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Computer simulation study of the Levy flight process

Author

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  • 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
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    Cited by:

    1. 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.
    2. 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.

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