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arXiv · 1612.00339

Anomalous diffusion on a fractal mesh

Trifce Sandev·Alexander Iomin·Holger Kantz
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Abstract

An exact analytical analysis of anomalous diffusion on a fractal mesh is presented. The fractal mesh structure is a direct product of two fractal sets which belong to a main branch of backbones and side branch of fingers. The fractal sets of both backbones and fingers are constructed on the entire (infinite) $y$ and $x$ axises. To this end we suggested a special algorithm of this special construction. The transport properties of the fractal mesh is studied, in particular, subdiffusion along the backbones is obtained with the dispersion relation $\langle x^2(t)\rangle\sim t^β$, where the transport exponent $β<1$ is determined by the fractal dimensions of both backbone and fingers. Superdiffusion with $β>1$ has been observed as well when the environment is controlled by means of a memory kernel.

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Trifce Sandev, Alexander Iomin, Holger Kantz. 2016-12-01. Anomalous diffusion on a fractal mesh. https://doi.org/10.1103/physreve.95.052107

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