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Anomalous diffusion in umbrella comb

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  • Iomin, A.

Abstract

Anomalous transport in a circular comb is studied. The circular motion takes place for a fixed radius, while radii are continuously distributed along the circle. Two scenarios of the anomalous transport are considered. The first scenario corresponds to the conformal mapping of a 2D comb Fokker-Planck equation on the circular comb. This topologically constraint motion is named umbrella comb model. In this case, the reflecting boundary conditions are imposed on the circular motion, while the radial motion corresponds to geometric Brownian motion with vanishing to zero boundary conditions on infinity. The radial diffusion is described by the log-normal distribution, which corresponds to exponentially fast motion with the mean squared displacement (MSD) of the order of et. The second scenario corresponds to the circular diffusion with periodic boundary conditions and the outward radial diffusion with vanishing to zero boundary conditions at infinity. In this case the radial motion corresponds to normal diffusion. The circular motion in both scenarios is a superposition of cosine functions that results in the stationary Bernoulli polynomials for the probability distributions.

Suggested Citation

  • Iomin, A., 2021. "Anomalous diffusion in umbrella comb," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308808
    DOI: 10.1016/j.chaos.2020.110488
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. 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.
    2. Suleiman, Kheder & Song, Qixuan & Zhang, Xuelan & Liu, Shengna & Zheng, Liancun, 2022. "Anomalous diffusion in a circular comb with external velocity field," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Liu, Lin & Chen, Siyu & Bao, Chunxu & Feng, Libo & Zheng, Liancun & Zhu, Jing & Zhang, Jiangshan, 2023. "Analysis of the absorbing boundary conditions for anomalous diffusion in comb model with Cattaneo model in an unbounded region," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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