Propagation of ultra-high energy protons in the nearby universe
  We present a new calculation of the propagation of protons with energies above $10^{19}$ eV over distances of up to several hundred Mpc. The calculation is based on a Monte Carlo approach using the event generator   SOPHIA for the simulation of hadronic nucleon-photon interactions and a realistic integration of the particle trajectories in a random extragalactic magnetic field. Accounting for the proton scattering in the magnetic field affects noticeably the nucleon energy as a function of the distance to their source and allows us to give realistic predictions on arrival energy, time delay, and arrival angle distributions and correlations as well as secondary particle production spectra. 
Todor Stanev, Ralph Engel, Anita Muecke, Raymond J. Protheroe and   Joerg P. Rachen