Directed transport of coupled systems in symmetric periodic potentials

In this paper, we discuss the damped unidirectional motions of a coupled lattice in a periodic potential. Each particle in the lattice is subject to a time-periodic ac force. Our studies reveal that a directed transport process can be observed when the ac forces acting on the coupled lattice have a phase shift (mismatch). This directed motion is a collaboration of the coupling, the substrate potential, and the periodic force, which are all symmetric. The absence of any one of these three factors will not give rise to a directed current. We discuss the complex relations between the directed current and parameters in the system. Results in this paper can be accomplished in experiments. Moreover,our results can be generalized to the studies of directed transport processes in more complicated spatially extended systems.     

Collective directed transport of symmetrically coupled lattices in symmetric periodic potentials

A mechanism responsible for the directed transport of symmetrically coupled lattices in a symmetric periodic potential is proposed. Under the action of an external wave that breaks the spatiotemporal symmetry and introduces inhomogeneities of the lattice, a net unidirectional current can be observed, originating from a collaboration of the lattice (periodic potential and mutual interactions) and the wave (amplitude, frequency, and phase shifts). Mode-locking induced resonant steps are observed and predicted. The directed transport can be optimized and furthermore controlled by suitably adjusting the parameters of the system.     

时间非对称外力驱动分数阶布朗马达的定向输运

本文研究了周期对称势中时间非对称外力驱动的布朗粒子输运现象, 建立了分数阶布朗马达输运模型. 其中外力是零均值的, 而分数阶阶数则刻画了客观环境的非均匀性程度. 通过将模型离散化进行数值模拟, 讨论了分数阶阶数、系统参量和外部参量与定向流之间的依赖关系. 研究表明, 即使没有倾斜势场的作用, 时间非对称外力也可以诱导系统产生定向输运; 输运速度随分数阶阶数的增大而单调递增; 当阶数固定时, 系统的输运速度会随着势垒高度、噪声强度非单调变化, 表现出广义随机共振现象. 分析指出, 分数阶郎之万方程所刻画的输运现象是在整数阶模型基础上的一个推广, 进而为输运现象提供了一个可能更为真实的模型.     

Biased Motion in a Symmetric Periodic Potential by Breaking Temporal Symmetry

Unidirectional transport of a particle in a spatially periodic and symmetric potential under a periodic force with broken temporal symmetry is studied.With a collaboration of the potential field and the asymmetric ac force,a dc current can be observed.Resonant current steps are found for a finite period of the ac force.A phase diagram of these resonant steps is given.Stochastic-resonance-like directional transport induced by thermal nonises is revealed.     

Investigation on a temporal asymmetric oscillating temperature ratchet

We study the directed motion of Brownian particles in a periodic potential due to a periodically oscillating temperature of the thermal environment. The steady average velocity of Brownian particles is evaluated by using the Langevin simulation. The features of current are discussed in detail. The results obtained here show that the periodically oscillating temperature produces a directed transport of the particles in a ratchet system and that through changing some parameters of this system, the magnitude and direction of transport can be controlled. Moreover, it is found that the temporal symmetric temperature oscillation may not be the best choice and the mode of temperature oscillation can be optimized.     

Rotational effect in two-dimensional cooperative directed transport

In this review we investigate the rotation effect in the motion of coupled dimer in a two-dimensional asymmetric periodic potential. Free rotation does not generate directed transport in translational direction, while we find it plays an critical role in the motors motility when the dimer moves under the effect of asymmetry ratchet potential. In the presence of external force, we study the relation between the average current and the force numerically and theoretically. The numerical results show that only appropriate driving force could produce nonzero current and there are current transitions when the force is large enough. An analysis of stability analysis of limit cycles is applied to explain the occurrence of these transitions. Moreover, we numerically simulate the transport of this coupled dimer driven by the random fluctuations in the rotational direction. The existence of noise smooths the current transitions induced by the driving force and the resonance-like peaks which depend on the rod length emerge in small noise strength. Thanks to the noise in the rotational direction, autonomous motion emerges without the external force and large noise could make the current reversal happen. Eventually, the new mechanism to generate directed transport by the rotation is studied.     

二维耦合定向输运模型研究

建立了外部驱动力及噪声作用下的二维耦合定向输运模型, 其中的一个维度上为周期性分段棘齿势, 另一垂直维度上为周期性对称非棘齿势, 外部驱动力及噪声加在周期对称非棘齿势方向上, 而棘齿势方向不加任何驱动, 采用非平衡统计及非线性动力学理论研究了过阻尼情况下耦合系统在两个维度上的输运性质. 结果显示, 棘齿势与非棘齿势方向均可产生定向输运, 其中棘齿势方向的系统平均速度对耦合强度、噪声强度、驱动力强度及粒子数目均有明显的依赖性, 合适的耦合强度、噪声强度、驱动力强度或粒子数目下均可产生最大输运速度. 而非棘齿势方向的系统平均速度受非棘齿势势垒高度影响显著, 但随耦合强度、驱动力强度、驱动力初相位差及粒子数目的变化均出现波动现象, 表现出平均速度对这些参量的依赖性较弱.     

Slowly rocking symmetric, spatially periodic Hamiltonians: The role of escape and the emergence of giant transient directed transport

The nonintegrable Hamiltonian dynamics of particles placed in a symmetric, spatially periodic potential and subjected to a periodically varying field is explored. Such systems can exhibit a rich diversity of unusual transport features. In particular, depending on the setting of the initial phase of the drive, the possibility of a giant transient directed transport in a symmetric, space-periodic potential when driven with an adiabatically varying field arises. Here, we study the escape scenario and corresponding mean escape times of particles from a trapping region with the subsequent generation of a transient directed flow of an ensemble of particles. It is shown that for adiabatically slow inclination modulations the unidirectional flow proceeds over giant distances. The direction of escape and, hence, of the flow is entirely governed whether the periodic force, modulating the inclination of the potential, starts out initially positive or negative. In the phase space, this transient directed flow is associated with a long-lasting motion taking place within ballistic channels contained in the non-uniform chaotic layer. We demonstrate that for adiabatic modulations all escaping particles move ballistically into the same direction, leading to a giant directed current.     

Current reversal and mass separation of inertial Brownian motors in a two-noise ratchet

Transport of an inertial Brownian motor moving in an asymmetric periodic potential driven by an external force and correlated noises is investigated. Using the numerical algorithm, the asymptotic mean velocity (AMV) for characterizing directed transport is obtained. The effects of the external driving force f and the correlation λ between the two noises on the AMV are discussed. The results manifest: (1) the external driving force and the correlation between the two noises can lead to the phenomena like current reversal. (2) The competitions among the external driving force and the correlation between the two noises are necessary for current reversal, i.e., fλ>0. (3) Different directions of transport are found for different masses of the Brownian particles under the condition fλ>0. Therefore a theoretical study is suggested for separating Brownian particles according to their different masses in the ratchet system.     

非对称耦合粒子链在棘齿势中的确定性定向输运

针对不受外力和噪声驱动的非对称耦合粒子链在棘齿势中的运动, 建立了相应的数学模型, 并对其确定性定向输运现象进行研究. 仿真结果表明: 在粒子间的非对称耦合和具有空间反演非对称的棘齿势的共同作用下, 粒子链能够产生定向输运现象, 并在适当参数条件下还能形成反向定向流; 粒子链平均速度关于耦合系数、势垒高度、弹簧自由长度等系统参数分别都存在广义共振现象, 即存在最佳参数使得定向输运速度达到最大; 在其他参数固定的情况下, 粒子链平均速度关于弹簧自由长度变化的曲线具有近似反对称的特点, 并存在广义多峰共振现象.     

Anomalous transport and diffusion phenomena induced by biharmonic forces in deformable potential systems

We study transport properties of an inertial Brownian motor which moves in a deformable Remoissenet-Peyrad periodic potential and is subjected to both a static bias force and time periodic driving biharmonic force. By modifying the shape of the potential, the anomalous transport is identified for a particular set of the system parameters. For a particular potential shape, the mean velocity of a particle is modified by going from negative to positive values according to the external bias force. These features also depend on both the biharmonic parameter and the phase-lag of two signals. A remarkable transition of the negative velocity depending on the shape of the potential is observed. We also focus on the efficiency of the motor and discuss velocity fluctuation. In addition, within selected system parameters, different types of diffusion particle such as subdiffusion, superdiffusion, normal diffusion, ballistic diffusion, hyperdiffusion and dispersionless transport phenomena are generated in the system.     

Dipole-induced vortex ratchets in superconducting films with arrays of micromagnets

We investigate the transport properties of superconducting films with periodic arrays of in-plane magnetized micromagnets. Two different magnetic textures are studied: a square array of magnetic bars and a close-packed array of triangular microrings. As confirmed by magnetic force microscopy imaging, the magnetic state of both systems can be adjusted to produce arrays of almost pointlike magnetic dipoles. By carrying out transport measurements with ac drive, we observed experimentally a recently predicted ratchet effect induced by the interaction between superconducting vortices and the magnetic dipoles. Moreover, we find that these magnetic textures produce vortex-antivortex patterns, which have a crucial role in the transport properties of this hybrid system.     

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 the 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 transport 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 asymmetric 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. Directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.     

Efficiency and current in a correlated ratchet

We present a detailed study of the transport and the efficiency of a ratchet system in a periodic potential in the presence of correlated noises. The current and the efficiency of the system are investigated. It is found that, when the potential is spatially symmetric, the correlation between the two noises can induce a net transport. The efficiency shows many interesting features as a function of the applied force, the noise intensity, the external load, etc. The efficiency can be maximized as a function of noise intensity (or temperature), which shows that the thermal fluctuation can facilitate the efficiency of energy transformation.     

二维势场中弹性耦合粒子的定向输运研究

建立了二维势场中弹性耦合粒子的输运模型, 其中一维上加交流驱动及噪声, 另一维上不加驱动及噪声, 分析讨论了过阻尼情形下系统和外部参量对定向流的影响. 结果表明, 粒子可以通过相互耦合使一个方向上输入的驱动能量转化到垂直方向上, 从而使无能量输入的方向产生定向流. 适当的弹簧自由长度及耦合强度可以使定向流达到极值, 特别是当耦合强度及噪声强度固定时, 定向流会随弹簧自由长度的变化而振荡, 出现多峰现象. 研究还发现, 定向流随噪声强度的变化出现随机共振现象. 当产生定向流方向上的势的不对称度达到一定程度时会出现流反转现象. 关键词： 弹性耦合 定向输运 随机共振 流反转     

Directed transient long-range transport in a slowly driven Hamiltonian system of interacting particles

We study the Hamiltonian dynamics of a one-dimensional chain of linearly coupled particles in a spatially periodic potential which is subjected to a time-periodic mono-frequency external field. The average over time and space of the related force vanishes and hence, the system is effectively without bias which excludes any ratchet effect. We pay special attention to the escape of the entire chain when initially all of its units are distributed in a potential well. Moreover for an escaping chain we explore the possibility of the successive generation of a directed flow based on large accelerations. We find that for adiabatic slope-modulations due to the ac-field transient long-range transport dynamics arises whose direction is governed by the initial phase of the modulation. Most strikingly, that for the driven many particle Hamiltonian system directed collective motion is observed provides evidence for the existence of families of transporting invariant tori confining orbits in ballistic channels in the high-dimensional phase spaces.     

过阻尼布朗棘轮的斯托克斯效率研究

根据随机能量理论解析得到阻尼环境中布朗粒子的概率流和斯托克斯效率,并进一步研究布朗粒子的输运性能.详细讨论了空间的不对称性、外偏置力及外势结构等对棘轮定向输运的影响.研究发现,合适的外偏置力能使棘轮的定向输运达到最强.通过调节外势的不对称性可使棘轮中粒子的运动反向,当选择合适的空间不对称性时布朗粒子的反向输运可获得最强.此外,一定条件下合适的外势高度也能增强棘轮输运,且能使粒子克服黏滞阻力的斯托克斯效率达到最大.所得结论能够启发实验上设计合适的外势及外偏置来优化布朗棘轮的定向输运性能,并为生物纳米器件的研制提供一定的理论参考.     

Cooperative dynamics of coupled motor–cargoes system with stochastic interactions in the crowded environment

In this study, we investigate the cooperative transport behaviors of coupled motor–cargoes system, in which multiple passive cargoes stochastically interact with one active Brownian motor. The environment with stochastic interactions is characterized by the concentration (reflecting the cargo’s number in unit volume) and switching rate (reflecting the interacting stability between motor and cargoes), based on which the stationary multiple-state process can be employed to describe the fluctuating-cargo state in the coupled system. By analyzing the average probability current of decoupled system in the thermodynamic limit, we effectively study the possibility of cooperative transport through stochastic cargoes to behave rich dynamical behaviors, including the directed current, current reversal, stochastic resonance (SR) and stochastic inhibition (SI), inverse SR and SI, even without the effect of external driving force. Based on numerical results, we systematically discuss the transport dependence on various parameters, including the cargo concentration in the crowded environment, cargo capacity of the motor, driving amplitude of external periodic force, and medium temperature. Obviously, the sensitivity of transport process to parameter changes can be used by the environment to regulate its cargo traffic, which also provides latent support for manipulating the transport performance and optimizing the coupled structure in artificial nano-machines.     

Collective directional transport in coupled nonlinear oscillators without external bias

Directed collective motion in a circular array of unidirectionally coupled oscillators with symmetric potential is obtained numerically in the absence of external bias. This striking feature is interpreted as the effect of the spontaneous breaking of temporal symmetry of the coupling. It is revealed that a proper match of various control parameters is important in generating an optimal coherent global transport. Noise-sustained directed transport is also observed, and the related stochastic resonance in an autonomous system is identified.     

Ratchet motion and current reversal of coupled Brownian motors in pulsating 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 the 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 manipulated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.