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In the mean-field theory of magnetic fields, turbulent transport, i.e. the turbulent electromotive force, is described by a combination of the alpha effect and turbulent magnetic diffusion, which are usually assumed to be proportional respectively to the mean field and its spatial derivatives. For a passive scalar there is just turbulent diffusion, where the mean flux of concentration depends on the gradient of the mean concentration. However, these proportionalities are approximations that are valid only if the mean field or the mean concentration vary slowly in time. Examples are presented where turbulent transport possesses memory, i.e. where it depends crucially on the past history of the mean field. Such effects are captured by replacing turbulent transport coefficients with time integral kernels, resulting in transport coefficients that depend effectively on the frequency or the growth rate of the mean field itself. In this paper we perform numerical experiments to find the characteristic timescale (or memory length) of this effect as well as simple analytical models of the integral kernels in the case of passive scalar concentrations and kinematic dynamos. The integral kernels can then be used to find self-consistent growth or decay rates of the mean fields. In mean-field dynamos the growth rates and cycle periods based on steady state values of alpha effect and turbulent diffusivity can be quite different from the actual values.
We analyze how the turbulent transport of $mathbf{E}times mathbf{B}$ type in magnetically confined plasmas is affected by intermittent features of turbulence. The latter are captured by the non-Gaussian distribution $P(phi)$ of the turbulent electric
Compressibility effects in a turbulent transport of temperature field are investigated applying the quasi-linear approach for small Peclet numbers and the spectral $tau$ approach for large Peclet numbers. Compressibility of a fluid flow reduces the t
We demonstrate the phenomenon of cumulative inertia in intracellular transport involving multiple motor proteins in human epithelial cells by measuring the empirical survival probability of cargoes on the microtubule and their detachment rates. We fo
We discuss memory effects in the conductance of hopping insulators due to slow rearrangements of many-electron clusters leading to formation of polarons close to the electron hopping sites. An abrupt change in the gate voltage and corresponding shift
The effect of oscillatory shear flows on turbulent transport of passive scalar fields is studied by numerical computations based on the results provided by E. Kim [emph{Physics of Plasmas}, {bf 13}, 022308, 2006]. Turbulent diffusion is found to depe