2014/10/31 by Trifce Sandev, Alexander Iomin, Holger Kantz +1 · 40 citations
Mathematics · Physics and Astronomy · #Anomalous diffusion #Combinatorics #Computer science #Diffusion #Dimension (graph theory) #Exponent #Fractal #Fractal dimension #Fractional Differential Equations Solutions #Generalization #Geometry #Grid #Innovation diffusion #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.91.032108
published in Physical Review E 91(3), 032108 (American Physical Society) · 6 pages, 1 figure
openalex publication_date 2015/03/04 · arxiv created 2015/03/05 · arxiv updated 2015/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.