Brownian diode: Molecular motor based on a semi-permeable Brownian particle with internal potential drop

A model of an autonomous isothermal Brownian motor with an internal propulsion mechanism is considered. The motor is a Brownian particle which is semi-transparent for molecules of surrounding ideal gas. Molecular passage through the particle is controlled by a potential similar to that in the transition rate theory, i.e. characterized by two stationary states with a finite energy difference separated by a potential barrier. The internal potential drop maintains the diode-like asymmetry of molecular fluxes through the particle, which results in the particle?s stationary drift.     

Mean first passage time of active Brownian particle in one dimension

We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modelled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate r on the mean first passage time to a fixed target of a single free active Brownian particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate r* for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.     

Brownian local time and quantum mechanics

LetV be any (sufficiently regular) attractive potential in one and two dimensions. We make rigorous an argument of M. Kac [1], relating the recurrence of the Brownian motion to the existence of at least one bound state for the quantum HamiltonianH = –(/2)+ V.     

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.     

Tunneling and transport problems for a quantum mechanical Brownian particle

The Kanai model of a quantum mechanical Brownian particle is used to examine the effect of interactions between particles and their environment. Random forces cause the thermalization of the particle. Reflection of a particle from a step barrier is analyzed. The problem of tunneling of the Brownian particle through a rectangular barrier is solved. Finally, a solution for a Brownian particle in a box is presented.     

Effect of time delay in FitzHugh-Nagumo neural model with correlations between multiplicative and additive noises

We study the effect of time delay in the FitzHugh-Nagumo neural model with correlations between multiplicative and additive noise terms. Based on the corresponding Fokker-Planck equation, the explicit expressions of the stationary probability distribution function (SPDF), the mean first passage time (MFPT) and the signal-to-noise ratio (SNR) are obtained, respectively. Research results show that: (i) the system undergoes a succession of two phase transitions (i.e., the reentrance phenomenon) as the noise correlation parameter is increased and a (single) phase transition as the time delay is increased. (ii) The MFPT as a function of the multiplicative noise intensity exhibits a maximum. This maximum for MFPT identifies the noise enhanced stability (NES) effect, the noise correlation parameter intensifies the NES effect while the time delay, and the additive noise intensity weakens it. (iii) The existence of a maximum in the SNR as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance (SR) phenomenon, the noise correlation parameter enhances the SR while the time delay, and the additive noise intensity weaken it.     

Escape rate of an active Brownian particle in a rough potential

We discuss the escape problem with the consideration of both the activity of particles and the roughness of potentials. We derive analytic expressions for the escape rate of an active Brownian particle in two types of rough potentials by employing the effective equilibrium approach and the Zwanzig method. We find that activity enhances the escape rate, but both the oscillating perturbation and the random amplitude hinder escaping.     

Missing ordinal patterns in correlated noises

Recent research aiming at the distinction between deterministic or stochastic behavior in observational time series has looked into the properties of the “ordinal patterns” [C. Bandt, B. Pompe, Phys. Rev. Lett. 88 (2002) 174102]. In particular, new insight has been obtained considering the emergence of the so-called “forbidden ordinal patterns” [J.M. Amigó, S. Zambrano, M.A. F Sanjuán, Europhys. Lett. 79 (2007) 50001]. It was shown that deterministic one-dimensional maps always have forbidden ordinal patterns, in contrast with time series generated by an unconstrained stochastic process in which all the patterns appear with probability one. Techniques based on the comparison of this property in an observational time series and in white Gaussian noise were implemented. However, the comparison with correlated stochastic processes was not considered. In this paper we used the concept of “missing ordinal patterns” to study their decay rate as a function of the time series length in three stochastic processes with different degrees of correlation: fractional Brownian motion, fractional Gaussian noise and, noises with f^−k power spectrum. We show that the decay rate of “missing ordinal patterns” in these processes depend on their correlation structures. We finally discuss the implications of the present results for the use of these properties as a tool for distinguishing deterministic from stochastic processes.     

Brownian motion of a classical particle in quantum environment

The Klein–Kramers equation, governing the Brownian motion of a classical particle in a quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.     

Effects of diversity and coupling on transport properties of globally coupled active Brownian particles

Based on recent work [B. Lindner and E. M., Nicola, Phys. Rev. Lett. 101 (2008) 190603], the transport of N$N$ globally coupled Brownian motors with diversity is investigated. By applying the mean-field approximation, the effects of the diversity disturbance and the coupling strength on the transport of the coupled system are discussed both theoretically and numerically. It is found that the diversity reduces the diffusion dramatically for small bias and increases the diffusion gradually for large bias. The collective motion shows a resonant dependence on the coupling strength in a region of small bias.     

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.     

Brownian motion and correlation in particle image velocimetry

In particle image velocimetry applications involving either low velocities or small seed particles, Brownian motion can be significant. This paper addresses the effects of Brownian motion. First, general equations describing cross-correlation particle image velocimetry are derived that include Brownian motion. When light-sheet illumination particle image velocimetry (PIV) is used Brownian motion diminishes the signal strength. A parameter describing this effect is introduced, and a weighting function describing the contribution to the measured velocity as a function of position is derived. The latter is unaffected by Brownian motion. Microscopic PIV Brownian motion also diminishes the signal strength. The weighting function for microscopic PIV is found to depend on Brownian motion, thus affecting an important experimental parameter, the depth of correlation. For both light-sheet illumination and microscopic PIV, a major consequence of Brownian motion is the spreading of the correlation signal peak. Because the magnitude of the spreading is dependent on temperature, PIV can, in principle, be used to simultaneously measure velocity and temperature. The location of the signal peak provides the velocity data, while the spreading of the peak yields temperature.     

基于自回归模型的光阱中粒子运动模拟

通过分析光阱中颗粒位移信号特性, 建立描述粒子受限布朗运动过程的自回归模型, 进而提出了一种基于自回归模型的光阱中颗粒运动信号模拟的新方法. 对半径为1 μm的粒子处于光阱刚度分别为10, 20, 50 pN/μm 光阱时的位移信号进行了模拟, 得到的模拟位移信号的自相关函数与理论值相一致. 为了进一步阐明自回归模型的有效性, 在相同光阱参数下, 分别采用自回归模型与蒙特卡罗方法模拟光阱中微粒的位移信号, 采用功率谱法分别对两种模拟方法所得的微粒位移标定光阱刚度, 结果表明自回归模型方法能够取得和蒙特卡洛法相同的精度. 因此, 本文为分析光阱中粒子的随机运动提出了一种新的模拟方法, 可以用来对光阱中的噪声及特性进行分析. 关键词： 光阱 布朗运动 信号模拟 自回归模型     

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.     

Microscopic derivation of non-Markovian thermalization of a Brownian particle

In this paper, the first microscopic approach to Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended Boltzmann equation, which describes correctly the interaction with the fluid, we derive systematically via multiple-time-scale analysis a reduced equation controlling the thermalization of the B particle, i.e., the relaxation toward the Maxwell distribution in velocity space. In contradistinction to the Fokker-Planck equation, the derived new evolution equation is nonlocal both in time and in velocity space, owing to correlated recollision events between the fluid and particle B. In the long-time limit, it describes a non-Markovian generalized Ornstein-Uhlenbeck process. However, in spite of this complex dynamical behavior, the Stokes-Einstein law relating the friction and diffusion coefficients is shown to remain valid. A microscopic expression for the friction coefficient is derived, which acquires the form of the Stokes law in the limit where the meanfree path in the gas is small compared to the radius of particle B.Knowing the interest of Matthieu Ernst in the subtle and fundamental problems of kinetic theory, we have the pleasure to dedicate this study to him.     

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.     

Effects of time delay on stochastic resonance of the stock prices in financial system

The effect of time delay on stochastic resonance of the stock prices in finance system was investigated. The time delay is introduced into the Heston model driven by the extrinsic and intrinsic periodic information for stock price. The signal power amplification (SPA) was calculated by numerical simulation. The results indicate that an optimal critical value of delay time maximally enhances the reverse-resonance in the behaviors of SPA as a function of long-run variance of volatility or cross correlation coefficient between noises for both cases of intrinsic and extrinsic periodic information. Moreover, in both cases, being a critical value in the delay time, when the delay time takes value below the critical value, reverse-resonance increases with the delay time increasing, however, when the delay time takes value above the critical value, the reverse-resonance decrease with the delay time increasing.     

Spherical particle Brownian motion in viscous medium as non-Markovian random process

The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered.     

活性布朗粒子运动的稳态解

拟可积Hamilton系统随机平均法可以用来研究活性布朗粒子运动.介绍了该随机平均法，利用它详细求解了布朗粒子运动的动力学方程，该方程描述了活性布朗粒子在平面上的运动，粒子受到的激励是Gaussian白噪声，受到的阻尼是Schienbein-Gruler速度依赖的磨擦模型.通过与数字模拟和与实验数据的比较，证明所得稳态解正确.对于Rayleigh和Erdamnn速度依赖的磨擦模型，也给出了稳态解. 关键词： 活性布朗粒子 拟可积Hamilton系统随机平均法 可积性 稳态解