Fermi acceleration at shocks with arbitrary velocity profiles

Diffusive particle acceleration in modified shock fronts is considered. A method by means of which to obtain the resulting particle spectrum for an arbitrary flow profile is outlined; this method is based on a reformulation of the transport equation as a nonlinear first-order equation. Besides the shape of the flow profile, the spectral index of particles depends on the Peclet number of the shock. Results are given for some sample profiles.