IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v255y1998i1p65-92.html
   My bibliography  Save this article

Anomalous transport equations and their application to fractal walking

Author

Listed:
  • Uchaikin, Vladimir V.

Abstract

Generalized transport equations covering both normal transport processes (such as neutron transport) and anomalous ones including Lévy walk and trapping are derived. The behaviours of the spatial distribution and mean-square displacement are investigated for fractal space–time processes. Exact solutions for the spatial distribution have been found in the one-dimensional case and numerical results are obtained for the case when the free paths and waiting times obey the one-sided stable distributions with the same characteristic exponent α=β=1/2. The principal result of the performed analysis is that the finite speed of a moving particle has a direct bearing on the spatial distribution. In the case of anomalous diffusion this effect does not vanish with time and has an influence on the asymptotic behaviour of the distribution form in contrast with normal diffusion when the speed affects only diffusivity but does not affect the form.

Suggested Citation

  • Uchaikin, Vladimir V., 1998. "Anomalous transport equations and their application to fractal walking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 255(1), pages 65-92.
    • Handle: RePEc:eee:phsmap:v:255:y:1998:i:1:p:65-92
    DOI: 10.1016/S0378-4371(98)00047-8
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437198000478
    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/S0378-4371(98)00047-8?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rukolaine, Sergey A., 2016. "Generalized linear Boltzmann equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 205-216.
    2. Uchaikin, V.V. & Sibatov, R.T., 2017. "Fractional derivatives on cosmic scales," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 197-209.
    3. Viacheslav V. Saenko & Vladislav N. Kovalnogov & Ruslan V. Fedorov & Dmitry A. Generalov & Ekaterina V. Tsvetova, 2022. "Numerical Method for Solving of the Anomalous Diffusion Equation Based on a Local Estimate of the Monte Carlo Method," Mathematics, MDPI, vol. 10(3), pages 1-19, February.
    4. Saenko, Viacheslav V., 2016. "The influence of the finite velocity on spatial distribution of particles in the frame of Levy walk model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 765-782.
    5. Viacheslav V. Saenko & Vladislav N. Kovalnogov & Ruslan V. Fedorov & Yuri E. Chamchiyan, 2021. "Numerical Solution to Anomalous Diffusion Equations for Levy Walks," Mathematics, MDPI, vol. 9(24), pages 1-17, December.

    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:255:y:1998:i:1:p:65-92. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.