  Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas.
Plasma waves and their associated instabilities (e.g., the Buneman instability,
two-streaming instability, and the Weibel instability) created in the shocks
are responsible for particle (electron, positron, and ion) acceleration. Using
a 3-D relativistic electromagnetic particle (REMP) code, we have investigated
particle acceleration associated with a relativistic jet front propagating
through an ambient plasma with and without initial magnetic fields. We find
only small differences in the results between no ambient and weak ambient
magnetic fields. Simulations show that the Weibel instability created in the
collisionless shock front accelerates particles perpendicular and parallel to
the jet propagation direction. The simulation results show that this
instability is responsible for generating and amplifying highly nonuniform,
small-scale magnetic fields, which contribute to the electron's transverse
deflection behind the jet head. The ``jitter'' radiation from deflected
electrons has different properties than synchrotron radiation which is
calculated in a uniform magnetic field. This jitter radiation may be important
to understanding the complex time evolution and/or spectral structure in
gamma-ray bursts, relativistic jets, and supernova remnants.
