Stationary probability flow and vortices for the Smoluchowski–Feynman ratchet

Smoluchowski–Feynman ratchet is in contact with two heat reservoirs with different temperatures. We study the non-equilibrium stationary state with a ratchet rotating unidirectionally, based on the probability flow field, which are obtained either by solving the Fokker–Planck equation (with no inertial effect) or by computer simulations (with an inertial effect). Vortex pattern in the probability flow is found, whose sense of rotation, on the one hand, is determined by a simple thermodynamic argument and, on the other hand, determines rotational direction of the ratchet. Small efficiency of the ratchet is also discussed within this vortex framework.     

Irreversible Brownian Heat Engine

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine \(\eta =1-\sqrt{{T_{c}/T_{h}}}\) [23]. On the other hand, the maximum power efficiency of the engine approaches \(\eta ^{MAX}=1-({T_{c}/T_{h}})^{1\over 4}\). It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.     

Recent advance on the efficiency at maximum power of heat engines

This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years. The analytical results of efficiency at maximum power for the Curzon-Ahlborn heat engine, the stochastic heat engine constructed from a Brownian particle, and Feynman's ratchet as a heat engine are presented. It is found that: the efficiency at maximum power exhibits universal behavior at small relative temperature differences; the lower and the upper bounds might exist under quite general conditions; and the problem of efficiency at maximum power comes down to seeking for the minimum irreversible entropy production in each finite-time isothermal process for a given time.     

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     

摇摆型棘齿热电子隧穿制冷

本文利用传输矩阵法数值模拟了电子在加入周期性正负偏压的双势垒("摇摆"棘齿)异质结中的传输特性,获得了两电子库间的净电流以及所伴随的净热流的表达式.进一步分析了净电流、净热流和制冷系数等性能参数的特征,获得的结果对介观热电子器件的研制有一定的理论指导意义. 关键词： 热电子制冷机 摇摆棘齿 性能参数 传输矩阵法     

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.     

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.     

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     

Performance characteristics and parametric optimization of an irreversible magnetic Ericsson heat-pump

Taking into account the finite-rate heat transfer in the heat-transfer processes, heat leak between the two external heat reservoirs, regenerative loss, regeneration time, and internal irreversibility due to dissipation of the cycle working substance, an irreversible magnetic Ericsson heat-pump cycle is presented. On the basis of the thermodynamic properties of magnetic materials, the performance characteristics of the irreversible magnetic Ericsson heat-pump are investigated and the relationship between the optimal heating load and the coefficient of performance (COP) is derived. Moreover, the maximum heating load and the corresponding COP as well as the maximum COP and the corresponding heating load are obtained. Furthermore, the other optimal performance characteristics are discussed in detail. The results obtained here may provide some new information for the optimal parameter design and the development of real magnetic Ericsson heat-pumps.     

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利用调制送气过程中观察到的冷脉冲传播,研究了在HL-2A装置欧姆放电条件下的电子热输运。从扰动输运方程出发,分析了电子热输运过程,利用在实验中获得的数据,进行了曲线拟合和数值计算,得到了在HL-2A装置欧姆放电条件下强场侧电子热输运系数的分布特征为χ=15-14(1-r2)2m2.s-1。     

Effect of anomalous diffusion on directed motion in a multiplicative noise driven flashing ratchet system

In this paper we have studied the directed motion of a Brownian particle in a multiplicative noise driven flashing ratchet system. Our investigation shows the current (j) is either maximum or minimum in the super-diffusion (SPD) region depending on the asymmetric character of the ratchet potential. But the optimum behavior disappears for the symmetric ratchet potential and there is a current inversion around the normal diffusion (ND). With increase of half cycle period(t_p/2) (which controls the on-off operation mechanism of the potential), j passes through a maximum and the peak height is the highest for the SPD. Also at low asymmetry in the system, the mobility is more dominating for the normal and the super-diffusion cases than the sub-diffusion. For large asymmetry in the ratchet potential, the diffusion control positive current is larger for the ND compared to the other cases. Finally, we observe that there is a maximum in the variation of current as a function of noise correlation time for SPD. But it disappears for the other cases.     

不可逆四热源吸收式热变换器的最优性能

在恒温内可逆四热源吸收式热变换器循环模型的基础上,建立了线性(牛顿)传热定律下考虑泵热空间向环境的热漏、工质的内部牦散以及工质与外部热源间的热阻损失的不可逆四热源吸收式热变换器循环模型。导出了在总换热面积一定的条件下,循环泵热率和泵热系数的基本优化关系、最大泵热率和相应的泵热系数、最大泵热系数和相应的泵热率以及最佳工质工怍温度和最佳换热面积分配关系。     

Optimal choice of the performance parameters of an absorption heat transformer

The optimal performance of an absorption heat transformer, i.e. a type II absorption heat pump, is investigated by using the cyclic model with continuous flow. The effect of thermal resistances between the heat transformer and the heat reservoirs is considered in the model. A general expression related to the rate of heat-pumping, the coefficient of performance and the overall heat transfer area of the heat transformer is derived. The expression is used to optimise the main performance parameters of the heat transformer. The maximum rate of heat-pumping and the corresponding coefficient of performance are calculated. For a given overall heat transfer area of the heat transformer, the optimal relation of the heat transfer areas of the heat exchangers is obtained. The problems concerning the optimal choices of other performance parameters are discussed. The results obtained here can not only enrich the theory of finite time thermodynamics, but also provide some new theoretical bases for the optimal design and operation of real absorption heat transformers.     

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.     

"Ω"形微槽热管传热性能的实验研究

本文对一定型"Ω"形轴向槽道热管传热性能进行了实验研究,着重分析了该型热管在水平工况下的轴向温度分布、当量导热系数和总热阻、蒸发/凝结传热系数和最大传热能力.研究表明,该型热管元件具有良好的等温特性和导热性能,可实现高热流、长距离、低温差的热量传输;热管的最大传热能力受其工作温度影响较大,在工作温度较低时具有良好的传热能力,但在高温工况下,传热能力受到削弱.     

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.     

Influence of T-semi attached rib on turbulent flow and heat transfer parameters of a silver-water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel

This study aimed at exploring influence of T-semi attached rib on the turbulent flow and heat transfer parameters of a silver-water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel. For this purpose, convection heat transfer of the silver-water nanofluid in a ribbed microchannel was numerically studied under a constant heat flux on upper and lower walls as well as isolated side walls. Calculations were done for a range of Reynolds numbers between 10,000 and 16,000, and in four different sorts of serrations with proportion of rib width to hole of serration width (R/W). The results of this research are presented as the coefficient of friction, Nusselt number, heat transfer coefficient and thermal efficiency, four different R/W microchannels. The results of numerical modeling showed that the fluid's convection heat transfer coefficient is increased as the Reynolds number and volume fraction of solid nanoparticle are increased. For R/W=0.5, it was also maximum for all the volume fractions of nanoparticle and different Reynolds numbers in comparison to other similar R/W situations. That's while friction coefficient, pressure drop and pumping power is maximum for serration with R/W=0 compared to other serration ratios which lead to decreased fluid-heat transfer performance.     

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.     

Transport properties under the influence of finite friction

Using the Langevin Monte Carlo method,the influence of friction on the directed motion of a Brownian particle driven by an external noise source is investigated.The results show that the exitence and change of the environment friction influence the establishment and development of the steady motion of a Brownian particle derived by nonequilibrium fluctuation.The most probable correlation time,which corresponds to the maximum current,is inversely proportional to the friction coefficient.The abnormal transition of the current with different friction appears because of the coupling between the effective ratchet potential and coloured noise intensity.