IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v549y2020ics0378437119321594.html
   My bibliography  Save this article

Anomalous diffusion in inclined comb-branch structure

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119321594
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123889?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Arkhincheev, V.E., 2020. "The capture of particles on absorbing traps in the medium with anomalous diffusion: The effective fractional order diffusion equation and the slow temporal asymptotic of survival probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    3. Tawfik, Ashraf M. & Abdelhamid, Hamdi M., 2021. "Generalized fractional diffusion equation with arbitrary time varying diffusivity," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    4. Awad, Emad, 2019. "On the time-fractional Cattaneo equation of distributed order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 210-233.
    5. Guo, Wei & Liu, Ying-Zhou & Huang, Fei-Jie & Shi, Hong-Da & Du, Lu-Chun, 2023. "Brownian particles in a periodic potential corrugated by disorder: Anomalous diffusion and ergodicity breaking," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Khalili Golmankhaneh, Alireza & Ontiveros, Lilián Aurora Ochoa, 2023. "Fractal calculus approach to diffusion on fractal combs," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. Tawfik, Ashraf M. & Elkamash, I.S., 2022. "On the correlation between Kappa and Lévy stable distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
    8. Liu, Zhengguang & Cheng, Aijie & Li, Xiaoli, 2017. "A second order Crank–Nicolson scheme for fractional Cattaneo equation based on new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 361-374.
    9. Mishra, T.N. & Rai, K.N., 2016. "Numerical solution of FSPL heat conduction equation for analysis of thermal propagation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1006-1017.
    10. Tawfik, Ashraf M. & Fichtner, Horst & Elhanbaly, A. & Schlickeiser, Reinhard, 2018. "Analytical solution of the space–time fractional hyperdiffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 178-187.
    11. Kostrobij, P.P. & Markovych, B.M. & Viznovych, O.V. & Tokarchuk, M.V., 2019. "Generalized transport equation with nonlocality of space–time. Zubarev’s NSO method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 63-70.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:549:y:2020:i:c:s0378437119321594. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.