identically on both half periods with a large energetic shift DeltaV . The two mechanisms exhibit radically different limiting behavior of the maximum possible efficiency: eta(m) approximately 1-exp (-beta V0 /2) for the former and eta(m) approximately 1-ln (2betaDeltaV) /betaDeltaV for the latter ( beta being the reciprocal temperature in energy units). The flux and the efficiency for a Brownian motor with a piecewise-linear potential are calculated using the transfer matrix method; an exact analytical solution can thus be obtained for an extremely asymmetric sawtooth potential, the simplest example of the second high-efficiency mechanism. As demonstrated, the mechanisms considered are also characteristic of a two-well periodic potential treated in terms of the kinetic approach.

Flashing ratchet model with high efficiency.

As a simple model of the Brownian motor, we consider hopping motion of a particle in a periodic asymmetric double-well potential which randomly switches between two states. The potential profiles of the states are identical but shifted by half a period. The current and the efficiency are explicitly calculated as functions of the parameters of the model, including also a load force. Such a flashing ratchet is shown to be particularly efficient, with the efficiency tending to unity when the highest peak of the potential is high enough to suppress the backward motion.

[Evaluation of the effectiveness of work of medical personnel]. / Otsenka éffektivnosti truda vrachebnogo personala.

Methods for expert evaluation of physicians' labour are suggested which provide recommendations on physician's category and performance pay, a suggestion is also made of methods for sociometric study identifying informal structure of the collective. Heads of subunit, informal leaders and clinical workers from chairs of medical institute are also engaged in expert evaluations. Unbiased attitude towards evaluation is controlled by correlation analysis. Socio-psychological characteristics of leaders are provided, coefficient of their managerial skills is determined. The results of studying the qualification level of physicians from central regional hospital N 4 of the city of Kiev are discussed.