Abstract

We obtain an analytic description of the excitation front propagation in a medium during nonstationary superdiffusive (nonlocal) transport in the case of a finite fixed velocity of perturbation carriers (so-called Lévy walks with stops). This problem embraces phenomena such as resonance radiation transport in astrophysical gases and plasma, biological migration, and energy transfer by waves in a plasma. In this approach, the result obtained by integrating the exact solution to the kinetic equation for the Green function is independent of the coordinate space dimensionality. The results are compared with data obtained using another more exact method of determining the front and with the results of numerical calculations of the statistics of trajectories using the Monte Carlo method. Comparison demonstrates the applicability of our results in a wide range of parameters of the problem. We propose a universal description of the perturbation front dynamics in the medium for an arbitrary (including infinitely high) fixed velocity of perturbation carriers. This corresponds to the combination of expressions for the front in the case of transport by Lévy flights and by Lévy walks. We consider the criteria of transition between these regimes of the superdiffusive transport, which corresponds, in particular, to the account for the finite velocity of light in the superdiffusive transport of resonance radiation in gases and plasmas. For Lévy walks, we have obtained a relation between the integral characteristic of perturbation of the medium and its carriers.