Fractional diffusion on a fractal grid comb

TL;DR

This paper analyzes a generalized grid comb model with multiple backbones, deriving exact expressions for the anomalous diffusion transport exponent, revealing dependence on the number of backbones and their fractal dimension.

Contribution

It provides an exact analytical evaluation of the transport exponent in a generalized comb model with multiple backbones, highlighting the impact of fractal structure on diffusion behavior.

Findings

Transport exponent remains unchanged for finite number of backbones.

Transport exponent depends on fractal dimension for infinite backbones.

Analytical expressions for anomalous diffusion in complex grid structures.

Abstract

A grid comb model is a generalization of the well known comb model, and it consists of $N$ backbones. For $N=1$ the system reduces to the comb model where subdiffusion takes place with the transport exponent $1/2$. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that for an arbitrarily large but finite number of backbones the transport exponent does not change. Contrary to that, for an infinite number of backbones, the transport exponent depends on the fractal dimension of the backbone structure.