Non-Diffusive Propagation of Ultra High Energy Cosmic Rays
  We report the results of 3-D simulations of non-diffusive propagation of Ultra-High Energy Cosmic Rays (UHECR) (E > 10^{20} eV) through the intergalactic and extended halo media. We quantify the expected angular and temporal correlations between the events and the sources, and the temporal delay between protons and gamma-ray counterparts with a common origin for both halo and extragalactic origins. It is shown that the proposed UHECR-supergalactic plane source associations require either extremely high values of the halo magnetic field over as much as 100 kpc length scale or a very large correlation length for the IGM, even for the largest possible values of the intergalactic magnetic field. It can be stated that the UHECR seem to point to the sources even more strongly than previously believed. The simulations also show that the calculated time delays between UHE protons and gamma-ray counterparts do not match the claimed GRB-UHECR associations for either cosmological or extended halo distance scales. 
Gustavo A. Medina Tanco, Elisabete M. de Gouveia Dal Pino and Jorge E.   Horvath