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Anomalous diffusion in inclined comb-branch structure

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  • Wang, Zhaoyang
  • Zheng, Liancun

Abstract

This paper presents a research for anomalous diffusion in inclined comb branch structure which has the potential in modeling many problems in medical science and nature. Mathematical model are formulated for two types of branch diffusion, i.e., bilateral branch and unilateral branch. Exact solutions are obtained by Laplace transform and separate variable techniques. The particle distribution on the backbone is represented by the Fox H-function. Results show that both types of diffusion are anomalous sub-diffusion and the inclination angle of branches has remarkable effect on particles transport behavior. For bilateral branch, the total number of particles on x axis is 〈P〉=sinθ∕[2(πt)1∕2], the mean square displacement (MSD) is 〈ξ2(t)〉=(πt)1∕2∕sinθ with invariant 〈ξ2P〉=1∕2, and with a symmetric particle distribution. For unilateral branch, the total number of particles on ξ axis is twice to that of bilateral branch diffusion. Moreover, some other characteristics of solutions are also graphically analyzed in detail.

Suggested Citation

  • Wang, Zhaoyang & Zheng, Liancun, 2020. "Anomalous diffusion in inclined comb-branch structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    • Handle: RePEc:eee:phsmap:v:549:y:2020:i:c:s0378437119321594
    DOI: 10.1016/j.physa.2019.123889
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    References listed on IDEAS

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    1. Arkhincheev, V.E., 2002. "Diffusion on random comb structure: effective medium approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(1), pages 131-141.
    2. Sandev, Trifce & Schulz, Alexander & Kantz, Holger & Iomin, Alexander, 2018. "Heterogeneous diffusion in comb and fractal grid structures," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 551-555.
    3. Qi, Haitao & Jiang, Xiaoyun, 2011. "Solutions of the space-time fractional Cattaneo diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1876-1883.
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