surroundings and subject to relevant physical processes, such as cooling and heating, as in nature. The low resolution simulation used in this paper has compared several galaxy properties that depend critically on the feedback method to observations and found strong agreement (Cen 2011a-c; Cen 2012). We do not include a prescription for AGN feedback in this simulation, and as a result, our simulation overproduces luminous galaxies at the centers of groups and clusters of galaxies. This is discussed in detail in Cen (2011c), who shows that the luminosity function of the simulated galaxies agrees well with observations at $z$=0 except at the high-luminosity end. When Cen (2011c) adds an AGN feedback correction in the post-simulation analysis for halos with masses greater than 10$^{13}$ M$_{\odot}$ or for galaxies with stellar masses above 4$\times$10$^{12}$ M$_{\odot}$, the simulated luminosity function also agrees with observations at the high luminosity end. In the low resolution run, each star particle has a mass of $\sim$10$^6$ M$_\odot$, which is similar to the mass of a coeval globular cluster. In the high resolution run, each star particle has a mass of $\sim$10$^5$ M$_\odot$.

Galaxies {#sec:galaxyselection}
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We use HOP (Eisenstein & Hut 1998) to identify galaxies using the 