IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v388y2009i8p1509-1514.html
   My bibliography  Save this article

Computer simulation study of the Levy flight process

Author

Listed:
  • Ghaemi, Mehrdad
  • Zabihinpour, Zahra
  • Asgari, Yazdan

Abstract

The random walk simulation of a Levy flight shows a linear relation between the mean square displacement 〈r2〉 and time. We have analyzed different aspects of this linearity. It is shown that the restriction of jump length to a maximum value (lm) affects the diffusion coefficient, even though it remains constant for lm greater than 1464. So, this factor has no effect on the linearity. In addition, it is shown that the number of samples does not affect the results. We have demonstrated that the relation between the mean square displacement and time remains linear in a continuous space, while continuous variables just reduce the diffusion coefficient. The results also imply that the movement of a Levy flight particle is similar to the case in which the particle moves in each time step with an average jump length 〈l〉. Finally, it is shown that the non-linear relation of the Levy flight will be satisfied if we use a time average instead of an ensemble average. The difference between the time average and ensemble average results shows that the Levy distribution may be a non-ergodic distribution.

Suggested Citation

  • Ghaemi, Mehrdad & Zabihinpour, Zahra & Asgari, Yazdan, 2009. "Computer simulation study of the Levy flight process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1509-1514.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:8:p:1509-1514
    DOI: 10.1016/j.physa.2008.12.071
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437108010947
    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.2008.12.071?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. Cao, Jiajia & Zhou, Yanbin & Wei, Kun, 2024. "Modeling ants’ walks in patrolling multiple resources using stochastic approximation partial momentum refreshment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    2. Kang, Chaogui & Ma, Xiujun & Tong, Daoqin & Liu, Yu, 2012. "Intra-urban human mobility patterns: An urban morphology perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1702-1717.
    3. Pereira, A.P.P. & Fernandes, J.P. & Atman, A.P.F. & Acebal, J.L., 2018. "Parameter calibration between models and simulations: Connecting linear and non-linear descriptions of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 369-382.

    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:388:y:2009:i:8:p:1509-1514. 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.