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.     

粗糙势中耦合布朗粒子的定向输运性能

研究了粗糙棘轮中耦合粒子的定向输运行为,并进一步讨论了阻尼条件下粗糙棘轮的扰动振幅、扰动波数、粒子间的耦合强度及自由长度等因素对耦合布朗粒子质心平均速度及斯托克斯效率的影响.研究发现,合适的粗糙棘轮扰动振幅和扰动波数能促进耦合布朗粒子的定向输运,同时还能增强其斯托克斯效率.此外,合适的耦合强度和自由长度还能使粗糙棘轮的输运性能达到最强.还发现小扰动振幅条件下,通过改变耦合强度和自由长度能够诱导粗糙棘轮的流反转.通过研究更具实际意义的粗糙棘轮,本文所得结论能为实验上理解分子马达的运动行为提供理论指导,还可为纳米量级分子机器的设计及粒子分离技术的实现提供实验启发.     

摩擦不对称耦合布朗马达的定向输运

本文研究了耦合布朗马达在溶液摩擦对称性破缺条件下的定向输运问题.详细讨论了溶液阻尼系数比,周期外力以及耦合作用对布朗粒子定向输运的影响.研究发现:溶液摩擦的不对称性不仅能促进摩擦棘轮的定向输运,且合适的溶液阻尼系数比还可以使耦合棘轮的定向输运达到最强.此外,一定摩擦阻尼条件下外力振幅可以使耦合粒子的定向输运呈现多峰结构.研究还发现合适的自由长度和耦合强度也能增强摩擦棘轮的输运特性.研究结果不仅能够启发实验上选取合适的摩擦阻尼来优化布朗马达的输运,也可为信息容量大、反应速度快的纳米器件的制备提供一定的理论参考.     

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.     

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     

温度反馈控制棘轮的最优控制

基于Cao的误差棘轮模型,通过引入温度因子进一步对反馈棘轮实施控制.本文详细讨论了温度因子、温度相位差和温度频率对耦合布朗粒子定向输运的影响.研究发现,温度因子并不总是减小温度反馈棘轮的定向输运,这意味着在一定条件下温度因子还可以增强反馈棘轮的定向输运.此外,在小温度振幅范围内耦合粒子的质心平均速度和Pe数随温度频率的变化都呈多峰结构.这一结果表明,合适的温度变化频率能够使反馈棘轮的定向输运获得多次的增强.本文所得结论不仅能够启发实验上通过选取合适的温度反馈信息来优化布朗棘轮的定向输运,还可为实验上的数据分析与处理特别是误差分析提供理论参考.     

非保守力作用下二维耦合布朗粒子的定向输运

本文主要研究二维耦合布朗粒子在非保守外力作用下的定向输运问题.研究发现,非保守外力有促进二维耦合棘轮定向输运的效果.同时,在保守力(弹簧弹力)和非保守外力的相互协作与竞争中耦合布朗粒子的反向输运能够获得增强.特别地,随着弹簧原长或弹性系数的改变,二维耦合布朗粒子的定向运动都能够产生反向,这意味着耦合作用能够诱导二维布朗棘轮流反转的产生.实验上,通过选取不同种类的外力(保守力及非保守力),能够对二维耦合布朗粒子的分离技术提供新的方案.     

涨落作用下周期驱动的分数阶过阻尼棘轮模型的混沌输运现象

考虑涨落作用下周期驱动的过阻尼分数阶棘轮模型, 通过模型的数值求解, 研究确定性棘轮的混沌特性与噪声的作用对输运行为的影响, 进而讨论过阻尼分数阶分子马达反向输运的机理. 分析表明: 随着势垒高度、 势不对称性与模型记忆性的变化, 随机棘轮的反向输运并不必然地要求确定性棘轮也反向输运; 随着模型阶数的减小, 亦即分数阻尼介质记忆性的增强, 确定性棘轮在反向输运之前会经历一个周期倍化导致的混沌状态, 但在噪声作用下, 反向流的发生会提前, 即混沌状态的确定性棘轮在噪声的作用下即可进行反向输运. 也就是说, 噪声能定性地改变棘轮的输运状态: 从无噪声时的混沌运动到有噪声时的定向输运. 这是过阻尼随机棘轮反向输运的一种机理, 也是噪声在定向输运过程中发挥积极作用的一个体现.     

系统非对称性及记忆性对布朗马达输运行为的影响

在对分数阶布朗马达输运现象研究的基础上,引入了描述系统势场对称性的参数(简称对称性参数),并详细分析了该参数及记忆性参数(分数阶阶数)对粒子输运状态的影响.仿真结果表明,分数阶阶数和对称性参数的共同作用会使得布朗粒子形成定向输运反向流,反向后达到最大平均流速所对应的阶数与外加驱动力频率无关联,但会随对称性参数的增加而单调递增.     

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     

Adiabatic Brownian ratchets with the inclusion of inertia

Inertial corrections to the drift velocity of a Brownian particle have been calculated for two main classes of Brownian ratchets operating in the adiabatic regime of fluctuations of the potential energy: first, the stationary periodic potential and dichotomic fluctuations of an external force with zero average value (rocking ratchet) and, second, dichotomic fluctuations of the periodic potential itself. It has been shown that, in contrast to passive transport at which the inertial correction always reduces the effective mobility and diffusion coefficients, inertial corrections for Brownian ratchets can play a constructive role, increasing the drift velocity at least at high temperatures.     

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.     

Performance characteristics of Brownian motors

Brownian motors are nonequilibrium systems that rectify thermal fluctuations to achieve directed motion, using spatial or temporal asymmetry. We provide a tutorial introduction to this basic concept using the well-known example of a flashing ratchet, discussing the micro- to nanoscopic scale on which such motors can operate. Because of the crucial role of thermal noise, the characterization of the performance of Brownian motors must include their fluctuations, and we review suitable performance measures for motor coherency and efficiency. Specifically, we highlight that it is possible to determine the energy efficiency of Brownian motors by measuring their velocity fluctuations, without detailed knowledge of the motor function and its energy input. Finally, we exemplify these concepts using a model for an artificial single-molecule motor with internal degrees of freedom.     

布朗马达的定向输运模型

将系统利用非平衡涨落能量做功，看作是布朗马达受到内外噪声作用的结果，并建立相应的含阻尼、双噪声的扩散模型．通过解析计算和数值模拟，在一维惯性锯齿势中，阐明了乘性噪声驱动布朗马达定向运动的机理，分析了黏滞阻力对定态流的影响．作为应用，解释了单个马达蛋白梯跳运动的实验现象． 关键词：     

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.     

Quantum ratchets and quantum heat pumps

Quantum ratchets are Brownian motors in which the quantum dynamics of particles induces qualitatively new behavior. We review a series of experiments in which asymmetric semiconductor devices of sub-micron dimensions are used to study quantum ratchets for electrons. In rocked quantum-dot ratchets electron-wave interference is used to create a non-linear voltage response, leading to a ratchet effect. The direction of the net ratchet current in this type of device can be sensitively controlled by changing one of the following experimental variables: a small external magnetic field, the amplitude of the rocking force, or the Fermi energy. We also describe a tunneling ratchet in which the current direction depends on temperature. In our discussion of the tunneling ratchet we distinguish between three contributions to the non-linear current–voltage characteristics that lead to the ratchet effect: thermal excitation over energy barriers, tunneling through barriers, and wave reflection from barriers. Finally, we discuss the operation of adiabatically rocked tunneling ratchets as heat pumps. Received: 8 February 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

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.