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In this contribution a broad overview of the methodologies of cosmological N-body simulations and a short introduction explaining the general idea behind such simulations is presented. After explaining how to set up the initial conditions using a set of N particles two (diverse) techniques are presented for evolving these particles forward in time under the influence of their self-gravity. One technique (tree codes) is solely based upon a sophistication of the direct particle-particle summation whereas the other method relies on the continuous (de-)construction of arbitrarily shaped grids and is realized in adaptive mesh refinement codes., Comment: 8 pages, 4 figures, accepted for publication in PASA (refereed proceedings contribution for the meeting "Gravity 2004" held in Sydney, April 15-16, 2004)

We present the study of ten random realizations of a density field characterized by a cosmological power spectrum P(k) at redshift z=50. The reliability of such initial conditions for n-body simulations are tested with respect to their correlation properties. The power spectrum P(k), and the mass variance sigmaM(r) do not show detectable deviations from the desired behavior in the intermediate range of scales between the mean interparticle distance and the simulation volume. The estimator for xi(r) is too noisy to detect any reliable signal at the initial redshift z=50. The particle distributions are then evolved forward until z=0. This allows us to explore the cosmic variance stemming from the random nature of the initial conditions. With cosmic variance we mean the fact that a simulation represents a single realization of the stochastic initial conditions whereas the real Universe contains many realizations of regions of the size of the box; this problem affects most importantly the scales at about the fundamental mode. We study morphological descriptors of the matter distribution such as the genus, as well as the internal properties of the largest object(s) forming in the box. We find that the scatter is at least comparable to the scatter in the fundamental mode., 22 pages, 12 figures, replaced with major revision to previous submission, PASA in press

The differences between cold (CDM) and warm (WDM) dark matter in the formation of a group of galaxies is examined by running two identical simulations where in the WDM case the initial power spectrum has been altered to mimic a 1keV dark matter particle. The CDM initial conditions were constrained to reproduce at z = 0 the correct local environment within which a "Local Group" (LG) of galaxies may form. Two significant differences between the two simulations are found. While in the CDM case a group of galaxies that resembles the real LG forms, the WDM run fails to reproduce a viable LG, instead forming a diffuse group which is still expanding at z = 0. This is surprising since, due to the suppression of small scale power in its power spectrum, WDM is naively expected to only affect the collapse of small haloes and not necessarily the dynamics on a scale of a group of galaxies. Furthermore the concentration of baryons in halo center's is greater in CDM than in WDM and the properties of the disks differ., 13 Pages, 5 figures, Accepted for publication in Publications of the Astronomical Society of Australia special issue on Warm Dark Matter