Current reversal and mass separation of inertial Brownian motors in a two-noise ratchet

Transport of an inertial Brownian motor moving in an asymmetric periodic potential driven by an external force and correlated noises is investigated. Using the numerical algorithm, the asymptotic mean velocity (AMV) for characterizing directed transport is obtained. The effects of the external driving force f and the correlation λ between the two noises on the AMV are discussed. The results manifest: (1) the external driving force and the correlation between the two noises can lead to the phenomena like current reversal. (2) The competitions among the external driving force and the correlation between the two noises are necessary for current reversal, i.e., fλ>0. (3) Different directions of transport are found for different masses of the Brownian particles under the condition fλ>0. Therefore a theoretical study is suggested for separating Brownian particles according to their different masses in the ratchet system.     

Dispersionless transport in a washboard potential

We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.     

Efficiency and current in a correlated ratchet

We present a detailed study of the transport and the efficiency of a ratchet system in a periodic potential in the presence of correlated noises. The current and the efficiency of the system are investigated. It is found that, when the potential is spatially symmetric, the correlation between the two noises can induce a net transport. The efficiency shows many interesting features as a function of the applied force, the noise intensity, the external load, etc. The efficiency can be maximized as a function of noise intensity (or temperature), which shows that the thermal fluctuation can facilitate the efficiency of energy transformation.     

具有质量及频率涨落的欠阻尼线性谐振子的随机共振

以往的研究大多考虑线性谐振子模型受频率涨落噪声的影响, 而当布朗粒子处于具有吸附能力的复杂环境时, 粒子质量也存在随机涨落. 因此, 本文研究具有质量及频率涨落两项噪声的二阶欠阻尼线性谐振子模型的随机共振现象. 利用Shapiro-Loginov公式和Laplace变换, 推导了系统响应一阶稳态矩及稳态响应振幅的解析表达式. 并根据稳态响应振幅的解析表达式, 建立了稳态响应振幅关于质量涨落噪声及频率涨落噪声各自的噪声强度能够诱导随机共振现象产生的充分必要条件. 仿真实验表明, 当系统参数满足本文所给出的充分必要条件要求时, 系统稳态响应振幅关于噪声强度的变化曲线具有明显的共振峰, 即此选定参数组合能够诱导系统产生随机共振现象.     

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.     

Resonant current in coupled inertial Brownian particles with delayed-feedback control

The transport of a walker in rocking feedback-controlled ratchets is investigated. The walker consists of two coupled “feet” that allow the interchange of the order of particles while the walker moves. In the underdamped case, the deterministic dynamics of the walker in a tilted asymmetric ratchet with an external periodic force is considered. It is found that delayed feedback ratchets with a switching-onand-off dependence of the states of the system can lead to absolute negative mobility. In such a novel phenomenon, the particles move against the bias. Moreover, the walker can acquire a series of resonant steps for different values of the current. It is interesting to find that the resonant currents of the walker are induced by the phase locked motion that corresponds to the synchronization of the motion with the change in the frequency of the external driving. These resonant steps can be well predicted in terms of time-space symmetry analysis, which is in good agreement with dynamics simulations. The transport performances can be optimized and controlled by suitably adjusting the parameters of the delayed-feedback ratchets.     

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.     

有结构壁面上液滴运动特征的耗散粒子动力学模拟

本文采用耗散粒子动力学方法, 研究了恒定外力驱动下液滴在有结构壁面上的运动过程. 通过研究液滴在通过壁面结构时前缘接触点和前进角的变化, 分析了液滴的运动特征. 研究结果表明, 在不同润湿性或不同外力驱动下, 存在使液滴运动最快的“最优”壁面结构, 并对其机理进行了讨论. 本文还探讨了壁面润湿性、热涨落以及外力对液滴运动状态的影响. 关键词： 微流体 有结构壁面 润湿性 耗散粒子动力学(DPD)     

Brownian pump with an unbiased external force

We investigate Brownian pump transport in the presence of an unbiased external force. The pumping system is embedded in a finite region bounded by two particle reservoirs. In the adiabatic limit, we obtain the analytical expressions of the current and the concentration ratio. We find that Brownian particles can be pumped through an asymmetric potential from a particle reservoir at low concentration to one at the same or higher concentration in the presence of an unbiased external force.      

Mobility in a periodic potential: A simple derivation

A simple derivation is given for the mobility of Brownian particles in a periodic potential in the overdamped regime. The method makes use of the fact that the steady state current density, in response to a uniform external force, is uniform in space and can be expressed as a product of the particle density and mean velocity field. To lowest order in the external force, the particle density is given by the equilibrium density in the absence of the external force.     

定向凝固过程中枝晶侧向分枝生长行为与强制调控规律

采用相场法数值模拟研究了定向凝固过程中随机噪声条件下枝晶侧向分枝生成行为与强制扰动条件下侧向分枝调控规律. 模拟结果表明: 随机噪声条件下, 侧向分枝整体上并无规则性, 但产生频率存在一定分布范围, 且在一定时间段内会出现生成频率一致且具有极强相关性的一组侧向分枝, 即波包; 不同波包之间不具有相关性, 但不同波包内部的侧枝生成频率基本相同, 且与侧枝整体频谱曲线峰值位置处的频率基本相当; 强制周期扰动条件下, 当扰动频率处于侧向分枝整体生成频率范围内时, 可激发枝晶产生规则侧向分枝, 且扰动频率与波包内侧枝生成频率一致时侧向分枝最发达. 研究结果可为向定向凝固枝晶形态的调控提供理论指导.     

圆锥料仓内颗粒周期性脉动特征研究

料仓卸料过程中的颗粒脉动会引起料仓振动甚至导致结构失效.为了明晰颗粒脉动特征,本文进行了椭球颗粒在不同半锥角深仓的模拟卸料实验,将料仓圆筒部划分为4个固定区域以研究区域内颗粒的运动信息,分析了料仓圆筒部颗粒系统的运动特征.研究结果表明:整个卸料过程颗粒速度始终处于波动变化中,卸料前期表现为大振幅、周期性的剧烈脉动,卸料后期平均速度的变化则是小振幅无规律的波动;剧烈脉动时段各区域的颗粒层平均受力的变化规律与颗粒速度脉动特征相似,越接近储料顶端颗粒脉动振幅越大,表现出更规律的周期性脉动,相邻颗粒层间的脉动波形相似且周期相同,剧烈脉动过程中顶面颗粒呈周期性的自由落体运动,该时段内顶层颗粒每一次的自由落体运动都会引起该范围内颗粒间接触力消失;料仓半锥角越小时剧烈脉动频率越高、振幅越大且脉动持续时间也越长,卸料速度越稳定,且颗粒速度不会出现带有上升趋势的波动.研究结果可为卸料设备的安全设计提供参考.     

Sorting on periodic surfaces

Particles moving on crystalline surfaces and driven by external forces or flow fields can acquire velocities along directions that deviate from that of the external force. This effect depends upon the characteristics of the particles, most notably particle size or particle index of refraction, and can therefore be (and has been) used to sort different particles. We introduce a simple model for particles subject to thermal fluctuations and moving in appropriate potential landscapes. Numerical results are compared to recent experiments on landscapes produced with holographic optical tweezers and microfabricated technology. Our approach clarifies the relevance of different parameters, the direction and magnitude of the external force, particle size, and temperature.     

Ratchet transport of self-propelled chimeras in an asymmetric periodic structure

We studied the rectified transport of underdamped particles subject to phase lag in an asymmetric periodic structure. When the inertia effect is considered, it is possible to observe reversals of the average velocity with small self-propelled force, whereas particles always move in the positive direction with large self-propelled force. The introduction of phase lag leads particles to follow circular orbits and suppress the polar motion. In addition, this can adjust the direction of particle motion. There exists an optimal value of polar interaction strength at which the rectification is maximal. These results open the way for many application processes, such as spatial sorting of particles mixture and separation based on their physical properties.     

Current Reversals of an Underdamped Brownian Particle in an Asymmetric Deformable Potential

Transport of an underdamped Brownian particle in a one-dimensional asymmetric deformable potential is investigated in the presence of both an ac force and a static force,respectively.From numerical simulations,we obtain the current average velocity.The current reversals and the absolute negative mobility are presented.The increasing of the deformation of the potential can cause the absolute negative mobility to be suppressed and even disappear.When the static force is small,the increase of the potential deformation suppresses the absolute negative mobility.When the force is large,the absolute negative mobility disappears.In particular,when the potential deformation is equal to0.015,the two current reversals present with the increasing of the force.Remarkably,when the potential deformation is small,there are three current reversals with the increasing of the friction coefficient and the average velocity presents a oscillation behavior.     

驻波声场中圆柱形管道周围颗粒的运动特性

针对圆柱形管道外部的流体与颗粒介质运动问题,提出了结合圆柱周围声辐射力和声流Stokes力的研究方法。从柱体外部声流方程出发,得到影响涡流结构的无量纲参数Rem≥325.27时,外涡最大流速大于内涡最大流速。在此基础上,采用Nyborg的边界滑移速度理论,获得管道外部声流的极限滑移速度,推导得出圆柱附近的声辐射力公式。基于此公式,在理论上推导出颗粒速度为0、声辐射力和声流Stokes力平衡时,颗粒临界直径的表达式。通过对圆柱位于不同位置时,圆柱外部的颗粒运动进行仿真模拟,得到与理论公式相一致的结论:颗粒的临界直径的大小与声波频率有关,当颗粒直径小于临界直径时,声流Stokes力为主导,颗粒随声流运动,颗粒直径大于等于临界直径时,声辐射力为主导,颗粒在声辐射力作用下逐渐向声辐射力的节点聚集。理论与仿真结果表明该方法可用于分析管道外颗粒的分布状态,其研究结果有助于解决电站中换热器的管道结垢、热交换率降低等问题。     

Collective escape processes in many-particle systems

We study collective escape phenomena in nonlinear chain models. First we investigate the fragmentation of an overdamped polymer chain due to thermal fluctuations in the absence of an external force. We calculate the activation times of individual bonds in the coupled chain system and compare them with times obtained from Brownian dynamics simulations. We also consider a grafted chain exposed to an external force which monotonically grows as time goes on. In underdamped situations we show that collective localized excitations in a nonlinear force field with absorbing states can cause polymer fragmentation. In a similar fashion, localized modes assist a thermally activated escape of interacting particles in a metastable potential landscape which is additionally subjected to a periodic driving. The latter is necessary to obtain overcritical elongations which create localized modes even in case of stronger damping.     

受碾区域内颗粒轴向流动特性的离散元模拟

为探讨受碾状态颗粒的稳定流动, 在碾辊轴与筛筒组成的受碾区域内, 建立了轴向运动的颗粒流离散元物理模型. 研究结果表明: 受碾区域内各颗粒沿轴向运动能力的差异造成了颗粒流密度不均匀; 颗粒与筛筒间的静摩擦系数影响颗粒轴向流动的形态、速率及集散程度, 受碾区域内单层颗粒的轴向均方偏差与流动时间的平方正相关, 属于“super”扩散; 整体分析受碾区域发现, 颗粒的轴向平均速度沿轴向坐标逐渐增大, 而颗粒的三轴合成平均速度沿轴向坐标逐渐降低; 受碾区域内各轴向位置处颗粒运动的剧烈程度不同, 沿轴向坐标颗粒的波动速度平方呈现先增大后降低而后又增大的趋势; 单颗粒的碰撞总能量损失能谱也表明了颗粒运动程度不同, 即轴向流动时在受碾区域的前半段碰撞剧烈, 能量损失多, 在后半段碰撞程度弱, 能量损失较少. 通过对受碾区域内颗粒流动的数值模拟分析, 明晰了颗粒在受碾条件下稳定流动特性, 有益于碾磨工业对产品品质控制及设备参数优化的研究.     

Particle transport in space-periodic potentials in underdamped systems

We consider the motion of an underdamped Brownian particle in a tilted periodic potentialin a wide temperature range. Based on the previous data and the new simulation results weshow that the underdamped motion of particles in space-periodic potentials can beconsidered as overdamped motion in the velocity space in the effective double-wellpotential. Simple analytic expressions for the particle mobility and diffusion coefficientare derived with the use of the presented model. These accurately match numericalsimulation results.     

工业中粉体颗粒的荷电机理及数值模拟方法

工业过程中粉体颗粒不可避免地会相互摩擦碰撞而荷电. 荷电颗粒的存在可能会危害正常的工业生产过程, 也可能对工业过程起促进作用. 因此, 荷电粉体颗粒及其特性受到了广泛的关注, 但目前对粉体颗粒的荷电机理依然缺乏透彻的了解, 尤其是在气固两相流动中的粉体颗粒荷电现象. 事实上, 工业中存在的粉体颗粒的运动都受到流体的影响, 是典型的气固两相流系统, 流体对粉体颗粒的作用使粉体颗粒接触的荷电现象变得更为复杂, 因此从两相流动的观点来研究粉体颗粒荷电的物理本质就显得越来越重要. 本文介绍了工业过程中的几种不同类型的粉体颗粒荷电行为, 回顾了颗粒的荷电机理与描述颗粒荷电的数学模型. 对于工业过程中颗粒的荷电现象及颗粒在多相流体中的动力学行为, 介绍了研究颗粒受流体影响时荷电特性的数值模拟方法. 本文旨在对粉体颗粒的荷电机理、应用以及研究方法进行梳理与探讨, 为正确认识工业过程中粉体颗粒的荷电现象并加以控制利用提供理论借鉴.