Anomalous diffusion in disordered multi-channel systems

Abstract

We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong disorder renormalization group method and Monte Carlo simulations are used. Generally, we observe anomalous diffusion, where the average distance travelled by the particle, [ x(t) ] av , has a power-law time-dependence [ x(t) ] av ∼ t µK (v) , with a diffusion exponent 0 ≤ µ K (v) ≤ 1. In the presence of left-right symmetry of the distribution of random rates the recurrent point of the multi-channel system is independent of K, and the diffusion exponent is found to increase with K and decrease with v. In the absence of this symmetry, the recurrent point may be shifted with K and the current can be reversed by varying the lane change rate v.

Phase segregation and transport in a two-species multi-lane system

“…It remains to be seen whether in that case, the system's behavior differs markedly from the behavior described in Ref. [27,28], where systems with boundary input of particles and uncorrelated switching between lanes was analyzed and shock localization in the bulk has been predicted. Suitable extensions of this model would be useful in the context of organelle intracellular transport along microtubules where oppositely directed particles are involved.…”

“…In order to circumvent these drawbacks, we present a two lane model which incorporates bidirectionality and correlated lane switching processes, wherein oppositely directed particles switch lanes with certain finite probability on encountering each other and they are also allowed to pass through each other with certain finite probability on the same lane. Different mechanisms of multiple-lane driven transport have been proposed and studied theoretically [21][22][23][24][25][26][27][28][29][30][31][32][33]. While inter-lane switching has not been considered in Refs.…”

Strong disorder RG approach – a short review of recent developments

“…The main principle is the iterative elimination of the fastest degree of freedom to obtain the effective dynamics for the slowest ones. In this field, new developments since 2005 include one-dimensional random walks with dilute absorbers [251] or with long-range connections [252], random walks on strips [253,254] and on arbitrary networks [255], and in two-dimensional selfaffine random potentials [256].…”

Transient Electromagnetic Method in the Keritis basin (Crete, Greece): Evidence of hierarchy in a complex geological structure in view of Tsallis distribution.

“…In contrast, in real earth we observe variations in spatial heterogeneity and thus an anomalous diffusion of the induction current. The anomalous diffusion can be generated by a random walk within the complex geometry of a disordered system [Hamrouni andAbdenndher 2016, Juhász andIglói 2010]. The parameter β introduced in the definition of anomalous conductivity, express the ability of fractal transport of charge carriers within a complex geometry (disordered medium) whose heterogeneities obey a spatial power law distribution.…”