Dynamical mechanism of Lévy flight driven by the nonlinear friction
Access Status
Authors
Date
2016Type
Metadata
Show full item recordCitation
Source Title
ISSN
School
Collection
Abstract
© 2016 Chinese Physical Society. As a basic problem, anomalous diffusions in various fields of physics and related science have been studied for several decades. One of the topic problems of anomalous diffusion is Lévy flight, which is employed as the statistical model to solve the problems in various fields. Therefore, studying the dynamical mechanism of Lévy flight, especially in the existence of external potential, is of importance for relative theoretical and experimental research. In this paper, within the framework of dynamical continuous time random walk method, the Lévy flight diffusive behaviors and dynamical mechanisms driven by nonlinear friction are studied in the forcefree potential and periodic potential. The nonlinear friction instead of Stokes friction is considered in each step of Lévy random walker through the dynamical continuous time random walk method. In the forcefree potential, the nonlinear friction term can be considered to be inharmonic potential in the velocity space which can restrain the velocity of random walker, so the anomalous superdiffusion of Lévy flight turns into a behavior in the normal case because of the strong dissipative effect of the nonlinear friction. Due to the introduction of the nonlinear friction, the velocity steady probability density distribution behaves as transitions between bimodal shape and unimodal shape, which is detrmined by the Lévy index µ and the friction indexes ?0 and ?2. The bimodality is most pronounced at µ = 1, with µ increasing the bimodality becomes weaker, and vanishes at µ = 2 which is the Gaussian case. Besides, there is a critical value ?0c = 0:793701, which also determines the bimodal behaviors. For ?0 = ? 0 the bimodality is most pronounced, as ?0 increases it smooths out and turns into a unimodal one for ?0 > ?0c. In the existence of periodic potential, the Lévy random walker can be captured by the periodical potential due to the introduction of nonlinear friction, which behaves as the mean square displacement < dx2(t) > of the random walker and can reach a steady state quite quickly after a short lag time. However, the restraint is not equivalent to truncation procedures. Since the velocity of random walker obeys Lévy distribution, there is still extremely large jump length for random walker with extremely small probability. When the extremely large jump length is long enough and the barrier height U0 is not comparably high, the random walker can cross the barrier height of the periodic potential and jump out of the periodic potential, which behaves as the mean square displacement < dx2(t) > and a leap from a steady state to another one appears. However, the restraint on the random walker from the nonlinear friction always exists, so the random walker is captured again by the periodic potential, which means that the mean square displacement comes into a steady state again.
Related items
Showing items related by title, author, creator and subject.

Liu, Jian; Chen, X. (2016)© EDP Sciences, Società Italiana di Fisica, SpringerVerlag 2016. The Lévy flights’ diffusive behavior is studied within the framework of the dynamical continuous time random walk (DCTRW) method, while the nonlinear ...

Dol, Sharul Sham; Mehdi Salek, M.; Martinuzzi, R. (2014)This work is concerned with the behavior of pulsatile flows over a backwardfacing step geometry. The paper mainly focuses on the effects of the pulsation frequency on the vortex development of a 2:1 backwardfacing step ...

Liu, Jian; Yang, B.; Chen, X.; Bao, J. (2015)© 2015, EDP Sciences, SIF, SpringerVerlag Berlin Heidelberg. We consider a continuous time random walk model in which each jump is considered to be dynamical process. Dissipative launch velocity and hopping time in each ...