Current transport and mass separation for an asymmetric fluctuation system with correlated noises

We discuss the transport of an underdamped particle driven by an external fluctuation force in a spatially periodic asymmetric potential with correlated noises. The corresponding mathematical model is established. The movement of the steady current of an underdamped particle is presented by the method of the numerical simulation. It is indicated that the value of the current may be negative, zero, or positive. The external fluctuation force and correlated noises can effect the current direction. Under the appropriate parameters, the correlated noises intensity may even raise a reversal of the current.Besides, we have noticed a phenomenon that particles with different weight have different directions during movement by the impact of the correlated noises and external fluctuation force. Therefore, the Brownian particles can be effectively separated according to their masses.     

Effect of correlated noises on Brownian motor

The Brownian motor operating between two correlated Gaussian white noises was investigated. The expressions of the current and the energy conversion efficiency of the Brownian motor were analytically derived by exploiting adiabatic approximation. The results indicates that: (i) Regulating the correlation strength λ between the two noises and the ratio D₂/D₁ of the two noise intensities can change the rotational direction of the motor; (ii) For the smaller D₂/D₁, an optimal λ can make the positive current and the efficiency be maximal, and for the smaller λ, an optimal D₂/D₁ also let the positive current be maximal. The results were explained from a viewpoint of modified potentials. The study is of important significance in the aspect of controlling the operation of the Brownian motor.     

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.     

Noise-induced transport in a periodic system driven by Gaussian white noises with intensive cross-correlation

An analytical investigation of overdamped Brownian particle in a periodic system driven by intensive cross-correlated Gaussian white noises is presented. The center idea of this Letter is to construct an exact soluble model to exhibit the possible new effect of the cross-correlated Gaussian white noises on the noise-induced transport. The model clearly shows the following new aspects of this transport: (1) There is one and only extreme in the J–Q curve for the case of weakly cross-correlated noises here J and Q denote the current and multiplicative noise intensity, respectively. (2) When the two noises are intensive correlative, the J–Q curve behaves three extrema. (3) The J–Q curve exhibits a giant suppression plateau between the two maxima as the noise correlation coefficient is increased further. (4) The direction of the current is controlled by two parameters.     

Entropic noise induced stability and double entropic stochastic resonance induced by correlated noises

For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time (MFPT) and the spectral power amplification (SPA) are obtained, respectively. Based on the numerical computations, it is found that: (i) The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises (λ>0), this maximum for MFPT shows the characteristic of the entropic noise induced stability (ENIS) effect. The intensity λ of correlations between two noises can enhance the ENIS effect. (ii) The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.     

Transport properties of coupled Brownian particles confined to a microchannel in an asymmetric periodic potential

On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we investigated an overdamped Brownian motion of two coupled particles with an asymmetric periodic potential in a two-dimensional microchannel theoretically and numerically, to reveal the dynamical mechanism of cooperative transport of particles with two heads, where the interactions between two particles are taken into consideration. Moreover, while moving in a confined structure, Brownian particles also could exhibit peculiar kinetic behavior. The dependence of directed current on various parameters is systematically studied. Our results indicate that the direction of motion can be reversed by modulating the coupling strength, free length, and microchannel width. In addition, we have achieved the conditions of forward motion in this study. That is, when the interparticle average horizontal interval Δx > 0.25L, where L is the spatial period of the external potential, the forward motion of coupled Brownian particles effected by the synchronized noise and confined to a microchannel can be generated in the strong-coupling case.     

Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam

We calculate the radiation force that is exerted by a focused continuous-wave Gaussian beam of wavelength λ on a non-absorbing nonlinear particle of radius a ? 50λ/π. The refractive index of the mechanically-rigid particle is proportional to the incident intensity according to the electro-optic Kerr effect. The force consists of two components representing the contributions of the electromagnetic field gradient and the light scattered by the Kerr particle. The focused intensity distribution is determined using expressions for the six electromagnetic components that are corrected to the fifth order in the numerical aperture (NA) of the focusing objective lens. We found that for particles with a < λ/21.28, the trapping force is dominated by the gradient force and the axial trapping force is symmetric about the geometrical focus. The two contributions are comparable with larger particles and the axial trapping force becomes asymmetric with its zero location displaced away from the focus and towards the beam propagation direction. We study the trapping force behavior versus incident beam power, NA, λ, and relative refractive index between the surrounding liquid and the particle. We also examine the confinement of a Kerr particle that exhibits Brownian motion in a focused beam. Numerical results show that the Kerr effect increases the trapping force strength and significantly improves the confinement of Brownian particles.     

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     

Effect of the Noise Correlation Time on the Stationary Current of Brownian Particle in a Spatially Symmetric Periodic Potential

We investigate the noise-induced transport of Brownian particle in a deterministic spatial symmetrical periodic potential driven by colored cross correlation between a multiplicative white noise and an additive white noise. We derive the general formula of the stationary current. Based on numerical computation, we found that directed motion of the Brownian particles can be induced by the correlation time τ of cross correlation between the multiplicative noise and the additive noise and the current reversal and the direction of the current is controlled by the τ.     

Current Reversal Due to Coupling Between Asymmetrical Driving Force and Ratchet Potential

Transport of a Brownian particle moving in a periodic potential is investigated in the presence of an asymmetric unbiased external force. The asymmetry of the external force and the asymmetry of the potential are the two ways of inducing a net current. It is found that the competition of the spatial asymmetry of potential with the temporal asymmetry of the external force leads to the phenomena like current reversal. The competition between the two opposite driving factors is a necessary but not a sufficient condition for current reversals.     

Transport enhancement and efficiency optimization in two heat reservoir ratchets

We study a Brownian motor moving in a sawtooth potential in the presence of an external driving force and two heat reservoirs. Based on the corresponding Fokker--Planck equation, the analytical expressions of the current and efficiency in the quasi-steady-state limit are obtained. The effects of temperature difference and the amplitude of the external driving force on the current and efficiency are discussed, respectively. The following is our findings. (i) The current increases with both δ and A. In other words, δ and A enhance the transport of the Brownian motor. (ii) The competition between the temperature difference and the amplitude of the external driving force can lead to efficiency optimization. The efficiency is a peaked function of temperature, i.e., δ>0 and a lower amplitude value of the external driving force is necessary for efficiency optimization. (iii) The efficiency increases with δ, and decreases with A. δ and A play opposite roles with respect to the efficiency, which indicates that δ enhances the efficiency of energy transformation while A weakens it.     

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.      

Collective dynamics of two-dimensional coupled Brownian motors

The transport properties of coupled Brownian particles in a two-dimensional rocking ratchet are investigated via Langevin simulation. The results show that the average center-of-mass velocity is multi-peaks function of the frequency of the driving force. Furthermore, in the 2D coupled Brownian motor system there are the collective effect and ratchet behavior, which can switch depending on the frequency of driving force. It turns out that the cooperative effect between the interaction of coupled particles and external rocking driving force facilitates collective directional motion and energy conversion.     

Cooperative dynamics of coupled motor–cargoes system with stochastic interactions in the crowded environment

In this study, we investigate the cooperative transport behaviors of coupled motor–cargoes system, in which multiple passive cargoes stochastically interact with one active Brownian motor. The environment with stochastic interactions is characterized by the concentration (reflecting the cargo’s number in unit volume) and switching rate (reflecting the interacting stability between motor and cargoes), based on which the stationary multiple-state process can be employed to describe the fluctuating-cargo state in the coupled system. By analyzing the average probability current of decoupled system in the thermodynamic limit, we effectively study the possibility of cooperative transport through stochastic cargoes to behave rich dynamical behaviors, including the directed current, current reversal, stochastic resonance (SR) and stochastic inhibition (SI), inverse SR and SI, even without the effect of external driving force. Based on numerical results, we systematically discuss the transport dependence on various parameters, including the cargo concentration in the crowded environment, cargo capacity of the motor, driving amplitude of external periodic force, and medium temperature. Obviously, the sensitivity of transport process to parameter changes can be used by the environment to regulate its cargo traffic, which also provides latent support for manipulating the transport performance and optimizing the coupled structure in artificial nano-machines.     

Intensity correlation function of an optical bistable system subjected to cross-correlated noises

The normalized correlation function C(s) of an optical bistable system driven by cross-correlated noises is investigated. Based on the numerical computation and simulation results, it is found that: (1) The intensity of multiplicative noise D and the intensity of additive noise Q play opposite roles on C(s), i.e., D enhances the rate of fluctuation decay of transmitted light intensity and Q slows down the rate of fluctuation decay of the transmitted light intensity; (2) The strength of correlations between the multiplicative and additive noises λ slows down the rate of decay of intensity fluctuation; (3) For the case of positive correlated noises (λ>0), the increasing cooperativity parameter C slows down the rate of decay of intensity fluctuation firstly and then enhances it; (4) For the case of negative correlated noises (λ<0), the increasing C almost does not affect the rate of decay of intensity fluctuation firstly and then enhances it.     

Stochastic resonance, reverse-resonance, and resonant activation induced by a multi-state noise

In this paper, we investigate the periodic response for a linear system driven by a multiplicative multi-state noise (which is composed of the multiplication of two dichotomous noises) to an input temporal oscillatory signal, and the escape of Brownian particles over the fluctuating potential barrier for a system with a piece-wise linear potential and driven by an additive multi-state noise (which is also composed of the multiplication of two dichotomous noises). For the first system, we get the stochastic resonance phenomenon for the amplitude of the periodic response vs. the two dichotomous noise strengths, and the phenomenon of reverse-resonance for the amplitude of the periodic response vs. k, which represents the asymmetry degree of the dichotomous noises. For the second system, we obtain the resonant activation phenomenon, for which the mean first passage time of the Brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi-state noise.     

Transportation of Two Coupled Particles in an Asymmetric Saw-Tooth Potential

Based on a simple model,we theoretically show the transport behaviors of two harmonically coupled Brownian particles in an asymmetric saw-tooth potential with two slopes.The coupled particles are subject to stochastic fluctuations.It is found that when the equilibrium distance of the coupled particles is between the two slopes of the potential,the transport direction of the coupled particles will be reversed with a certain harmonic coupling strength.This current reversal can be easily understood with the near rigid approximation,where the two coupled particles can be regarded as a single particle in an effective potential.Compared with the original saw-tooth potential,the asymmetry of the effective potential could be reversed when the equilibrium distance is between the two slopes of the original potential,which results in the current reversal.     

Statistical properties of turbulence in a toroidal magnetized ECR plasma

The statistical analyses of fluctuation data measured by electrostatic-probe arrays clearly show that the self-organized criticality (SOC) avalanches are not the dominant behaviors in a toroidal ECR plasma in the SMT (Simple Magnetic Torus) mode of KT-5D device. The f⁻¹ index region in the auto-correlation spectra of the floating potential Vf and the ion saturation current Is, which is a fingerprint of a SOC system, ranges only in a narrow frequency band. By investigating the Hurst exponents at increasingly coarse grained time series, we find that at a time scale of τ>100 μs, there exists no or a very weak long-range correlation over two decades in τ. The difference between the PDFs of Is and Vf clearly shows a more global nature of the latter. The transport flux induced by the turbulence suggests that the natural intermittency of turbulent transport maybe independent of the avalanche induced by near criticality. The drift instability is dominant in a SMT plasma generated by means of ECR discharges.     

Collective transport in locally asymmetric periodic structures

In this paper we give an overview of the cooperative effects in fluctuation driven transport arising from the interaction of a large number of particles. (i) First, we study a model with finite-sized, overdamped Brownian particles interacting via hard-core repulsion. Computer simulations and theoretical calculations reveal a number of novel cooperative transport phenomena in this system, including the reversal of direction of the net current as the particle density is increased, and a very strong and complex dependence of the average velocity on both the size and the average distance of the particles. (ii) Next, we consider the cooperation of a collection of motors rigidly attached to a backbone. This system possesses dynamical phase transition allowing spontaneous directed motion even if the system is spatially symmetric. (iii) Finally, we report on an experimental investigation exploring the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits complex collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. (c) 1998 American Institute of Physics.     

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