  We derive the maximum accelerated particle energy from first-order and
second-order Fermi acceleration at nonrelativistic and relativistic shocks for
explosions taking place in a uniform surrounding medium. Second-order
stochastic processes in relativistic flows are shown to be capable of
accelerating cosmic rays to ultra-high energies. Cosmic rays above the knee of
the cosmic ray spectrum can be accelerated by the second-order Fermi mechanism
in relativistic flows, such as those occuring in gamma-ray bursts and unusual
supernovae like SN 1998bw.
