Effects of an oscillating field on a diffusion process in the presence of a trap

Consider a diffusion process on an infinite line terminated by a trap and modulated by a periodic field. When the frequency is equal to zero the mean time to trapping will be finite or infinite, depending on the sign of the field. We ask whether this behavior can be changed by an oscillatory field, and show that it cannot for pure Brownian motion. We suggest that transition can appear when the signal propagation velocity is finite as for the telegrapher's equation. We further suggest that the asymptotic time dependence of the survival probability is proportional tot ^–1/2 just as in the case of ordinary diffusion. The same conclusion is shown to hold for a system whose dynamics is governed by the equation , whereL is a constant.     

A simulation study of an asymmetric exclusion model with open and periodic boundaries for parallel dynamics

The effect of jumping rate probability on the phase diagram of an asymmetric exclusion model is studied by numerical simulations. Density, current and velocity of particles are calculated for parallel dynamics. In the open boundaries case for one species of particles (particles 1), a passage from first to second order transition occurs by decreasing the jumping rate. In the periodic boundaries case, by introducing another species of particle (particle 2) which plays the role of obstacle for particles 1, the average velocity of particles 1 increases with increasing the jumping rate for small density. While the average velocity of particle 2 decreases for small and intermediate densities. Received: 21 October 1997     

Effects of time delay on transport processes in an active Brownian particle

The transport properties of an active Brownian particle with a time-delayed feedback and an external bias are investigated theoretically. By virtue of the perturbation theory for small delay, analytical expressions for the mean velocity and effective diffusion coefficient are derived. There exists a critical absolute value of the bias, below and above which the delay, respectively, enhances and weakens the diffusion, for a fixed noise intensity. The effects of delay observed above are more pronounced for weaker noise. These results are further verified via direct numerical simulations.     

Escape of Brownian particles in an asymmetric bistable sawtooth potential driven by cross-correlated noises

The relative escape rate (RER) for Brownian particles in an asymmetric bistable sawtooth potential driven by cross correlations between multiplicative white noise and additive white noise is studied. A new expression of the mean first-passage time is derived under the condition of piecewise linear potentials and discontinuous diffusion function. Based on the results of RER numerically calculated, it is found that (i) under positively correlated noises action (i.e. λ > 0, and λ is the correlation strength), the escape rate exhibits the suppression platform as the intensity of multiplicative noise varies. The effect of suppression becomes more pronounced with the growth of height of the deterministic potential barrier for transition, and with the increase of λ. However, for the case of uncorrelated noises (λ = 0) and of negatively correlated noises (λ < 0), the suppression platform disappears. (ii) The positive correlation between noises amplifies the change of the escape rate with the height of barrier for transition, while the negative correlation between noises suppresses this change. Received 20 November 2002 / Received in final form 19 October 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: kmdcmei@public.km.yn.cn     

Directed transport of an asymmetric particle pair induced by non-equilibrium conditions

The hopping motion of a classical bounded pair of two particles along a chain is investigated. It is shown that in the asymmetric case of the system dynamics including excited states which differ from the respective ground states by the barrier to be overcome by one of the two particles, the over- and underpopulation of these excited states leads to a directed motion of the particle pair. Thereby, overpopulation results in one direction of motion, whereas underpopulation results in the opposite direction, and the mean velocity is determined by the amount of over-resp. underpopulation. For small deviations from equilibrium, the system exhibits linear response well known from other ratchet-type models. Possible generalizations and applications are discussed. Received 17 August 2001 and Received in final form 11 October 2001     

Brownian Particle in a Poisson-Shot-Noise Active Bath: Exact Statistics,Effective Temperature,and Inference

The dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles is studied. The particle moves in a harmonic potential and experiences Poisson shot-noise kicks with specified amplitude distribution due to moving active particles in the bath. From the Fokker–Planck equation for the particle dynamics, the stationary solution for the displacement distribution is derived along with the moments characterizing mean, variance, skewness, and kurtosis, as well as finite-time first and second moments. An effective temperature is also computed through the fluctuation–dissipation theorem and show that equipartition theorem holds for all zero-mean kick distributions, including those leading to non-Gaussian stationary statistics. For the case of Gaussian-distributed active kicks, a re-entrant behavior from non-Gaussian to Gaussian stationary states and a heavy-tailed leptokurtic distribution across a wide range of parameters are found as seen in recent experimental studies. Further analysis reveals statistical signatures of the irreversible dynamics of the particle displacement in terms of the time asymmetry of cross-correlation functions. Fruits of the work is the development of an compact inference scheme that may allow experimentalists to extract the rate and moments of underlying shot-noise solely from the statistics the particle position.     

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.     

Anisotropic transport of microalgae Chlorella vulgaris in microfluidic channel

In this work, we study the regional dependence of transport behavior of microalgae Chlorella vulgaris inside microfluidic channel on applied fluid flow rate. The microalgae are treated as spherical naturally buoyant particles. Deviation from the normal diffusion or Brownian transport is characterized based on the scaling behavior of the mean square displacement(MSD) of the particle trajectories by resolving the displacements in the streamwise(flow) and perpendicular directions.The channel is divided into three different flow regions, namely center region of the channel and two near-wall boundaries and the particle motions are analyzed at different flow rates. We use the scaled Brownian motion to model the transitional characteristics in the scaling behavior of the MSDs. We find that there exist anisotropic anomalous transports in all the three flow regions with mixed sub-diffusive, normal and super-diffusive behavior in both longitudinal and transverse directions.     

Dumbbell transport and deflection in a spatially periodic potential

We present theoretical results on the deterministic and stochastic motion of a dumbbell carried by a uniform flow through a three-dimensional spatially periodic potential. Depending on parameters like the flow velocity, there are two different kinds of movement: transport along a potential valley and a stair-like motion oblique to the potential trenches. The crossover between these two regimes, as well as the deflection angle, depend on the size of the dumbbell. Moreover, thermal fluctuations cause a resonance-like variation in the deflection angle as a function of the dumbbell extension.     

Fractal dimensionality and microscopic analysis of the dynamics in simple liquids

Summary The idea to evaluate the ?average fractal dimension? of the motion in a condensed phase system, on the basis of the analysis of the fractal properties of the trajectories of its microscopic components has been further developed. The fractal dimension of particle trajectories, evaluated through the correlation density integral, is formally related with the self-part of the dynamic structure factorG _s(r, t) (the self-part of the Van Hove function); so far a bridge between fractal and thermodynamical properties has been built up.

---

Riassunto L’idea di stimare la ?dimensione frattale media? del moto in un sistema nella fase condensata è ulteriormente sviluppata mediante l’analisi delle proprietà frattali delle traiettorie delle componenti microscopiche. La dimensione frattale delle traiettorie delle particelle, stimata attraverso le correlazioni di densità, obbedisce ad una relazione formale con la self-part del fattore di struttura dinamicoG _s(r, t); in questo modo si mostra un legame tra le proprietà frattali e quelle termodinamiche.

---

Резюме Развивается идея оценить ?среднюю фрактальную размерность? движения в конденсированной фазовой системе на основе анализа фрактальных свойств частицы траекторий для микроскопических компонент. Фрактальная размерность траекторий, определенная через корреляционный интеграл плотности, подчиняется формальному соотношеию с собтвенной частью динамического структурного фактораG _s(r,t) (собственная часть функции Ван Хава). Указывается связь между фрактальнымк и термодинамическими свойствами.

     

Exploring the operation of a tiny heat engine

We model a tiny heat engine as a Brownian particle that moves in a viscous medium in a sawtooth potential (with or without load) assisted by alternately placed hot and cold heat baths along its path. We find closed form expression for the steady-state current as a function of the model parameters. This enables us to deal with the energetics of the model and evaluate either its efficiency or its coefficient of performance depending upon whether the model functions either as a heat engine or as a refrigerator, respectively. We also study the way current changes with changes in parameters of interest. When we plot the phase diagrams showing the way the model operates, we not only find regions where it functions as a heat engine and as a refrigerator but we also identify a region where the model functions as neither of the two.     

On the quantum langevin equation

The quantum Langevin equation is the Heisenberg equation of motion for the (operator) coordinate of a Brownian particle coupled to a heat bath. We give an elementary derivation of this equation for a simple coupled-oscillator model of the heat bath.Deceased.     

Unified approach to quantum fluctuations in tunnelling including dissipation

Summary A simple procedure for evaluating quantum fluctuations at zero temperature has been applied to derive the decay rate for a metastable state in strongly anharmonic potentials (quartic and cubic). We also derive the tunnelling splitting and the energy shift in symmetrical and nearly symmetrical double-well potentials. Dissipation is then considered for the decay of a metastable state, both in the limit of weak and strong damping.

---

Riassunto Un metodo semplificato per la valutazione delle fluttuazioni quantistiche, a temperatura zero, è stato impiegato per ottenere la velocità di decadimento di uno stato metastabile in potenziali fortemente anarmonici (quartico e cubico). Si ricavano pure la separazione per tunnelling e lo spostamento di energia nel caso di potenziale a doppio pozzo, simmetrico e quasi simmetrico. Si considerano poi effetti dissipati per il decadimento di uno stato metastabile, sia nel limite di debole che di forte smorzamento.

---

Резюме Простая процедура оценки квантовых флуктуаций при нулевой температуре применяется для вывода скорости распада метастабильного состояния в сильно ангармонических потенциалах (четвертого и кубичкского порядков). Мы также выводим расщепление за счет туннелирования и сдвиг энергии в потенциалах симметричной и почти симметричной двойной ямы. Затем рассматривается влияние диссипации при распаде метастабильного состояния в пределе слабого и сильного затухания.

     

Two-dimensional random-random walks: Dynamical exponents in a quenched directed model

This paper presents a study of the dynamics of a particle undergoing a directed random walk in a two-dimensional disordered square lattice. We derive the asymptotical behaviors of the coordinate and of the mean square displacement. All the dynamical exponents are calculated both in the normal and the anomalous regimes. It is shown that, as contrasted to the one-dimensional case, the so-called quenched and annealed diffusion constants indeed coincide.     

Kubo-Einstein relation for quantum Brownian motion in a periodic potential

Using a previously derived general formalism for a dissipative quantum particle in a boson bath, we prove that when the damping is Ohmic, the Kubo-Einstein relation between the diffusion constant and the linear mobilityD=kTM holds to all orders in V₀ for a periodic potentialV(x)=V ₀ cos(k)₀ x).     

自驱动颗粒体系中的熵力

在许多纳米复合材料体系中熵力(entropy force)是普遍存在的,但由于熵力的存在会导致纳米颗粒的凝聚从而降低其许多性能,因此在大多数情况下熵力的存在对体系并无益处,所以研究如何减小熵力对体系的影响是非常重要的.不带角速度的自驱动粒子在熵力作用下会集聚在纳米颗粒(或者纳米棒)周围,这会对纳米颗粒(或者纳米棒)产生很大的相互作用力.对于纳米颗粒,在不带角速度的自驱动粒子体系中存在着非常大的排斥力.而对于纳米棒,由于纳米棒内外的不对称性,使得两个纳米棒之间会产生吸引-排斥转变,同时这个吸引-排斥转变与纳米棒之间的距离有关.当自驱动粒子加上一个自转角速度ω之后,熵力的作用就大大减弱,纳米颗粒不再集聚.研究结果有助于对非平衡态下纳米颗粒(或纳米棒)之间熵相互作用力的认识.     

周期混合信号和噪声联合激励下的非对称双稳系统的随机共振

研究了周期混合信号和关联的乘性和加性噪声联合激励下的非对称双稳系统的随机共振现象.运用两态理论,给出了基频和高阶谐频信噪比的理论结果.发现对于基频和高阶谐频情形下均出现随机共振，并且高阶谐频存在抑制现象.同时研究了非对称系数和噪声强度以及噪声之间关联强度对信噪比的影响.     

周期场中非各态历经布朗运动

将自由状态下呈弹道扩散的非各态历经系统置于周期场中,进而将非各态历经布朗运动分为两类.第一类是阻尼核的Laplace变换的低频为零的系统,当温度远大于势垒高度时,系统平均能量的动能部分依赖粒子的初始速度分布;随温度降低,系统的各态历经性得到恢复.然后将第一类系统的稳定速度变量作为一个内部噪声,再去驱动一个自由布朗粒子,则阻尼核的Laplace变换在零频时为无穷大.结果发现,粒子扩散系数随温度的增加而趋于零,显示一种经典局域化特征,系统的渐进分布依赖于初始坐标分布.这是第二类非各态历经性运动,不能通过外加势而恢复. 关键词： 非各态历经 非Markov布朗运动 扩散系数 噪声谱     

Diffusion on a random comb: Distribution function of the survival probability

We investigate the distribution functionQ(P) describing the survival probability on a comb consisting of a backbone with lateral, randomly disconnected infinite branches. Two different regimes are analyzed in some detail: (i) at short times,Q(P) is shown to have a self-similar structure (devil's staircase); (ii) at large times, this function becomes smooth and tends toward a rather well-defined unit step function. The disorder-averaged survival probability <p ₀(t)> is expected to decrease ast ^–3/4 at large times, whereas the relative fluctuations of the sample-dependentp ₀(t) display a very slow decay in time, going to zero liket ^–1/8.