The effect of the junction model on the anomalous diffusion in the 3D comb structure

TL;DR

This study examines how different junction models affect anomalous diffusion in 3D comb structures, revealing that rejuvenating and non-rejuvenating models lead to distinct diffusion behaviors along the backbone.

Contribution

It introduces a comparison between rejuvenating and non-rejuvenating junction models in 3D comb structures with anomalous sidebranch diffusion, highlighting their impact on diffusion dynamics.

Findings

Rejuvenating junctions cause only prefactor changes in ultra-slow diffusion.

Non-rejuvenating junctions lead to faster power-law subdiffusion.

Certain special cases were analyzed using generalized Fokker-Planck equations.

Abstract

The diffusion in the comb structures is a popular model of geometrically induced anomalous diffusion. In the present work we concentrate on the diffusion along the backbone in a system where sidebranches are planes, and the diffusion thereon is anomalous and described by continuous time random walks (CTRW). We show that the mean squared displacement (MSD) in the backbone of the comb behaves differently depending on whether the waiting time periods in the sidebranches are reset after the step in the backbone is done (a rejuvenating junction model), or not (a non-rejuvenating junction model). In the rejuvenating case the subdiffusion in the sidebranches only changes the prefactor in the ultra-slow (logarithmic) diffusion along the backbone, while in the non-rejuvenating case the ultraslow, logarithmic subdiffusion is changed to a much faster power-law subdiffusion (with a logarithmic correction) as it was found earlier by Iomin and Mendez [Chaos Solitons and Fractals 2016; 82:142]. Moreover, in the first case the result does not change if the diffusion in the backbone is itself anomalous, while in the second case it does. Two of the special cases of the considered models (the non-rejuvenating junction under normal diffusion in the backbone, and rejuvenating junction for the same waiting time distribution in the sidebranches and in junction points) were also investigated within the approach based on the corresponding generalized Fokker-Planck equations.