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We study the concentration of dark matter halos and its evolution in N-body simulations of the standard LCDM cosmology. The results presented in this paper are based on 4 large N-body simulations with about 10 billion particles each: the Millennium-I and II, Bolshoi, and MultiDark simulations. The MultiDark (or BigBolshoi) simulation is introduced in this paper. This suite of simulations with high mass resolution over a large volume allows us to compute with unprecedented accuracy the concentration over a large range of scales (about six orders of magnitude in mass), which constitutes the state-of-the-art of our current knowledge on this basic property of dark matter halos in the LCDM cosmology. We find that there is consistency among the different simulation data sets. We confirm a novel feature for halo concentrations at high redshifts: a flattening and upturn with increasing mass. The concentration c(M,z) as a function of mass and the redshift and for different cosmological parameters shows a remarkably complex pattern. However, when expressed in terms of the linear rms fluctuation of the density field sigma(M,z), the halo concentration c(sigma) shows a nearly-universal simple U-shaped behaviour with a minimum at a well defined scale at sigma=0.71. Yet, some small dependences with redshift and cosmology still remain. At the high-mass end (sigma < 1) the median halo kinematic profiles show large signatures of infall and highly radial orbits. This c-sigma(M,z) relation can be accurately parametrized and provides an analytical model for the dependence of concentration on halo mass. When applied to galaxy clusters, our estimates of concentrations are substantially larger -- by a factor up to 1.5 -- than previous results from smaller simulations, and are in much better agreement with results of observations. (abridged), Submitted to MNRAS

We provide a set of general tools for studying the alignments of dark matter halos and galaxies with respect to the large scale structure. The statistics of the positioning of these objects is represented by a Probability Distribution Function (PDF) of their Euler angles. The PDF corresponding to halos located in the shells of the cosmic voids is inferred from previous results. This PDF is used to show how to recover the outcomes found for the alignments of the axes of these halos in simulations. We also explore the orientation of the angular momentum of the halos, both with respect to the halo axes and with respect to the large scale structure. We present an expression which describes well numerical results for the alignment of the angular momentum of the halo with respect to the halo axes for randomly chosen halos. We also propose a model that relates the orientation of the angular momentum with the halos axes accounting for the orientation of the halo axes with the large scale structure. This model is shown to recover accurately the observed PDF of the halo angular momentum with respect to the void radial direction. In addition, we give an expression for determining the degradation of the angular momentum intrinsic alignment when observational errors are accounted. This expression is also used to determine the departure of the observed value of the alignment from the initial expectation (as provided by the tidal torque theory) due to the rotation of the angular momentum of the halo with respect to the initial torque. For voids, we find that the strength of the alignment is reduced to half the original value. We discuss how to adapt the void results to other cosmic large scale structures (i.e. filaments, walls, etc)., 18 pages, 5 figures, submitted to MNRAS