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Anomalous diffusion and charge relaxation on comb model: exact solutions

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  • Arkhincheev, V.E

Abstract

The random walks on the comb structure are considered. It is shown that due to fingers a diffusion has an anomalous character, that is an r.m.s. displacement depends on time by a power way with exponent 12. The generalized diffusion equation for an anomalous case is deduced. It essentially differs from a usual diffusion equation in the continuity equation form: instead of the first time derivative, the time derivative of fractal order 12 appears. In the second part the charge relaxation on the comb structure is studied. A non-Maxwell character is established. The reason is that the electric field has three components, but a charge may relax only along some conducting lines.

Suggested Citation

  • Arkhincheev, V.E, 2000. "Anomalous diffusion and charge relaxation on comb model: exact solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 304-314.
    • Handle: RePEc:eee:phsmap:v:280:y:2000:i:3:p:304-314
    DOI: 10.1016/S0378-4371(99)00593-2
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    Cited by:

    1. Endre Csáki & Antónia Földes, 2020. "Random Walks on Comb-Type Subsets of $$\mathbb {Z}^2$$ Z 2," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2233-2257, December.
    2. Trifce Sandev & Viktor Domazetoski & Alexander Iomin & Ljupco Kocarev, 2021. "Diffusion–Advection Equations on a Comb: Resetting and Random Search," Mathematics, MDPI, vol. 9(3), pages 1-24, January.
    3. Csáki, Endre & Csörgo, Miklós & Földes, Antónia & Révész, Pál, 2011. "On the local time of random walk on the 2-dimensional comb," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1290-1314, June.

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