  We present new results characterizing cosmological shocks within adaptive
mesh refinement N-Body/hydrodynamic simulations that are used to predict
non-thermal components of large-scale structure. This represents the first
study of shocks using adaptive mesh refinement. We propose a modified algorithm
for finding shocks from those used on unigrid simulations that reduces the
shock frequency of low Mach number shocks by a factor of ~3. We then apply our
new technique to a large, (512 Mpc/h)^3, cosmological volume and study the
shock Mach number (M) distribution as a function of pre-shock temperature,
density, and redshift. Because of the large volume of the simulation, we have
superb statistics that results from having thousands of galaxy clusters. We
find that the Mach number evolution can be interpreted as a method to visualize
large-scale structure formation. Shocks with Mach<5 typically trace mergers and
complex flows, while 5<Mach<20 and Mach>20 generally follow accretion onto
filaments and galaxy clusters, respectively. By applying results from nonlinear
diffusive shock acceleration models using the first-order Fermi process, we
calculate the amount of kinetic energy that is converted into cosmic ray
protons. The acceleration of cosmic ray protons is large enough that in order
to use galaxy clusters as cosmological probes, the dynamic response of the gas
to the cosmic rays must be included in future numerical simulations.
