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     

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.     

分数阶布朗马达在闪烁棘齿势中的合作输运现象

引入分数阶微积分理论,建立耦合分数阶布朗马达在闪烁棘齿势中的合作输运模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 发现在具有记忆性的分数阶棘齿系统中, 系统阶数与粒子间耦合强度不仅可影响粒子链输运速度, 还可使粒子链出现与整数阶方向相反的定向流; 在阶数固定下, 定向输运速度将随参数(噪声强度、耦合强度、棘齿势峰值高度)变化出现广义随机共振现象. 关键词： 分数阶布朗马达 闪烁棘齿势 合作定向输运 广义随机共振     

Collective dynamics of two-dimensional coupled Brownian motors

The transport properties of coupled Brownian particles in a two-dimensional rocking ratchet are investigated via Langevin simulation. The results show that the average center-of-mass velocity is multi-peaks function of the frequency of the driving force. Furthermore, in the 2D coupled Brownian motor system there are the collective effect and ratchet behavior, which can switch depending on the frequency of driving force. It turns out that the cooperative effect between the interaction of coupled particles and external rocking driving force facilitates collective directional motion and energy conversion.     

反馈脉冲棘轮的能量转化效率研究

研究了反馈脉冲棘轮的定向输运及能量转化效率.详细讨论了弹簧自由长度、耦合强度及脉冲相位等参量对耦合布朗粒子定向输运性能的影响.研究发现,一定自由长度和耦合强度都能促进反馈脉冲棘轮的定向输运,并能使耦合粒子拖动负载做功时的能量转化效率达到最大.此外,通过调节脉冲相位能使反馈棘轮在一个演化周期内获得两次流反转,且合适的相位还能增强反馈棘轮的定向输运.所得结论不仅可为实验上设计合适的反馈脉冲作用来优化棘轮的定向输运性能,而且还能为生物医疗上药物的精准投放提供一定的理论参考.     

内部棘轮

建立了一个内部棘轮模型,即将一个自由系统耦合到一个具有非对称周期结构的亚系统上,而后者处于一个热浴环境之中.计算了一个周期信号以两种方式驱动粒子的平均速度,并与相同参数下外部棘轮的结果进行了比较.结果表明,内部棘轮中的粒子定向流的极大值大于外部棘轮的;在相同温度下,内部棘轮中粒子更容易产生定向运动.     

反馈控制棘轮的定向输运效率研究

研究了反馈耦合布朗棘轮中粒子处于负载力、时变外力及噪声作用下的定向输运问题.详细讨论了外力作用时间的不对称性、外势空间的不对称性及外力周期等对反馈耦合棘轮中粒子输运效率的影响.研究发现,外力的时间不对称度能促进反馈棘轮中粒子的定向输运,随时间不对称度的增大,反馈棘轮中粒子能获得较大的效率.然而,外势空间的不对称度能有效抑制耦合棘轮中粒子的扩散,达到增强耦合粒子定向输运的效果.同时还发现,存在最优的噪声强度能使耦合粒子的输运效率达到最大.     

Brownian motors and stochastic resonance

We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.     

Quantitative simulations of ratchet potential in a dusty plasma ratchet

Using a dusty plasma ratchet, one can realize the rectification of charged dust particle in a plasma. To obtain the ratchet potential dominating the rectification, here we perform quantitative simulations based on a two-dimensional fluid model of capacitively coupled plasma. Plasma parameters are firstly calculated in two typical cross sections of the dusty plasma ratchet which cut vertically the saw channel at different azimuthal positions. The balance positions of charged dust particle in the two cross sections then can be found exactly. The electric potentials at the two balance positions have different values. Using interpolation in term of a double-sine function from previous experimental measurement, an asymmetrical ratchet potential along the saw channel is finally obtained. The asymmetrical orientation of the ratchet potential depends on discharge conditions. Quantitative simulations further reproduce our previous experimental phenomena such as the rectification of dust particle in the dusty plasma ratchet.     

Performance characteristics of an irreversible thermally driven Brownian microscopic heat engine

Brownian particles moving in a spatially asymmetric but periodic potential (ratchet), with an external load force and connected to an alternating hot and cold reservoir, are modeled as a microscopic heat engine, referred to as the Brownian heat engine. The heat flow via both the potential energy and the kinetic energy of the particles are considered simultaneously. The forward and backward particle currents are determined using an Arrhenius' factor. Expressions for the power output and efficiency are derived analytically. The maximum power output and efficiency are calculated. It is expounded that the Brownian heat engine is always irreversible and its efficiency cannot approach the efficiency η_C of the Carnot heat engine even in quasistatic limit. The influence of the main parameters such as the load, the barrier height of the potential, the asymmetry of the potential and the temperature ratio of the heat reservoirs on the performance of the Brownian heat engine is discussed in detail. It is found that the Brownian heat engines may be controlled to operate in different regions through variation of some parameters.     

Two particles with bistable coupling on a ratchet

We study the motion of two Brownian particles coupled by a bistable potential on a periodically rocked ratchet. Bistable coupling symmetrizes the two particles and admits a richer dynamics that cannot be found with linear coupling or a single particle. Depending on the coupling strength and the equilibrium distance we find different step patterns and current reversals. We present numerical results and compare them with analytical solutions in limiting cases of adiabatically slow rocking and of rigid coupling.     

带反馈的分数阶耦合布朗马达的定向输运

研究具有幂律记忆性的带反馈耦合布朗马达的定向输运现象, 引入分数阶理论, 建立了带反馈的分数阶耦合布朗马达模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 仿真结果表明, 系统的记忆性通过影响带反馈的棘齿势的打开和闭合而影响粒子的定向输运, 即当系统的阶数在较小的范围内, 系统的记忆性会使带反馈的棘齿势的开关频率增加, 从而增大定向流速; 当系统其他参数(势垒高度、噪声强度等)固定时, 输运速度随着阶数的变化出现广义随机共振现象.     

Transportation of Two Coupled Particles in an Asymmetric Saw-Tooth Potential

Based on a simple model,we theoretically show the transport behaviors of two harmonically coupled Brownian particles in an asymmetric saw-tooth potential with two slopes.The coupled particles are subject to stochastic fluctuations.It is found that when the equilibrium distance of the coupled particles is between the two slopes of the potential,the transport direction of the coupled particles will be reversed with a certain harmonic coupling strength.This current reversal can be easily understood with the near rigid approximation,where the two coupled particles can be regarded as a single particle in an effective potential.Compared with the original saw-tooth potential,the asymmetry of the effective potential could be reversed when the equilibrium distance is between the two slopes of the original potential,which results in the current reversal.     

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.     

Brownian Ratchet Driven by a Rocking Forcing with Broken Temporal Symmetry

The ratchet motion of a Brownian particle in a symmetric periodic potential under a rocking force thatbreaks the temporal symmetry is studied. As long as the relaxation time in the thermal background is much shorter thanthe forcing period, the unidirectional transport can be analytically treated. By solving the Fokker-Planck equations, weget an analytical expression of the current. This result indicates that with an appropriate match between the potentialfield, the asymmetric ac force and the thermal noise, a net current can be achieved. The current versus thermal noiseexhibits a stochastic-resonance-like behavior.     

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.     

Active Brownian motion models and applications to ratchets

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 sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.     

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.     

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.