Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusive propagation of UHECR and the propagation theorem   We present a detailed analytical study of the propagation of ultra high
energy (UHE) particles in extragalactic magnetic fields. The crucial parameter
which affects the diffuse spectrum is the separation between sources. In the
case of a uniform distribution of sources with a separation between them much
smaller than all characteristic propagation lengths, the diffuse spectrum of
UHE particles has a {\em universal} form, independent of the mode of
propagation. This statement has a status of theorem. The proof is obtained
using the particle number conservation during propagation, and also using the
kinetic equation for the propagation of UHE particles. This theorem can be also
proved with the help of the diffusion equation. In particular, it is shown
numerically, how the diffuse fluxes converge to this universal spectrum, when
the separation between sources diminishes. We study also the analytic solution
of the diffusion equation in weak and strong magnetic fields with energy losses
taken into account. In the case of strong magnetic fields and for a separation
between sources large enough, the GZK cutoff can practically disappear, as it
has been found early in numerical simulations. In practice, however, the source
luminosities required are too large for this possibility.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn