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     

Transport reversal in a delayed feedback ratchet

Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off of a periodic potential. They can induce directed transport even with symmetric potentials thanks to the asymmetry of the feedback protocol. We investigate here the dynamics of a feedback flashing ratchet when the asymmetry of the ratchet potential and of the feedback protocol favor transport in opposite directions. The introduction of a time delay in the control strategy allows one to nontrivially tune the relative relevance of the competing asymmetries leading to an interesting dynamics. We show that the competition between the asymmetries leads to a current reversal for large delays. For small ensembles of particles current reversal appears as the consequence of the emergence of an open-loop like dynamical regime, while for large ensembles of particles it can be understood as a consequence of the stabilization of quasiperiodic solutions. We also comment on the experimental feasibility of these feedback ratchets and their potential applications.     

Feedback control in a collective flashing ratchet

An ensemble of Brownian particles in a feedback controlled flashing ratchet is studied. The ratchet potential is switched on and off depending on the position of the particles, with the aim of maximizing the current. We study in detail a protocol which maximizes the instant velocity of the center of mass of the ensemble at any time. This protocol is optimal for one particle and performs better than any periodic flashing for ensembles of moderate size, but is defeated by a random or periodic switching for large ensembles.     

脉冲式棘齿势场作用下囚禁离子的规则与混沌运动

考虑赝势近似下囚禁于Paul阱中的单离子与由脉冲式双激光驻波构成的棘齿势场的相互作用.应用积分方程方法得到系统的经典运动精确解，通过数值方法作出相空间轨道并计算由平均速度定义的流，结合分析与数值结果研究囚禁离子的规则与混沌运动特性.与单驻波型激光脉冲情形相比，发现两个重要的棘齿效应：一是脉冲式棘齿势场的作用导致参数空间混沌区域的改变，从而适当调节第二驻波参数，可使离子的规则运动变为混沌运动，或者混沌运动变为规则运动；二是通过分析平均流随激光参数的变化，发现棘齿势场的介入能使囚禁离子作平均意义下的单向输运，随着势场强度增加到混沌区域，流的强度明显减小并改变方向，系统进入混沌运动. 关键词： 脉冲式棘齿势 囚禁离子 混沌 输运     

基于连续时间无规行走模型研究反常扩散

基于连续时间无规行走(CTRW)理论，数值研究了布朗粒子的欠扩散、正常扩散和超扩散三种扩散行为.解决了CTRW模型的跳跃步长和等待时间分布函数的可实现化问题，对Metropolis抽样方法进行了改进以适用于周期势.探讨了布朗马达依靠闪烁棘轮和摇摆棘轮整流反常扩散所获得的定向速度，结果显示，闪烁布朗马达定向流极大值出现在超扩散条件下；摇摆布朗马达定向流最大值出现在弹道扩散条件下.     

基于连续时间无规行走模型研究反常扩散

基于连续时间无规行走(CTRW)理论,数值研究了布朗粒子的欠扩散、正常扩散和超扩散三种扩散行为.解决了CTRW模型的跳跃步长和等待时间分布函数的可实现化问题,对Metropolis抽样方法进行了改进以适用于周期势.探讨了布朗马达依靠闪烁棘轮和摇摆棘轮整流反常扩散所获得的定向速度,结果显示,闪烁布朗马达定向流极大值出现在超扩散条件下;摇摆布朗马达定向流最大值出现在弹道扩散条件下. 关键词： 无规行走 反常扩散 Metropolis抽样 棘轮势     

Feedback control in a coupled Brownian ratchet

On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally, the influences of the time delay, the coupling constant, and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated. The centre-of-mass velocity of two coupled Brownian particles, the average effective diffusion coefficient, and the Pe number are calculated. It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential. It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case. It is expected that the results obtained here may be observed in some physical and biological systems.     

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.     

A random walker on a ratchet

We analyze a model for a walker moving on a ratchet potential. This model is motivated by the properties of transport of motor proteins, like kinesin and myosin. The walker consists of two feet that are represented as two particles coupled nonlinearly through a bistable potential. In contrast to linear coupling, the bistable potential admits a richer dynamics, where the ordering of the particles can alternate during the walking. The transitions between the two stable states on the bistable potential correspond to a walking with alternating particles. We distinguish between two main walking styles: alternating and no alternating, resembling the hand-over-hand and the inchworm walking in motor proteins, respectively. When the equilibrium distance between the two particles divided by the periodicity of the ratchet is an integer, we obtain a maximum for the current, indicating optimal transport.     

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.     

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.     

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.     

Transport in a flashing ratchet in the presence of anomalous diffusion

Transport of a particle in a flashing ratchet coupled to a non-Ohmic environment with spectrum ∝ω^μ−1 (0<μ<2) is considered. If the temperature is much less than the barrier height of the ratchet potential and the waiting time of the particle in the potential on is long enough, the current J is evaluated approximately by the step periodic number per cycle. The results show that the maximum of peak for J is a non-monotonous function of μ, the optimal μ appears in the region of superdiffusion. The current in the anomalous ratchet is much larger than in the normal one.     

A feedback-controlled Brownian ratchet operated by a temperature switch

In this paper, we present a model of the Brownian motor in a feedback controlled ratchet, in which the application of the flashing potential depends on the state of the particle to be controlled. We derive an analytical expression for the velocity induced by the feedback ratchet, which is a function of several parameters, including the ratio of the two switching temperatures and the asymmetry parameter of the potential field. The motor shows a current inversion when either parameter is varied.     

A feedback controlled Brownian ratchet operated by temperature switch

In this paper, we present a model of the Brownian motor in a feedback controlled ratchet, in which the application of the flashing potential depends on the state of the particle to be controlled. We derive an analytical expression for the velocity induced by the feedback ratchet, which is a function of several parameters, including the ratio of the two switching temperatures and the asymmetry parameter of the potential field. The motor shows a current inversion when either parameter is varied.     

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.     

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.     

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