Computer simulation study of the Levy flight process

Mehrdad Ghaemi, Zahra Zabihinpour and Yazdan Asgari

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 8, 1509-1514

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.

Keywords: Levy flight; Anomalous diffusion; Nonlinearity; Non-ergodicity (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:8:p:1509-1514

DOI: 10.1016/j.physa.2008.12.071

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