Dynamical continuous time random lévy flights

Abstract

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2016. The Lévy flights’ diffusive behavior is studied within the framework of the dynamical continuous time random walk (DCTRW) method, while the nonlinear friction is introduced in each step. Through the DCTRW method, Lévy random walker in each step flies by obeying the Newton’s Second Law while the nonlinear friction f(v) = -?0v - ?2v3 being considered instead of Stokes friction. It is shown that after introducing the nonlinear friction, the superdiffusive Lévy flights converges, behaves localization phenomenon with long time limit, but for the Lévy index µ = 2 case, it is still Brownian motion.