  We have examined cutoffs and pile-ups due to various processes in the spectra
of particles produced by shock acceleration, and found that, even in the
absence of energy losses, the shape of the spectrum of accelerated particles at
energies well below the nominal maximum energy depends strongly on the energy
dependence of the diffusion coefficient. This has implications in many areas,
for example, in fitting the observed cosmic ray spectrum with models based on
power-law source spectra and rigidity dependent diffusive escape from the
galaxy. With continuous energy losses, prominent pile-ups may arise, and these
should be included when modelling synchrotron X-ray and inverse Compton
gamma-ray spectra from a shock-accelerated electron population.
  We have developed a Monte Carlo/numerical technique to model the shape of the
spectrum for the case of non-continuous energy losses such as inverse Compton
scattering in the Klein-Nishina regime. We find that the shapes of the
resulting cut-offs differ substantially from those arising from continuous
processes, and we suggest that such differences could be observable through
their effect on the spectrum of radiation emitted by a population of recently
accelerated electrons as, for example, may exist in young supernova remnants.
