Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Anomalous Diffusion (joint session DY/ CPP)

DY 3.8: Vortrag

Montag, 16. März 2015, 11:30–11:45, BH-N 334

Fractal grid comb model — •Trifce Sandev^1,2, Alexander Iomin^2,3, and Holger Kantz² — ¹Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia — ²Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany — ³Department of Physics, Technion, Haifa 32000, Israel

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 (fractal grid comb), the transport exponent depends on the fractal dimension of the backbone structure. Thus, the grid comb model, suggested here, establishes an exact relation between a complicated fractal geometry and the transport exponent. Such a product structure of backbones times comb is an idealization of more complex comb-like fractal networks, as they may appear e.g., in certain anisotropic porous media.