  I discuss the shape of the high energy end of the spectrum of particles
arising from diffusive shock acceleration in the presence of (i) additional
diffusive escape from the accelerator, (ii) continuous energy losses, (iii)
energy changes arising from interactions. The form of the spectrum near cut-off
is sensitive to these processes as well as to the momentum-dependence of the
diffusion coefficients and the compression ratio, and so the spectrum of any
radiation emitted by the accelerated particles may reflect the physical
conditions of the acceleration region. Results presented in this paper have
applications in interpreting the spectral energy distributions of many types of
astrophysical object including supernova remnants (SNR), active galactic nuclei
(AGN) and acceleration sources of ultra high energy cosmic rays (UHE CR).
Except for extremely nearby sources, spectral features imprinted on the
spectrum of UHE CR during the acceleration process will be largely eroded
during propagation, but the spectrum of UHE neutrinos produced in interactions
of UHE CR with radiation, both during cosmic ray acceleration and subsequent
propagation through the cosmic microwave background radiation, contains
sufficient information to determine the cut-off momentum of the UHE CR just
after acceleration for reasonable assumptions. Observation of these UHE
neutrinos by the Pierre Auger Observatory may help in identifying the sources
of the highest energy cosmic rays.
