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Using a set of high-resolution simulations we study the statistical correlation of dark matter halo properties with the large-scale environment. We consider halo populations split into four Cosmic Web (CW) elements: voids, walls, filaments, and nodes. For the first time we present a study of CW effects for halos covering six decades in mass: $10^{8}-10^{14}{h^{-1}{rm M}_{odot}}$. We find that the fraction of halos living in various web components is a strong function of mass, with the majority of $M>10^{12}{h^{-1}{rm M}_{odot}}$ halos living in filaments and nodes. Low mass halos are more equitably distributed in filaments, walls, and voids. For halo density profiles and formation times we find a universal mass threshold of $M_{th}sim6times10^{10}{h^{-1}{rm M}_{odot}}$ below which these properties vary with environment. Here, filament halos have the steepest concentration-mass relation, walls are close to the overall mean, and void halos have the flattest relation. This amounts to $c_{200}$ for filament and void halos that are respectively $14%$ higher and $7%$ lower than the mean at $M=2times10^8{h^{-1}{rm M}_{odot}}$, with low-mass node halos being most likely splashed-back. We find double power-law fits that very well describe $c(M)$ for the four environments in the whole probed mass range. A complementary picture is found for the average formation times, with the mass-formation time relations following trends shown for the concentrations: the nodes halos being the oldest and void halo the youngest. The CW environmental effect is much weaker when studying the halo spin and shapes. The trends with halo mass is reversed: the small halos with $M<10^{10}{h^{-1}{rm M}_{odot}}$ seem to be unaffected by the CW environment. Some weak trends are visible for more massive void and walls halos, which, on average, are characterized by lower spin and higher triaxiality parameters.
We explore the evolution of halo spins in the cosmic web using a very large sample of dark matter haloes in the $Lambda$CDM Planck-Millennium N-body simulation. We use the NEXUS+ multiscale formalism to identify the hierarchy of filaments and sheets
We investigate the alignment of haloes with the filaments of the cosmic web using an unprecedently large sample of dark matter haloes taken from the P-Millennium $Lambda$CDM cosmological N-body simulation. We use the state-of-the-art NEXUS morphologi
We investigate the spin evolution of dark matter haloes and their dependence on the number of connected filaments from the cosmic web at high redshift (spin-filament relation hereafter). To this purpose, we have simulated $5000$ haloes in the mass ra
We present evidence for halo assembly bias as a function of geometric environment. By classifying GAMA galaxy groups as residing in voids, sheets, filaments or knots using a tidal tensor method, we find that low-mass haloes that reside in knots are o
Both simulation and observational data have shown that the spin and shape of dark matter halos are correlated with their nearby large-scale environment. As structure formation on different scales is strongly coupled, it is trick to disentangle the fo