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.

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.

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.

On the Feynman Ratchet and the Brownian Motor

We study the Brownian ratchet conditions starting with Feynman’s proposal. We show that this proposal is incomplete, and is in fact non-workable. We give the correct model for this ratchet.

Hydrodynamic Interactions Introduce Differences in the Behaviour of a Ratchet Dimer Brownian Motor

We use the Brownian dynamics with hydrodynamic interactions simulation in order to describe the movement of an elastically coupled dimer Brownian motor in a ratchet potential. The only external forces considered in our system were the load, the random thermal noise and an unbiased thermal fluctuation. We observe differences in the dynamic behaviour if hydrodynamic interactions are considered as compared with the case without them. In conclusion, hydrodynamic interactions influence substantially the dynamics of a ratchet dimer Brownian motor;consequently they have to be considered in any theory where the molecular motors are in a liquid medium.

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.

二维Brownianmotor工作模型

研究了 Brownian(布朗 ) motor在二维耦合的非对称性周期势中同时受热噪声和外部非平衡涨落驱动下的定向输运 ,讨论了耦合对流行为的影响 .发现在二维摇摆棘轮中 ,流和效率的极大值出现在有限温度 ;而在二维关联棘轮中 ,流的极大值比一维的大

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.

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.

Coulomb Friction Driving Brownian Motors

We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation(linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a "collisional noise", that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein–Kramers equation. In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced.

Symmetric linear potential and imperfect Brownian ratchet in molecular motor function

Biomolecular motors are tiny engines that transport materials at the microscopic level within biological cells. In recent years, Elston and Peskin et al have investigated the effect of the elastic properties of the tether that connects the motor to its cargo at the speed of the motor. In this paper we extend their work and present a tether in the form of symmetric linear potential. Our results show that when the driving mechanism is an imperfect Brownian ratchet, the average speed decreases as the stiffness of the tether increases in the limit of large motor diffusion coefficient, which is similar to the results of Elston and Peskin. However, a threshold for the stiffness of the tether connecting the motor to its cargo is found in our model. Only when the tether is stiffer than the threshold can the motor and its cargo function co-operatively, otherwise, the motor and its cargo depart from each other. This result is more realistic than that of the spring model of Elston and Peskin.

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.

三热源热布朗热变换器的生态学性能优化

基于[火用]分析的生态学函数,研究了三热源热布朗热变换器循环的生态学性能。导出了生态学函数的解析式,并研究了循环在最大生态学函数目标下的供热率和供热系数特性。通过与供热率目标下的性能进行比较,说明了生态学函数作为优化目标时三热源热布朗热变换器的性能优势。结果表明:通过调整势垒高度和外力,可使三热源热布朗热变换器工作在最大生态学函数目标下。当以生态学函数代替供热率作为优化目标时,三热源热布朗热变换器可以以牺牲较小的供热率为代价,换取供热系数的较大提升。

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.

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.

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.

A simplified tether model for molecular motor transporting cargo

Molecular motors are proteins or protein complexes which function as transporting engines in biological cells. This paper models the tether between motor and its cargo as a symmetric linear potential. Different from Elston and Peskin＇s work for which performance of the system was discussed only in some limiting cases, this study produces analytic solutions of the problem for general cases by simplifying the transport system into two physical states, which makes it possible to discuss the dynamics of the motor--cargo system in detail. It turns out that the tether strength between motor and cargo should be greater than a threshold or the motor will fail to transport the cargo, which was not discussed by former researchers yet. Value of the threshold depends on the diffusion coefficients of cargo and motor and also on the strength of the Brownian ratchets dragging the system. The threshold approaches a finite constant when the strength of the ratchet tends to infinity.

Brownian ratchet mechanism of translocation in T7 RNA polymerase facilitated by a post-translocation energy bias arising from the conformational change of the enzyme

T7 RNA polymerase can transcribe DNA to RNA by translocating along the DNA. Structural studies suggest that the pivoting rotation of the O helix in the fingers domain may drive the movement of the O helix C-terminal Tyr639 from pre- to post-translocation positions. In a series of all-atom molecular dynamics simulations, we show that the movement of Tyr639 is not tightly coupled to the rotation of the O helix, and that the two processes are only weakly dependent on each other. We also show that the internal potential of the enzyme itself generates a small difference in free energy （△E） between the post- and pre-translocation positions of Tyr639. The calculated value of △E is consistent with that obtained from single-molecule experimental data. These findings lend support to a model in which the translocation takes place via a Brownian ratchet mechanism, with the small free energy bias △E arising from the conformational change of the enzyme itself.