The motion of a Brownian particle in the presence of Coulomb friction and an asymmetric spatial potential was evaluated in this study. The system exhibits a ratchet effect, i.e., an average directed motion even in the absence of an external force, induced by the coupling of non-equilibrium conditions with the spatial asymmetry. Both the average motion and the fluctuations of the Brownian particle were analysed. The stationary velocity shows a non-monotonic behaviour as a function of both the temperature and the viscosity of the bath. The diffusion properties of the particle, which show several time regimes, were also investigated. To highlight the role of non-linear friction in the dynamics, a comparison is presented with a linear model of a Brownian particle driven by a constant external force, which allows for analytical treatment. In particular, the study unveils that the passage times between different temporal regimes are strongly affected by the presence of Coulomb friction.
The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical non-equilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a net drift induced by friction. If the thermal bath is replaced by a granular gas, the well known granular ratchet effect also intervenes, becoming dominant at high collision rates. For our chosen wheel s…
We study the noise induced transport of an overdamped Brownian particle in frictional ratchet systems in the presence of external Gaussian white noise fluctuations. The analytical expressions for current and diffusion coefficient are derived and the reliability or coherence of transport are discussed by means of their ratio. We show that frictional ratchets exhibit larger coherence as compared to the flashing and rocking ratchets.
We investigate the performance of an inertial frictional ratchet in a sinusoidal potential driven by a sinusoidal external field. The dependence of the performance on the parameters of the sinusoidally varying friction, such as the mean friction coefficient and its phase difference with the potential, is studied in detail. Interestingly, under certain circumstances, the thermodynamic efficiency of the ratchet against an applied load shows a non-monotonic behavior as a function of the mean friction coefficient. Also, in the large friction ranges, the efficiency is shown to increase with increas…
Directed transport of interacting active (self-propelled)Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity firstly decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical …
Transport properties of overdamped Brownian paricles in a rocked thermal ratchet with space dependent friction coefficient is studied. By tuning the parameters, the direction of current exhibit multiple reversals, both as a function of the thermal noise strength as well as the amplitude of rocking force. Current reversals also occur under deterministic conditions and exhibits intriguing structure. All these features arise due to mutual interplay between potential asymmetry,noise, driving frequency and inhomogeneous friction.
Quantum Brownian motion in ratchet potentials is investigated by means of an approach based on a duality relation. This relation links the long-time dynamics in a tilted ratchet potential in the presence of dissipation with the one in a driven dissipative tight-binding model. The application to quantum ratchet yields a simple expression for the ratchet current in terms of the transition rates in the tight-binding system.
We show by numerical simulations that a non rotationally symmetric body, whose orientation is fixed and whose center of mass can only slide along a rectilinear guide, under the effect of inelastic collisions with a surrounding gas of particles, displays directed motion. We present a theory which explains how the lack of time reversal induced by the inelasticity of collisions can be exploited to generate a steady average drift. In the limit of an heavy ratchet, we derive an effective Langevin equation whose parameters depend on the microscopic properties of the system and obtain a fairly good q…
We study the phenomena of noise induced transport in frictional ratchet systems. For this we consider a Brownian particle moving in a space dependent frictional medium in the presence of external white noise fluctuations. To get the directed transport, unlike in other ratchet models like flashing or rocking ratchets etc., we do not require the potential experienced by the particle to be asymmetric nor do we require the external fluctuations to be correlated. We have obtained analytical expressions for current and the diffusion coefficient. We show that the frictional ratchet do not exhibit a p…
The effect of Coulomb friction is studied in the framework of collisional ratchets. It turns out that the average drift of these devices can be expressed as the combination of a term related to the lack of equipartition between the probe and the surrounding bath, and a term featuring the average frictional force. We illustrate this general result in the asymmetric Rayleigh piston, showing how Coulomb friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath. An explicit analytical expression for the average velocity of the piston is obtained in the rare co…
We present an analogy between the classic Gambler's Ruin problem and the thermally-activated dynamics in periodic Brownian ratchets. By considering each periodic unit of the ratchet as a site chain, we calculated the transition probabilities and mean first passage time for transitions between energy minima of adjacent units. We consider the specific case of Brownian ratchets driven by Markov dichotomous noise. The explicit solution for the current is derived for any arbitrary temperature, and is verified numerically by Langevin simulations. The conditions for vanishing current and current reve…
We show by numerical simulations that the presence of nonlinear velocity-dependent friction forces can induce a finite net drift in the stochastic motion of a particle in contact with an equilibrium thermal bath and in an asymmetric periodic spatial potential. In particular, we study the Kramers equation for a particle subjected to Coulomb friction, namely a constant force acting in the direction opposite to the particle's velocity. We characterize the nonequilibrium irreversible dynamics by studying the generalized fluctuation-dissipation relation for this ratchet model driven by Coulomb fric…
We study the coherence of transport of an overdamped Brownian particle in frictional ratchet system in the presence of external Gaussian white noise fluctuations. The analytical expressions for the particle velocity and diffusion coefficient are derived for this system and the reliability or coherence of transport is analysed by means of their ratio in terms of a dimensionless P$\acute{e}$clet number. We show that the coherence in the transport can be enhanced or degraded depending sensitively on the frictional profile with respect to the underlying potential.
We present a detailed study of the transport and energetics of a Brownian particle moving in a periodic potential in the presence of an adiabatic external periodic drive. The particle is considered to move in a medium with periodic space dependent friction with the same periodicity as that of the potential but with a phase lag. We obtain several results, most of them arising due to the medium being inhomogeneous and are sensitive to the phase lag. When the potential is symmetric we show that efficiency of energy transduction can be maximised as a function of noise strength or temperature. Howe…
Three, interrelated biologically-relevant examples of biased random walks are presented: (1) A model for DNA melting, modelled as DNA unzipping, which provides a way to illustrate the role of the Boltzmann factor in a venue well-known to biology and pre-medical students; (2) the activity of helicase motor proteins in unzipping double-stranded DNA, for example, at the replication fork, which is an example of a Brownian ratchet; (3) force generation by actin polymerization, which is another Brownian ratchet, and for which the force and actin-concentration dependence of the velocity of actin poly…
We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of …
Based on Brownian ratchets, a counter-intuitive phenomenon has recently emerged -- namely, that two losing games can yield, when combined, a paradoxical tendency to win. A restriction of this phenomenon is that the rules depend on the current capital of the player. Here we present new games where all the rules depend only on the history of the game and not on the capital. This new history-dependent structure significantly increases the parameter space for which the effect operates.
We propose a stochastic process wherein molecular transport is mediated by asymmetric nucleation of domains on a one-dimensional substrate. Track-driven mechanisms of molecular transport arise in biophysical applications such as Holliday junction positioning and collagenase processivity. In contrast to molecular motors that hydrolyze nucleotide triphosphates and undergo a local molecular conformational change, we show that asymmetric nucleation of hydrolysis waves on a track can also result in directed motion of an attached particle. Asymmetrically cooperative kinetics between ``hydrolyzed'' a…
We consider the motion of a overdamped Brownian particle in periodic asymmetric potential with space dependent friction coefficient. In the presence of external time periodic forcing, the system shows multiple current reversals on varying the amplitude of the external forcing and the temperature of the thermal bath. In the adiabatic regime we find a single reversal of current as a function of noise strength which can only be accounted due to the presence of space dependent friction coefficient. For very large forcing term, the current does not go to zero, instead it asymptotically tends to a l…
It is well-known that Brownian ratchets can exhibit current reversals, wherein the sign of the current switches as a function of the driving frequency. We introduce a spatial discretization of such a two-dimensional Brownian ratchet to enable spectral methods that efficiently compute those currents. These discrete-space models provide a convenient way to study the Markovian dynamics conditioned upon generating particular values of the currents. By studying such conditioned processes, we demonstrate that low-frequency negative values of current arise from typical events and high-frequency posit…
The flashing Brownian ratchet is a stochastic process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, the latter being a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. The result is directed motion. In the presence of a static homogeneous force that acts in the direction opposite that of the directed motion, there is a reduction (or even a reversal) of the directed motion effect. Such a process may be called a tilted flashing Brownian ratchet. We show how one can study this process nume…
Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this paper we review this paradox, from Brownian ratchets to the most recent studies on collective games, providing some intuitive explanations of the unexpected phenomena that we will find along the way.
Closed-loop or feedback controlled ratchets are Brownian motors that operate using information about the state of the system. For these ratchets, we compute the power output and we investigate its relation with the information used in the feedback control. We get analytical expressions for one-particle and few-particle flashing ratchets, and we find that the maximum power output has an upper bound proportional to the information. In addition, we show that the increase of the power output that results from changing the optimal open-loop ratchet to a closed-loop ratchet also has an upper bound t…
Energy-Efficient Pseudo-Ratchet for Brownian Computers through One-Dimensional Quantum Brownian Motion
Advanced ICT Research Institute, National Institute of Information and Communications Technology（先进ICT研究所，信息通信研究机构）；Department of Electrical and Electronics Engineering, Mie University（电气电子工程系，三重大学）；Department of Physics and Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University（物理学系及南部阳一郎理论与实验物理研究所（NITEP），大阪公立大学）；Center for Complex Quantum Systems, The University of Texas at Austin（复杂量子系统中心，德克萨斯大学奥斯汀分校）；Institute of Industrial Science, The University of Tokyo（工业科学研究所，东京大学）
Many forms of cell motility rely on Brownian ratchet mechanisms that involve multiple stochastic processes. We present a computational and theoretical study of the nonequilibrium statistical dynamics of such a many-body ratchet, in the specific form of a growing polymer gel that pushes a diffusing obstacle. We find that oft-neglected correlations among constituent filaments impact steady-state kinetics and significantly deplete the gel's density within molecular distances of its leading edge. These behaviors are captured quantitatively by a self-consistent theory for extreme fluctuations in fi…
We discuss two-dimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different noise intensities, or temperatures, in the transversal and longitudinal directions. The model is inspired by the famous Feynman's ratchet and pawl. Using ideas of the Fick-Jacobs approximation we derive the mean velocity of the particle, the effective diffusion coefficient, and the stationary probability density in the potential unit cell. The derived results are exact for small channel width. …
Risken's matrix continued fraction method is used to solve the Fokker-Planck equation to calculate particle current in an inertial symmetric (sinusoidal) periodic potential under the action of a constant force. The particle moves in a medium with friction coefficient also varying periodically in space as the potential but with a finite phase difference $ϕ(\ne nπ, n=0,1,2, ...)$. The algebraic sum of current with applied forces $\pm|F|$ gives the ratchet current in the adiabatic limit. Even though, the effect of frictional inhomogeneity is weak, the ratchet current shows very rich qualitative c…
We analyze the rectified motion of a Brownian particle in a confined environment. We show the emergence of strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may develop even in situations where separately the ratchet and the geometric restrictions do not give rise to particle motion. The combined rectification effects can lead to bidirectional transport depending on particle size, resulting in a new route for segregation. The reported mechanism can be used to control t…
With a model for two-dimensional (2D) Brownian rotary ratchets being capable of producing a net torque under athermal random forces, its optimization for mean angular momentum ($L$), mean angular velocity ($ω$), and efficiency ($η$) is considered. In the model, supposing that such a small ratchet system is placed in a thermal bath, the motion of the rotor in the stator is described by the Langevin dynamics of a particle in a 2D ratchet potential, which consists of a static and a time-dependent interaction between rotor and stator; for the latter, we examine a force [randomly directed d.c. fiel…
Moving against the odds with a cyclic active Brownian ratchet: current enhancement and reversal
Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；Institute for the Dynamics of Complex Systems, University of Göttingen（哥廷根大学复杂系统动力学研究所）；Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS（蒙彼利埃大学查尔斯·库隆实验室（L2C），法国国家科学研究中心）
We investigate the dynamics of quantum particles in a ratchet potential subject to an ac force field. We develop a perturbative approach for weak ratchet potentials and force fields. Within this approach, we obtain an analytic description of dc current rectification and current reversals. Transport characteristics for various limiting cases -- such as the classical limit, limit of high or low frequencies, and/or high temperatures -- are derived explicitly. To gain insight into the intricate dependence of the rectified current on the relevant parameters, we identify characteristic scales and ob…
Within the context of the Brownian ratchet model, a molecular rotary system was studied that can perform unidirectional rotations induced by linearly polarized ac fields, and produce positive work under loads. The model is based on the Langevin equation for a particle in a two-dimensional (2D) three-tooth ratchet potential of threefold symmetry. The performance of the system is characterized by the coercive torque, i.e., the strength of the load competing with the torque induced by the ac driving field, and the energy efficiency in force conversion from the driving field to torque. We propose …
We develop an exactly-solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations we obtain the steady-state probabilities. Generally the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space we find the null-curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null-curve, an additional source of external random noise …
We study the mean velocity and diffusion constant in three related models of molecular Brownian ratchets. Brownian ratchets can be used to describe translocation of biopolymers like DNA through nanopores in cells in the presence of chaperones on the trans side of the pore. Chaperones can bind to the polymer and prevent it from sliding back through the pore. First, we study a simple model that describes the translocation in terms of an asymmetric random walk. It serves as an introductory example but already captures the main features of a Brownian ratchet. We then provide an analytical expressi…
We study a feedback control version of the flashing Brownian ratchet, in which the application of the flashing potential depends on the state of the particles to be controlled. Taking the view that the ratchet acts as a Maxwell's demon, we study the relationship that exists between the performance of the demon as a rectifier of random motion and the amount of information gathered by the demon through measurements. In the context of a simple measurement model, we derive analytic expressions for the flux induced by the feedback ratchet when acting on one particle and a few particles, and compare…
The study of Brownian ratchets has taught how time-periodic driving supports a time-periodic steady state that generates nonequilibrium transport. When a single particle is transported in one dimension, it is possible to rationalize the current in terms of the potential, but experimental efforts have ventured beyond that single-body case to systems with many interacting carriers. Working with a lattice model of volume-excluding particles in one dimension, we analyze the impact of interactions on a flashing ratchet's current. To surmount the many-body problem, we employ the time-dependent varia…
We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e. a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force which takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum and finally it mono…
Living cells are known to generate non-Gaussian active fluctuations significantly larger than thermal fluctuations owing to various active processes. Understanding the effect of these active fluctuations on various physicochemical processes, such as the transport of molecular motors, is a fundamental problem in nonequilibrium physics. Therefore, we experimentally and numerically study an active Brownian ratchet comprising a colloidal particle in an optically generated asymmetric periodic potential driven by non-Gaussian noise having finite-amplitude active bursts, each arriving at random and d…
The transport of interacting Brownian particles in a periodic asymmetric (ratchet) substrate is studied numerically. In a zero-temperature regime, the system behaves as a reversible step motor, undergoing multiple sign reversals of the particle current as any of the following parameters are varied: the pinning potential parameters, the particle occupation number, and the excitation amplitude. The reversals are induced by successive changes in the symmetry of the effective ratchet potential produced by the substrate and the fraction of particles which are effectively pinned. At high temperature…
In recent single-particle tracking (SPT) measurements on {\it Listeria monocytogenes} motility {\em in vitro}, the actin-based stochastic dynamics of the bacterium movement is analyzed statistically (Kuo and McGrath, 2000). The mean-square displacement (MSD) of the detrended trajectory exhibit a linear behavior; it has been suggested that a corresponding analysis for the Brownian ratchet model (Peskin, Odell, & Oster, 1993) leads to a non-monotonic MSD. A simplified version of the Brownian ratchet, when its motion is limited by the bacterium movement, is proposed and analyzed stochastically. A…
We study subdiffusive ratchet transport in periodically and randomly flashing potentials. Central Brownian particle is elastically coupled to surrounding auxiliary Brownian quasi-particles which account for the influence of viscoelastic environment. Similar to standard dynamical modeling of Brownian motion, the external force influences only the motion of central particle not affecting directly the environmental degrees of freedom (see video). Just a handful of auxiliary Brownian particles suffice to model subdiffusion over many temporal decades. Time-modulation of the potential violates the s…
Transport of Brownian particles interacting with each other via the Morse potential is investigated in the presence of an ac driving force applied locally at one end of the chain. By using numerical simulations, we find that the system can behave as a particle diode for both overdamped and underdamped cases. For low frequencies, the transport from the free end to the ac acting end is prohibited, while the transport from the ac acting end to the free end is permitted. However, the polarity of the particle diode will reverse for medium frequencies. There exists an optimal value of the well depth…
We construct and exactly solve a model of an extended Brownian ratchet. The model comprises an arbitrary number of heterogeneous, growing and shrinking filaments which together move a rigid membrane by a ratchet mechanism. The model draws parallels with the dynamics of actin filament networks at the leading edge of the cell. In the model, the filaments grow and contract stochastically. The model also includes forces which derive from a potential dependent on the separation between the filaments and the membrane. These forces serve to attract the filaments to the membrane or generate a surface …
We study the rectified transport of underdamped active noninteracting particles in an asymmetric periodic potential. It is found that the ratchet effect of active noninteracting particles occurs in a single direction (along the easy direction of the substrate asymmetry) in the overdamped limit. However, when the inertia is considered, it is possible to observe reversals of the ratchet effect, where the motion is along the hard direction of the substrate asymmetry. By changing the friction coefficient or the self-propulsion force, the average velocity can change its direction several times. The…
We study a general model of granular Brownian ratchet consisting of an asymmetric object moving on a line and surrounded by a two-dimensional granular gas, which in turn is coupled to an external random driving force. We discuss the two resulting Boltzmann equations describing the gas and the object in the dilute limit and obtain a closed system for the first few moments of the system velocity distributions. Predictions for the net ratchet drift, the variance of its velocity fluctuations and the transition rates in the Markovian limit, are compared to numerical simulations and a fair agreement…
Motivated by a biased diffusion of molecular motors with the bias dependent on the state of the substrate, we investigate a random walk on a one-dimensional lattice that contains weak links (called "bridges'') which are affected by the walker. Namely, a bridge is destroyed with probability p when the walker crosses it; the walker is not allowed to cross it again and this leads to a directed motion. The velocity of the walker is determined analytically for equidistant bridges. The special case of p=1 is more tractable -- both the velocity and the diffusion constant are calculated for uncorrelat…
Brownian motors, or ratchets, are devices which "rectify" Brownian motion, i.e. they can generate a current of particles out of unbiased fluctuations. The ratchet effect is a very general phenomenon which applies to a wide range of physical systems, and indeed ratchets have been realized with a variety of solid state devices, with optical trap setups as well as with synthetic molecules and granular gases. The present article reviews recent experimental realizations of ac driven ratchets with cold atoms in driven optical lattices. This is quite an unusual system for a Brownian motor as there is…
Bartussek, Hanggi and Kissner studied a rocking ratchet system, in which a Brownian particle is subject to an asymmetric periodic potential together with an oscillating force, and found that the direction of the macroscopic current can be reversed by changing the parameter values characterizing the model [Europhys. Lett., 28 (1994) 459]. In this letter, we apply their ratchet theory to a rotary motor-protein, F1-ATPase. In this work, we construct a model of a rocking ratchet in which F1-ATPase rotates not as a result of ATP hydrolysis but through the influence of an oscillating force. We then …
We consider thermal ratchets modeled by overdamped Brownian motion in a spatially periodic potential with a tilting process, both unbiased on average. We investigate the impact of the introduction of roughness in the potential profile, over the flux and efficiency of the ratchet. Both amplitude and wavelength that characterize roughness are varied. We show that depending on the ratchet parameters, rugosity can either spoil or enhance the ratchet performance.
The efficiency of different types of Brownian motors is calculated analytically and numerically. We find that motors based on flashing ratchets present a low efficiency and an unavoidable entropy production. On the other hand, a certain class of motors based on adiabatically changing potentials, named reversible ratchets, exhibit a higher efficiency and the entropy production can be arbitrarily reduced.
By using the Kirkwood formula, the friction coefficient of a solvated Brownian particle is determined from the integration on time of the autocorrelation function of the force that the solvent exerts on this particle. Extensive molecular dynamics simulations show that above a definite size of the studied systems the value of the integral defining the friction coefficient goes to a quasi constant value (a plateau) when the upper bound on time increases. The minimal value of the system size where the integral exhibits this asymptotic behavior, rises with the Brownian particle size. From the plat…
An optical model of classical photons propagating through array of many beam splitters is developed to give a physical analogy of Parrondo's game and Parrondo-Harmer-Abbott game. We showed both the two games are reasonable game without so-called game paradox and they are essentially the same. We designed the games with long-term memory on loop lattice and history-entangled game. The strong correlation between nearest two rounds of game can make the combination of two losing game win, lose or oscillate between win and loss. The periodic potential in Brownian ratchet is analogous to a long chain…
Inspired by the flashing ratchet, Parrondo's game presents an apparently paradoxical situation. Parrondo's game consists of two individual games, game A and game B. Game A is a slightly losing coin-tossing game. Game B has two coins, with an integer parameter $M$. If the current cumulative capital (in discrete unit) is a multiple of $M$, an unfavorable coin $p_b$ is used, otherwise a favorable $p_g$ coin is used. Paradoxically, combination of game A and game B could lead to a winning game, which is the Parrondo effect. We extend the original Parrondo's game to include the possibility of $M$ be…
Under rapid undercooling, glass forming liquids freeze in an amorphous state that can equilibrate only on enormously long time-scales, This is the characteristic sign of aging, which has been observed in a wide range of systems. Brownian ratchet is a widely studied system that exhibits many types of anomalous dynamical behavior. We have investigated the possibility of aging in the collective motion of Brownian particles in a periodic ratchet potential with quenched disorder. We find that when a slowly growing fraction of particles are trapped for long time, the collective movement tends to bec…
This work puts forward a generalization of the well-known rocking Markovian Brownian ratchets to the realm of antipersistent non-Markovian subdiffusion in viscoelastic media. A periodically forced subdiffusion in a parity-broken ratchet potential is considered within the non-Markovian generalized Langevin equation (GLE) description with a power-law memory kernel $η(t)\propto t^{-α}$ ($0<α<1$). It is shown that subdiffusive rectification currents, defined through the mean displacement and subvelocity $v_α$, $<δx(t)>\sim v_α t^α/ Γ(1+α)$, emerge asymptotically due to the breaking of the detailed…
We present a generic formalism to describe Brownian motion of particles with intrinsic asymmetry and give predictions for the drift behavior in unbiased time-dependent force fields. Our findings are supported by molecular dynamics simulations.
We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-i…
Ratchet effects can arise for single or collectively interacting Brownian particles on an asymmetric substrate when a net dc transport is produced by an externally applied ac driving force or by periodically flashing the substrate. Recently, a new class of active ratchet systems has been realized through the use of active matter, which are self-propelled units that can be biological or non-biological in nature. When active materials such as swimming bacteria interact with an asymmetric substrate, a net dc directed motion can arise even without external driving, opening a wealth of possibilitie…
The present work studies a non-Markovian forced thermal ratchet model on an asymmetric periodic potential. The Brownian dynamics is described by a generalized Langevin equation with an Ornstein-Uhlenbeck-type friction memory kernel. We show that for the case of a time-dependent driving force, also in the form of an Ornstein-Uhlenbeck-like process, an exact expression of the probability current can be derived. We also obtain the behavior of the particle's average rate of flow as a function of the external amplitude force and of the bath temperature when the driving force behaves as a square wav…
