Leaky-box approximation to the fractional diffusion model of cosmic rays

TL;DR

This paper compares two models of cosmic ray diffusion within the leaky-box approximation, highlighting that the coupled fractional walk model yields more realistic results than the decoupled Lévý flights model.

Contribution

It introduces a comparison between two anomalous diffusion models for cosmic rays, emphasizing the advantages of the coupled fractional walk approach.

Findings

Coupled fractional walk model provides more realistic diffusion results.

Distributions of first passage time and paths are computed.

Diffusion packets evolve to equilibrium states in both models.

Abstract

Two models of anomalous diffusion of cosmic ray in the leaky-box approximation are compared: one of them is based on the decoupled time-space L\'evy flights and the other on fractional walks with a finite free motion velocity. Distributions of first passage time and paths are computed and evolution of diffusion packets to equilibrium state is shown. Calculations demonstrate essential difference between the two models: the coupled scheme gives more realistic results.