Fractional diffusion on a fractal grid comb

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.

6 pages, 1 figure

References in corpus (10)

• Observation of anomalous diffusion and fractional self-similarity in one dimension
• Fractional Generalization of Liouville Equations
• Hot carrier diffusion in graphene
• Comb-like models for transport along spiny dendrites
• Paradoxes of Subdiffusive Infiltration in Disordered Systems
• Subdiffusion on a Fractal Comb
• Negative superdiffusion due to the inhomogeneous convection
• Anomalous transport of a tracer on percolating clusters
• Occupation times on a comb with ramified teeth
• Superdiffusive comb: Application to experimental observation of anomalous diffusion in one dimension

Cited by in corpus (8)

• Comb model with slow and ultraslow diffusion
• Heterogeneous diffusion in comb and fractal grid structures
• Anomalous diffusion on a fractal mesh
• Ornstein-Uhlenbeck process and generalizations: particle's dynamics under comb constraints and stochastic resetting
• Lévy processes on a generalized fractal comb
• Quenched and Annealed Disorder Mechanisms in Comb-Models with Fractional Operators
• Probability distribution functions of sub- and super-diffusive systems
• Anomalous diffusion and FRAP dynamics in the random comb model