电动效应作用下微通道内粒子运动的数值模拟

本文采用有限体积法数值模拟了轴向方波电场和直流电场作用下,具有不同电泳淌度粒子的运动情况.结果表明,在半个方波电场周期内,具有不同电泳淌度的粒子在相同的时间内达到各自的稳定速度,周期变化的方波电场使微粒子在微通道内做往复的运动;在直流电场作用下,两个不同电泳淌度的粒子会在轴向方向上产生位移差.定义从溶液中分离粒子的最短距离与微通道高度的比值为分离效率,数值模拟结果表明,分离效率随横向电场强度和粒子电泳淌度的增加而减小.     

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.     

空间非均匀摩擦棘轮的输运性能

本文研究了耦合布朗粒子在空间非均匀摩擦环境下的定向输运问题,并进一步讨论了摩擦系数振幅、空间相位差等因素对耦合粒子质心平均速度及能量转化效率的影响.研究发现,耦合粒子的质心平均速度和能量转化效率随摩擦系数振幅的变化都能呈现多峰结构.这一结果表明摩擦阻尼并不总是阻碍布朗粒子的定向运动,一定条件下合适的摩擦环境还能多次增强耦合布朗棘轮的输运性能.此外,在小摩擦系数振幅条件下通过改变外力振幅、外势不对称度、空间相位差还能诱导摩擦棘轮流反转的产生.本文所得结论不仅有助于理解摩擦环境中耦合布朗粒子的输运性能,还可为微观纳米机器的设计与粒子的筛选分离技术提供理论指导.     

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     

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     

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.     

双稳系统随机共振的能量输入机理

从布朗粒子运动所遵循的Langevin方程出发，分析了周期性外力提供给布朗粒子的瞬时功率和平均功率．揭示了双稳系统随机共振的能量输入机理．理论分析与数值仿真结果表明，布朗粒子吸收的瞬时功率随时间作周期性变化，其变化的频率是周期性外力的2倍，而其幅值和均值的大小都受控于噪声强度．改变布朗粒子所处热环境的参数，能有效地控制周期性外力的能量输入形式．     

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.     

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.     

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.     

Hydrodynamic interactions in Brownian dynamics: I. Periodic boundary conditions for computer simulations

Because of the long range nature of hydrodynamic interactions, the problem of boundary conditions on a finite simulation cell of a hydrodynamically dense suspension of particles in Brownian motion is quite as complicated as the analogous problem in simulation of the statistical mechanics of charged and dipolar systems. One resolution of this problem is to use periodic boundary conditions and to view them as a way of describing a physical system composed of a large spherical array of periodic replicas of the simulation cell. The hydrodynamic interactions are calculated using the quasi-static linearized Navier-Stokes equation. This requires that the suspending fluid velocity remains small throughout the array. That the sum of the particle velocities in the simulation cell be zero is insufficient to force boundedness of the fluid velocity as the array becomes large. Boundedness in the array of the suspending fluid velocity is achieved if a rigid wall boundary condition is applied at the outer edge of the array as the array becomes large. With this condition the net particle velocity equals zero condition is not needed. The condition allows lattice sum representations for the suspending fluid velocity to be derived. These lattice sums are absolutely and rapidly convergent and periodic. Representations of the velocity in the array with boundary condition allow calculation of mobility tensors which are also periodic and can be evaluated numerically in tolerable amounts of computer time. A major effect of these calculations is to identify the physical model system corresponding to a truly periodic fluid velocity and mobility tensor as a large array with rigid wall boundary condition.     

Simulation of spatial correlations of impurity ions in solids using configurational entropy and the hard-sphere model

Based on the hard-sphere model, the spatial correlations are considered in a system of impurities with variable valency. In a zeroth approximation, the configurational entropy of the spatially correlated system of impurity ions is identified with the configurational entropy of a system of hard spheres. The electron mobility limited by scattering on the correlated system of impurity ions at finite temperatures is found. The theory developed explains experimentally observed anomalies of the carrier mobility in an iron-doped HgSe gapless semiconductor.     

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.     

Configurational entropy of systems with non-additive lateral interactions

The configurational entropy per site of a lattice gas model with non-additive interactions between adsorbed particles for square, triangular and honeycomb lattices is discussed in the present study. The model used here assumes that the energy which links a certain atom with any of its nearest-neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the canonical ensemble by following the algorithm of parallel tempering and the thermodynamic integration method the configurational entropy per site has been calculated. By analyzing the behavior of the configurational entropy per site, the different low-temperature-ordered phases are described. The dependency of the critical temperature of the system as a function of characteristic parameters of the model is established.     

Diffusion coefficient for a Brownian particle in a periodic field of force: I. Large friction limit

The diffusion tensor for a Brownian particle in a periodic field of force is studied in the strong damping limit, in which the Smoluchowski equation is valid.A general relation between the diffusion tensor and the Smoluchowski “relaxation operator” is derived; the effect of the periodic force, at least in the simplest situation of diagonal and uniform friction, appears as a dressing of the bare particle mass to an effective tensor mass.From this the explicit form of the diffusion coefficient as a functional of the potential energy in the one-dimensional case is obtained, showing a temperature dependence which deviates at high temperatures from a simple Arrhenius behaviour.Finally, the expression for the mobility of the Brownian particle is derived, and by comparison with the expression for the diffusion coefficient the Einstein relation between diffusion and mobility is proved to be satisfied.     

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.     

Quantum Brownian motion in a one-dimensional disordered system

We study the diffusion of a quantum Brownian particle in a one-dimensional periodic potential with substitutional disorder. The particle is coupled to a dissipative environment, which induces a frictional force proportional to the velocity. The dynamics for arbitrary temperature is studied by using Feynman's influence-functional theory. We calculate the mobility to lowest order in the disorder and strength of the periodic potential. It is shown that for weak dissipation the linear mobility, which vanishes atT=0 due to localization effects, may exhibit a maximum and a subsequent minimum with increasing temperature. The relation to the diffusion of heavy particles in metals or doped semiconductors is briefly discussed.     

Diffusion in flashing periodic potentials

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated by: (i) an external white Gaussian noise and (ii) a Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down, for all parameters of noise and of potential, in comparison with the case when particles diffuse freely.     

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.     

Configurational Entropy of Confined Yukawa Clusters

Confined strongly coupled systems, such as dust clusters in complex plasmas, are known to support multiple stable configurations corresponding to the same number of particles. In this work, we exploit the recently introduced concept of configurational entropy as a robust measure of the uncertainty arising due to the existence of multiple stable states with different occurrence probabilities. We apply this concept to classical Yukawa clusters of up to 100 particles in two‐ and three‐dimensional parabolic traps and investigate the dependence of the entropy on the system size, dimensionality, interparticle interaction range and anisotropy of the parabolic confinement. A universal behaviour of the configurational entropy close to the dimensional (zigzag) transition is reported (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)