We present the evolution of dark matter halos in six large cosmological N-body simulations, called the $ u^2$GC (New Numerical Galaxy Catalog) simulations on the basis of the LCDM cosmology consistent with observational results obtained by the Planck satellite. The largest simulation consists of $8192^3$ (550 billion) dark matter particles in a box of $1.12 , h^{-1} rm Gpc$ (a mass resolution of $2.20 times 10^{8} , h^{-1} M_{odot}$). Among simulations utilizing boxes larger than $1 , h^{-1} rm Gpc$, our simulation yields the highest resolution simulation that has ever been achieved. A $ u^2$GC simulation with the smallest box consists of eight billions particles in a box of $70 , h^{-1} rm Mpc$ (a mass resolution of $3.44 times 10^{6} , h^{-1} M_{odot}$). These simulations can follow the evolution of halos over masses of eight orders of magnitude, from small dwarf galaxies to massive clusters. Using the unprecedentedly high resolution and powerful statistics of the $ u^2$GC simulations, we provide statistical results of the halo mass function, mass accretion rate, formation redshift, and merger statistics, and present accurate fitting functions for the Planck cosmology. By combining the $ u^2$GC simulations with our new semi-analytic galaxy formation model, we are able to prepare mock catalogs of galaxies and active galactic nuclei, which will be made publicly available in the near future.
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