  Recent observations of galaxy clusters in radio and X-ray indicate that
cosmic rays and magnetic fields may be energetically important in the
intracluster medium. According to the estimates based on theses observational
studies, the combined pressure of these two components of the intracluster
medium may range between $10% \sim 100 %$ of gas pressure, although their total
energy is probably time dependent. Hence, these non-thermal components may have
influenced the formation and evolution of cosmic structures, and may provide
unique and vital diagnostic information through various radiations emitted via
their interactions with surrounding matter and cosmic background photons. We
suggest that shock waves associated with cosmic structures, along with
individual sources such as active galactic nuclei and radio galaxies, supply
the cosmic rays and magnetic fields to the intracluster medium and to
surrounding large scale structures. In order to study 1) the properties of
cosmic shock waves emerging during the large scale structure formation of the
universe, and 2) the dynamical influence of cosmic rays, which were ejected by
AGN-like sources into the intracluster medium, on structure formation, we have
performed two sets of N-body/hydrodynamic simulations of cosmic structure
formation. In this contribution, we report the preliminary results of these
simulations.
