[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: We study the drift of a Brownian particle in a periodically tapered tube, induced by a longitudinal time-periodic force of amplitude ∣F∣ that alternates in sign every half-period. The focus is on the velocity dependence on the force period, which is usually considered not tractable analytically. For large ∣F∣ we derive an analytical solution that gives the velocity as a function of the amplitude and the period of the force as well as the geometric parameters of the tube. The solution shows how the velocity decreases from its maximum value to zero as the force period decreases from infinity (adiabatic regime) to zero. Our analytical results are in excellent agreement with those obtained from 3D Brownian dynamics simulations.
The Journal of chemical physics 09/2011; 135(12):121102. · 3.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: We study the effect of a driving force F on drift and diffusion of a point Brownian particle in a tube formed by identical cylindrical compartments, which create periodic entropy barriers for the particle motion along the tube axis. The particle transport exhibits striking features: the effective mobility monotonically decreases with increasing F, and the effective diffusivity diverges as F→∞, which indicates that the entropic effects in diffusive transport are enhanced by the driving force. Our consideration is based on two different scenarios of the particle motion at small and large F, homogeneous and intermittent, respectively. The scenarios are deduced from the careful analysis of statistics of the particle transition times between neighboring openings. From this qualitative picture, the limiting small-F and large-F behaviors of the effective mobility and diffusivity are derived analytically. Brownian dynamics simulations are used to find these quantities at intermediate values of the driving force for various compartment lengths and opening radii. This work shows that the driving force may lead to qualitatively different anomalous transport features, depending on the geometry design.
The Journal of Physical Chemistry B 03/2011; 115(14):3992-4002. · 3.61 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
The Journal of Physical Chemistry B 02/2010; 114(5):1959-66. · 3.61 Impact Factor
[show abstract][hide abstract] ABSTRACT: The paper deals with diffusion of a particle in a tube that consists of alternating wide and narrow sections. At sufficiently long times the particle motion can be coarse-grained and described as effective free-diffusion along the tube axis. In the coarse-grained description all the details of the tube geometry are packed into the effective diffusion coefficient of the particle. We derive a formula for the effective diffusion coefficient, which shows how it depends on the geometric parameters of the tube. To test the accuracy of this formula we compare its predictions with the values of the effective diffusion coefficient found in Brownian dynamics simulations. The comparison shows that the formula is applicable at arbitrary values of the length and radius of the narrow sections on condition that the radius of the wide sections does not exceed their length.
Chemical Physics 01/2010; 370:238-243. · 1.96 Impact Factor
[show abstract][hide abstract] ABSTRACT: The presence of obstacles leads to a slowdown of diffusion. We study the slowdown when diffusion occurs in a tube, and obstacles are periodically spaced identical partitions with circular apertures of arbitrary radius in their centers. The mean squared displacement of a particle diffusing in such a system at large times is given by ⟨Δx2(t)⟩=2Defft, t→∞, where Deff is the effective diffusion coefficient, which is smaller than the particle diffusion coefficient in the tube with no partitions, D0. The latter characterizes the short-time behavior of the mean squared displacement, ⟨Δx2(t)⟩=2D0t, t→0. Thus, the particle diffusion coefficient decreases from D0 to Deff as time goes from zero to infinity. We derive analytical solutions for the Laplace transforms of the time-dependent diffusion coefficient and the mean squared displacement that show how these functions depend on the geometric parameters of the tube. To obtain these solutions we replace nonuniform partitions with apertures by effective partitions that are uniformly permeable for diffusing particles. Our choice of the partition permeability is based on the recent result for the corresponding effective trapping rate obtained by means of boundary homogenization. To establish the range of applicability of our approximate theory we compare its predictions with the results found in Brownian dynamics simulations. Comparison shows excellent agreement between the two at arbitrary value of the aperture radius when the tube radius does not exceed the interpartition distance.
The Journal of Chemical Physics 01/2009; · 3.16 Impact Factor
[show abstract][hide abstract] ABSTRACT: The problem of diffusion of particles in a tube with periodically positioned partitions with circular orifices at the center
of each was considered. Using an approach based on the methods and results of the theory of diffusion-controlled reactions
and the idea of homogenization of the permeability of partitions, we derived a formula for the effective diffusion coefficient
for the steady-state regime of the process. The accuracy and applicability domain of the formula were determined by comparing
its predictions with computer simulation results.
Russian Journal of Physical Chemistry B 01/2009; 3(2):313-319. · 0.21 Impact Factor
[show abstract][hide abstract] ABSTRACT: The problem of diffusion in a porous medium with stagnation zones, which reduce the rate of transport of particles, is considered.
A method based on the concept of entropy barriers associated with the small size of inlets into the stagnation zone is used
to solve the diffusion problem. This method made it possible to reduce the diffusion problem in 3D structures to a set of
one-dimensional equations that can be solved analytically. The calculations yielded an exact value of the effective diffusion
coefficient, which is reduced due to random delays in the stagnation zones, and the transition time required to attain this
Russian Journal of Physical Chemistry B 07/2008; 2(4):650-656. · 0.21 Impact Factor
[show abstract][hide abstract] ABSTRACT: The problem of the diffusion of a particle in a porous medium with dead ends entering which is related to overcoming high
entropy barriers is considered. Dead ends effectively decelerate migration, because, while residing in them, a particle does
not participate in diffusion transfer. A new approach to the problem was suggested. The approach was based on the possibility
of splitting the diffusion process into separate well-defined stages thanks to the presence of high entropy barriers. An analysis
of these stages was performed using methods developed in the theory of diffusion-controlled reactions. The new approach was
used to calculate the effective diffusion coefficient (characterizing the limiting particle migration deceleration caused
by the presence of dead ends in a porous medium) and estimate the time of its establishment.
[show abstract][hide abstract] ABSTRACT: 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.
The Journal of Physical Chemistry A 10/2007; 111(38):9486-93. · 2.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006
Physics of Condensed Matter 01/2006; 52(4):501-505. · 1.28 Impact Factor
[show abstract][hide abstract] ABSTRACT: The escape of a point particle from a cavity of an arbitrary configuration through a small orifice in a cavity wall is considered
as a model of entropy barrier overcoming. The dynamics of the particle is determined by collisions with the wall and the dissipative
action of the medium. As in reactions with overcoming energy barriers (the Kramers theory), three characteristic regimes can
be identified depending on the intensity of friction: diffusion and intermediate regimes and the region of weak friction.
For all of them, analytic dependences of rate constants on problem parameters were obtained. The procedure for sewing solutions
together, similar to that employed in the Kramers theory, gives a unified equation for the transmission factor over the whole
range of friction values. In the weak friction mode, overcoming the entropy barrier generally leads to a nonexponential kinetics.
[show abstract][hide abstract] ABSTRACT: The problem of the trapping of diffusing particles by nonoverlapping absorbing patches randomly distributed over a reflecting
surface is considered. The suggested approach to its solution is based on the replacement of the inhomogeneous boundary condition
on the surface by a radiation boundary condition with an effective rate of trapping the same at all surface points. An equation
for the effective rate of the trapping of particles was obtained for absorbing round disks equal in size as reaction patches.
The equation, which also described cooperative effects, was generalized to absorbing patches of different sizes and shapes.
The possibility of finite absorption by reaction patches was included. The results obtained were in close agreement with computer
simulation data obtained by the Brownian dynamics method.
[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: Diffusion of a particle in a medium in the presence of absorbing traps of various size is considered. A theory describing
the kinetics of particle trapping in the entire interval of time is suggested. Analytical relations for the probability of
a particle survival in situations when many-body effects are weak and when they dominate are obtained. It is shown that polydispersity
of traps leads to the slowdown of particle trapping and to attenuation of many-body effects inherent in the problem.
Journal of Experimental and Theoretical Physics 01/2002; 94(2):403-410. · 0.92 Impact Factor
[show abstract][hide abstract] ABSTRACT: The volume of a region visited by a spherical Brownian particle for a time t, known as the Wiener sausage, is an important random variable characterizing Brownian motion. A Brownian dynamics simulation is used to study statistical properties of the Wiener sausage volume. We show that the probability density is closely approximated by a Gaussian distribution not only at asymptotically long times, but over a wide range of times as well. We also refine the expression for the dispersion by finding a correction term for the long-time asymptotic dependence.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 10/2000; 62(3 Pt A):3116-20.
[show abstract][hide abstract] ABSTRACT: We study how the trapping kinetics is modified when traps are gathered in clusters. Recently, we have proposed a mean-field theory of trapping by clusters of traps valid at the initial stage of the process [J. Chem. Phys. 111, 711 (1999)]. Here by using the optimal-fluctuation method we incorporate fluctuation effects in the theory and discuss the manifestation of trap clustering in the kinetics over the entire time domain. Notable observations are that due to trap clustering (1) the trapping kinetics can be significantly modified from the very beginning of the process; (2) the fluctuation-induced kinetics exhibits more rich behavior; (3) the fraction of particles reacting according to a stretched-exponential law can be substantially increased.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 07/2000; 61(6 Pt A):6302-7.
[show abstract][hide abstract] ABSTRACT: The problem of Brownian survival among randomly located traps is considered with emphasis on the role of trap correlations. We proceed from the general representation of the survival probability as the expected value of the emptiness probability function applied to the Wiener sausage. Using the definition of (pure) trap attraction vs. repulsion in terms of the empti-ness probability function, we prove the physical conjecture about the trapping slowdown or acceleration, according to the "sign" of correlations. Two specific models are studied along this line, in which the emptiness probability can be found explicitly; in particular, the long-time survival asymptotics is derived. A remarkable correlation effect of the survival probability dependence on the trap size in one dimension is also discussed.
Canadian Mathematical Society Conference Proceedings Volume. 01/2000; 29.
[show abstract][hide abstract] ABSTRACT: The influence of trap diffusion on the fluctuation slow-down of death of Brownian particles, discovered earlier in the case of stationary traps, is analysed. It is shown that fluctuation slow-down also takes place with movable traps if the diffusion is slow enough.
Journal of Physics A General Physics 12/1998; 22(13):L615.