Nonequilibrium fluctuation-induced transport

Exactly solvable nonlinear model with two multiplicative Gaussian colored noises

“…The appropriate Fokker-Planck equation is derived and the two-noise Langevin equation can be reduced to a stochastically equivalent one-noise Langevin equation [13,14,15]. However, models which demonstrate, for example, nonequilibrium fluctuation-induced transport [16,17,18], double stochastic resonance [19], require to consider a colored noise source and a white noise source. The Ornstein-Uhlenbeck process with exponential correlation function is widely used as Gaussian colored noise.…”

A multiscale approach to Brownian motors

“…The small τ asymptotics for the effective drift were also studied in [2,8] for the model considered in this section and in [7,36] when the external fluctuations are given by a continuous time Markov chain. It was shown in [7,36] that, for the case of dichotomous noise, the small τ expansion for U ef f is valid only for sufficiently smooth potentials.…”

Overdamped thermal ratchets in one and more dimensions. Kinesin transport and protein folding

“…During the last few years there has been an increasing interest in studying the statistical behavior of the transport phenomena inside the cell carried out by protein motors and it has been proposed by several authors that ratchet models may be relevant in the description of these processes [1,2,8,9,10,19]. Protein motors are responsible for carrying diverse kind of vesicles from one site to another in the cell in a much more efficient way than the obtained by simple diffusion [12].…”

“…[1], or stochastic in nature, see Ref. [8]. In any case, any of those forces should be of zero average in time in order not to produce any biased current; in the present article we shall be concerned with external stochastic forces only.…”