Feedback control of two-headed Brownian motors in flashing ratchet potential

We presented a detailed investigation on the movement of two-headed Brownian motors in an asymmetric potential under a feedback control. By numerical simulations the direct current is obtained. The current is periodic in the initial length of spring. There is an optimal value of the spring constant. And the dependence of the current on the opposing force is reversed. Then we found that when the change of the temperature and the opposing force have optimal values, the Brownian motors can also obtain the optimal efficiency.

Directed transport of coupled Brownian motors in a two-dimensional traveling-wave potential

Considering an elastically coupled Brownian motors system in a two-dimensional traveling-wave potential, we investigate the effects of the angular frequency of the traveling wave, wavelength, coupling strength, free length of the spring, and the noise intensity on the current of the system. It is found that the traveling wave is the essential condition of the directed transport. The current is dominated by the traveling wave and varies nonmonotonically with both the angular frequency and the wavelength. At an optimal angular frequency or wavelength, the current can be optimized. The coupling strength and the free length of the spring can locally modulate the current, especially at small angular frequencies. Moreover, the current decreases rapidly with the increase of the noise intensity, indicating the interference effect of noise on the directed transport.

Collective Transport of Coupled Brownian Motors with Low Randomness

The transport properties of coupled Brownian motors in rocking ratchet are investigated via solving Langevin equation. By means of velocity, diffusion coefficient, and their ratio （Peclet number）, different features from a single particle have been found. In the regime of low-to-moderate D, the average velocity of elastically coupled Brownian motors is larger than that of a single Brownian particles; the Peclet number of elastically coupled Brownian motors is peaked functions of intensity of noise D but the Peclet number of a single Brownian motor decreases monotonously with the increase of a single Brownian motor. The results exhibit an interesting cooperative behavior between coupled particles subjected to a rocking force, which can generate directed transport with low randomness or high transport coherence in symmetrical periodic potential.

Double-temperature ratchet model and current reversal of coupled Brownian motors

On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal tile dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional trans- port of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asym- metric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Di- rected transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.

Symmetric Brownian motor subjected to Lévy noise

In the past few years,attention has mainly been focused on the symmetric Brownian motor(BM)with Gaussian noises,whose current and energy conversion efficiency are very low.Here,we investigate the operating performance of the symmetric BM subjected to Lévy noise.Through numerical simulations,it is found that the operating performance of the motor can be greatly improved in asymmetric Lévy noise.Without any load,the Lévy noises with smaller stable indexes can let the motor give rise to a much greater current.With a load,the energy conversion efficiency of the motor can be enhanced by adjusting the stable indexes of the Lévy noises with symmetry breaking.The results of this research are of great significance for opening up BM’s intrinsic physical mechanism and promoting the development of nanotechnology.

Two-dimensional model of elastically coupled molecular motors

A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins. Extensive Langevin simulations of the model are performed. We discuss the dependences of motion and efficiency on the model parameters, including the external force and the temperature. A good qualitative agreement with the expected behavior is observed.

A composite micromotor driven by self-thermophoresis and Brownian rectification

Brownian motors and self-phoretic microswimmers are two typical micromotors,for which thermal fluctuations play different roles.Brownian motors utilize thermal noise to acquire unidirectional motion,while thermal fluctuations randomize the self-propulsion of self-phoretic microswimmers.Here we perform mesoscale simulations to study a composite micromotor composed of a self-thermophoretic Janus particle under a time-modulated external ratchet potential.The composite motor exhibits a unidirectional transport,whose direction can be reversed by tuning the modulation frequency of the external potential.The maximum transport capability is close to the superposition of the drift speed of the pure Brownian motor and the self-propelling speed of the pure self-thermophoretic particle.Moreover,the hydrodynamic effect influences the orientation of the Janus particle in the ratched potential,hence also the performance of the composite motor.Our work thus provides an enlightening attempt to actively exploit inevitable thermal fluctuations in the implementation of the self-phoretic microswimmers.

The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor

Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle＇s motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.

Dipole—Dipole Interaction and the Directional Motion of Brownian

The electric field of the microtubule is calculated according to its dipole distribution. The conformational change of a molecular motor is described by the rotation of a dipole which interacts with the microtubule. The numerical simulation for the particle current shows that this interaction helps to produce a directional motion along the microtubule. And the average displacement executes step changes that resemble the experimental result for kinesin motors.

Current and efficiency of Brownian particles under oscillating forces in entropic barriers

In this study, considering the temporarily unbiased force and different forms of oscillating forces, we investigate the current and efficiency of Brownian particles in an entropic tube structure and present the numerically obtained results. We show that different force forms give rise to different current and efficiency profiles in different optimized parameter intervals. We find that an unbiased oscillating force and an unbiased temporal force lead to the current and efficiency, which are dependent on these parameters. We also observe that the current and efficiency caused by temporal and different oscillating forces have maximum and minimum values in different parameter intervals. We conclude that the current or efficiency can be controlled dynamically by adjusting the parameters of entropic barriers and applied force.

Ratchet motion and current motors in pulsating reversal of coupled Brownian symmetric potentials

In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two particles can induce symmetry breaking and consequently collective directed motion. Moreover, the direction of motion can be reversed under certain conditions. The dependence of directed current on various parameters is systematically studied, reverse motion can be achieved by modulating the coupling free length and the phase shift of tile pulsating potential. The dynamical mechanism of these transport properties is understood in terms of the effective-potential theory and the space-time transformation invariance. The directed transport of coupled Brownian motors can be maniplflated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.

Average Cycle Period in Asymmetrical Flashing Ratchet

The directed motion of a Brownian particle in a Bashing potential with various transition probabilities and waiting times in one of two states is studied. An expression for the average cycle period is proposed and the steady current J of the particle is calculated via Langevin simulation. The results show that the optimal cycle period (Tm), which takes the maximum of J, is shifted to a small value when the transition probability A from the potential on to the potential off decreases, the maximal current appears in the case of the average waiting time in the potential on being longer than in the potential off, and the direction of current depends on the ratio of the average times waiting in two states.

Symmetry properties of fluctuations in an actively driven rotor

We investigate rotational dynamics of an actively driven rotor through experiments and numerical simulations. While probability density distributions of rotor angular velocity are strongly non-Gaussian, relative probabilities of observing rotation in opposite directions are shown to be linearly related to the angular velocity magnitude. We construct a stochastic model to describe transitions between different states from rotor angular velocity data and use the stochastic model to show that symmetry properties in probability density distributions are related to the detailed fluctuation relation(FR) of entropy productions.

Self-powered macroscopic Brownian motion of spontaneously running liquid metal motors

We disclosed the interiorly driven macroscopic Brownian motion behavior of self-powered liquid metal motors. Such tiny motors in millimeter scale move randomly at a velocity magnitude of centimeters per second in aqueous alkaline solution, well resembling the classical Brownian motion. However, unlike the existing phenomena, where the particle motions were caused by collisions from the surrounding molecules, the current random liquid metal motions are internally enabled and self-powered, along with the colliding among neighboring motors, the substrate and the surrounding electrolyte molecules. Through uniformly dissolving only 1% （mass percentage） A1 into GaInl0, many tiny motors can be quickly fabricated and activated to take the Brownian-like random motions. Further, we introduced an experimental approach of using optical image contrast, which works just like the Wilson cloud chamber, to distinctively indicate the motor trajectory resulted from the generated hydrogen gas stream. A series of unusual complicated multi-phase fluid mechanics phenomena were observed. It was also identified that the main driving factor of the motors comes from the H2 bubbles generated at the bottom of these tiny motors, which is different from the large size self-fueled liquid metal machine. Several typical mechanisms for such unconventional Brownian-like motion phenomena were preliminarily interpreted.

Current and efficiency optimization under oscillating forces in entropic barriers

The transport of externally overdriven particles confined in entropic barriers is investigated under various types of oscillating and temporal forces.Temperature,load,and amplitude dependence of the particle current and energy conversion efficiency are investigated in three dimensions.For oscillating forces,the optimized temperature–load,amplitude–temperature,and amplitude–load intervals are determined when fixing the amplitude,load,and temperature,respectively.By using three-dimensional plots rather than two-dimensional ones,it is clearly shown that oscillating forces provide more efficiency compared with a temporal one in specified optimized parameter regions.Furthermore,the dependency of efficiency to the angle between the unbiased driving force and a constant force is investigated and an asymmetric angular dependence is found for all types of forces.Finally,it is shown that oscillating forces with a high amplitude and under a moderate load lead to higher efficiencies than a temporal force at both low and high temperatures for the entire range of contact angle.

Behaviour of the current in a two-dimensional Bttiker Landauer motor with entropic barriers

The behaviour of the current in a two-dimensional Biittiker-Landauer motor, which is a position-dependent temperature-driven Brownian motor, is investigated in the presence of entropic and energy barriers. It is found that the motion of the Brownian particles is influenced by the shape of the channel. The existence of an entropic barrier can cause an asymmetric current as the flatness ratio of the shape varies. There exists an optimized flatness ratio （nonzero） at which the current reaches its maximum value.

Rotation-translation coupling of a double-headed Brownian motor in a traveling-wave potential

Considering a double-headed Brownian motor moving with both translational and rotational degrees of freedom,we investigate the directed transport properties of the system in a traveling-wave potential.It is found that the traveling wave provides the essential condition of the directed transport for the system,and at an appropriate angular frequency,the positive current can be optimized.A general current reversal appears by modulating the angular frequency of the traveling wave,noise intensity,external driving force and the rod length.By transforming the dynamical equation in traveling-wave potential into that in a tilted potential,the mechanism of current reversal is analyzed.For both cases of Gaussian and Lévy noises,the currents show similar dependence on the parameters.Moreover,the current in the tilted potential shows a typical stochastic resonance effect.The external driving force has also a resonance-like effect on the current in the tilted potential.But the current in the traveling-wave potential exhibits the reverse behaviors of that in the tilted potential.Besides,the currents obviously depend on the stability index of the Lévy noise under certain conditions.