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.     

The Motion of Repulsive Brownian Particles in Quenched Disorder

Brownian motion of the particles with repulsive interaction is investigated. When the potential condition is satisfied, the eigenvalue problem of interaction Fokker-Planck equation under certain conditions can be transformed to that of a many-particle Schrödinger equation. Using the Green's function method, we obtain the effective single-variable Fokker-Planck equation in the low density limit. We find that the diffusion of coupled Brownian particles in quenched disorder media is also anomalous in 2D. The Mittag-Leffler relaxation of pancake vortices is investigated by fractional Fokker-Planck equation.     

Directional motion, current reversals and mass separation in a symmetrical periodic potential

The transport of a symmetric periodic potential driven by a static bias and correlated noises is investigated for both the over-damped case and the under-damped case. By both theoretical approximation and numerical simulations, we study steady current of an over-damped Brownian particle moving in the potential. It is shown that the symmetric periodic potential driven by a static bias and the correlated noises is simultaneously able to exhibit directional transport, a single current reversal, as well as a double current reversal. For the under-damped case, we examine the dynamic at various inertial strengths by direct simulations of the stochastic differential equations. We specially focus on the influence of inertial term in the particle dynamics for the noise induced, directed current. Different directions of the steady current is found for different masses of the particles, thus an efficient scheme to separate the Brownian particles according to their mass is suggested.     

Noise-induced transport with low randomness

We study the transport of overdamped Brownian particles in periodic potentials subject to a spatially modulated Gaussian white noise. We derive an analytical expression for the diffusion coefficient of particles. By means of velocity, diffusion coefficient, and their ratio (Péclet number) we discuss (a) symmetric potential and modulation of noise intensity and (b) a ratchet profile with strong noise modulation. It is shown that state dependent fluctuations may not only induce directed transport, but also a pronounced coherence of transport if the potential exhibits a strong asymmetry.     

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.     

Transport for System with Three-Value Poissonian Noise

The transport of the overdamped Brownian particles in a spatially periodic potential subject to the three value Poissonian noise in the stationary state is considered. We show that for the spatially periodic potential, no matter whether it is asymmetric, or is symmetric, flux can be induced. But the mechanism is different. The former is the common action of broken reflection symmetry and transition among three-value Poissonian noise in a cyclic way; the latter is single behavior of transition among three-value Poissonian noise in a cyclic way.     

Transport for System with Three-Value Poissonian Noise

The transport of the overdamped Brownian particles in a spatially periodic potential subject to the three-value Poissonian noise in the stationary state is considered. We show that for the spatially periodic potential, no matter whether it is asymmetric, or is symmetric, flux can be induced. But the mechanism is different. The former is the common action of broken reflection symmetry and transition among three-value Poissonian noise in a cyclic way; the latter is single behavior of transition among three-value Poissonian noise in a cyclic way.     

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.     

双稳系统的随机能量共振和作功效率

分析了处于双稳系统中的布朗粒子与外界的周期性外力和热随机力的功、热交互作用,建立了基于Langevin方程的随机能量平衡方程.围绕着受周期力、随机力和阻尼力共同作用的Langevin方程,采用动力学和非平衡热力学相结合的方法,从以"力"为立足点转到以"能量"为研究核心,深入分析了布朗粒子沿单一轨线运动时系统与环境之间的能量交换和作功效率,揭示了双稳系统的随机能量共振现象. 关键词： 双稳系统 随机能量共振 作功效率     

Noise-Induced Phase Transition: Zero-Dimensional Brownian Particles Varying between Ergodicity and Nonergodicity

We study in phase space a zero-dimensional system of Brownian particles which move in a periodic potential and subject to an internal time derivative Ornstein-Uhlenbeck noise. To resolve the Fokker-Planck equation in such a case, we propose an approximate analytical method. The theoretical predictions exhibit a second order noise-induced nonequilibrium phase transition, which is confirmed by numerical simulation results. The phase transition brings the system from an ergodicity to a nonergodicity phase as the potential barrier height decreases.     

Effect of the Noise Correlation Time on the Stationary Current of Brownian Particle in a Spatially Symmetric Periodic Potential

We investigate the noise-induced transport of Brownian particle in a deterministic spatial symmetrical periodic potential driven by colored cross correlation between a multiplicative white noise and an additive white noise. We derive the general formula of the stationary current. Based on numerical computation, we found that directed motion of the Brownian particles can be induced by the correlation time τ of cross correlation between the multiplicative noise and the additive noise and the current reversal and the direction of the current is controlled by the τ.     

周期场时间导数Ornstein-Uhlenbeck噪声Fokker-Planck方程的小参数展开求解

通过引入变量,周期场中内部时间导数Ornstein-Uhlenbeck噪声驱动的布朗运动可用高维Fokker-Planck方程来描述. 上述系统不能直接应用通常的小参数展开和势谷中心展开近似求解. 用一种变通的小参数展开方法近似求解了系统的Fokker-Planck方程,结果适用于小势垒高度、中等关联时间和较大的相空间区域,近似解析解可获得系统的改进. 关键词： Fokker-Planck方程 周期势 时间导数Ornstein-Uhlenbeck噪声 小参数展开     

Transport properties of coupled Brownian particles confined to a microchannel in an asymmetric periodic potential

On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we investigated an overdamped Brownian motion of two coupled particles with an asymmetric periodic potential in a two-dimensional microchannel theoretically and numerically, to reveal the dynamical mechanism of cooperative transport of particles with two heads, where the interactions between two particles are taken into consideration. Moreover, while moving in a confined structure, Brownian particles also could exhibit peculiar kinetic behavior. The dependence of directed current on various parameters is systematically studied. Our results indicate that the direction of motion can be reversed by modulating the coupling strength, free length, and microchannel width. In addition, we have achieved the conditions of forward motion in this study. That is, when the interparticle average horizontal interval Δx > 0.25L, where L is the spatial period of the external potential, the forward motion of coupled Brownian particles effected by the synchronized noise and confined to a microchannel can be generated in the strong-coupling case.     

Directed Current Induced by an Symmetrically ac Force Coexisting with a Time-Delayed Feedback

We study the transport of overdamped Brownian particles in a symmetrically periodic potential in the presence of an asymmetrically ac driving force and a time-delayed feedback.It is found that for low frequencies,the average velocity can be negative by changing the driving amplitude,for high frequencies,there exists an optimized driving amplitude at which the average velocity takes its maximum value.Additionally,there is a threshold value of driving amplitude below which no directed transport can be obtained for high frequencies.For the large value of the delay time,the average velocity is independent of the delay time.     

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.     

Brownian motion in periodic potentials in the low-friction-limit; nonlinear response to an external force

The Brownian motion of particles in a periodic potential in response to a constant external force is investigated in the low-friction-limit. By introducing an energy and a space variable and by making a proper self consistent ansatz, the Fokker-Planck equation is solved in the stationary state for small friction constants. We found out that, for fixed force to friction ratios, the mobility times the friction constant is a linear function of the square root of the friction constant if the damping is small enough. Explicit results for this linear function are presented for a cosine potential and compared to previous results.     

Neutron scattering in superionic conductors

The coherent dynamical structure factor S(q,ω) of one-dimensional superionic conductors is studied in a model of Brownian particles with harmonic interactions moving in a periodic potential. We present results for the q-dependence of the halfwidth of the quasielastic peak, which reflects the commensurability ratios of the periodic potential and the molten sublattice. Furthermore the influence of the periodic potential on the collective excitations of the mobile ions is discussed.     

Directed transport of coupled Brownian ratchets with time-delayed feedback

A time-delayed feedback ratchet consisting of two Brownian particles interacting through the elastic spring is consid ered. The model describes the directed transport of coupled Brownian particles in an asymmetric two-well ratchet potential which can be calculated theoretically and implemented experimentally. We explore how the centre-of-mass velocity is af fected by the time delay, natural length of the spring, amplitude strength, angular frequency, external force, and the structure of the potential. It is found that the enhancement of the current can be obtained by varying the coupling strength of the delayed feedback system. When the thermal fluctuation and the harmonic potential match appropriately, directed current evolves periodically with the natural length of the spring and can achieve a higher transport coherence. Moreover, the external force and the amplitude strength can enhance the directed transport of coupled Brownian particles under certain conditions. It is expected that the polymer of large biological molecules may demonstrate a variety of novel cooperative effects in real propelling devices.     

Dynamical properties of colloidal systems: 1. Derivation of stochastic transport equations

To describe dynamical properties of a system of interacting Brownian particles stochastic transport equations are derived for the positions of the particles and their concentration fluctuations. This is achieved by an expansion of the Langevin equation for the momenta in terms of the reciprocal of the friction coefficient. As a by-product this procedure gives a new derivation of the generalized Smoluchowski equation. Using a local equilibrium approximation for the configurational distribution function a mode-mode coupling equation is derived for the local concentration, which still depends on the random forces of the solvent. For the interaction free case the relation to the ordinary diffusion approach is established.     

外力作用下反馈耦合布朗棘轮的定向输运

本文研究了处于外力作用下双阱棘轮势中两个反馈耦合布朗粒子的定向输运性能. 通过对过阻尼朗之万方程的数值求解, 详细讨论了外力、热噪声与势阱的不对称参数等对耦合布朗粒子的平均速度、 有效扩散系数及Pe数的影响. 研究发现, 平均速度随外力呈周期性的变化规律. 同时耦合系统存在最优噪声强度会使定向输运达到最强. 值得指出的是棘轮系统可通过改变双阱势的结构来获得较强的定向流. 关键词： 耦合布朗棘轮 外力 双阱棘轮势 平均速度