Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11007533 | Chaos, Solitons & Fractals | 2018 | 5 Pages |
Abstract
We give exact analytical results for diffusion with a power-law position dependent diffusion coefficient along the main channel (backbone) on a comb and grid comb structures. For the mean square displacement along the backbone of the comb we obtain behavior ãx2(t)ãâ¼t1/(2âα), where α is the power-law exponent of the position dependent diffusion coefficient D(x) â¼ |x|α. Depending on the value of α we observe different regimes, from anomalous subdiffusion, superdiffusion, and hyperdiffusion. For the case of the fractal grid we observe the mean square displacement, which depends on the fractal dimension of the structure of the backbones, i.e., ãx2(t)ãâ¼t(1+ν)/(2âα), where 0 < ν < 1 is the fractal dimension of the backbones structure. The reduced probability distribution functions for both cases are obtained by help of the Fox H-functions.
Keywords
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Trifce Sandev, Alexander Schulz, Holger Kantz, Alexander Iomin,