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We study the cosmic velocity-density relation using the spherical collapse model (SCM) as a proxy to non-linear dynamics. Although the dependence of this relation on cosmological parameters is known to be weak, we retain the density parameter Omega_m in SCM equations, in order to study the limit Omega_m -> 0. We show that in this regime the considered relation is strictly linear, for arbitrary values of the density contrast, on the contrary to some claims in the literature. On the other hand, we confirm that for realistic values of Omega_m the exact relation in the SCM is well approximated by the classic formula of Bernardeau (1992), both for voids (delta<0) and for overdensities up to delta ~ 3. Inspired by this fact, we find further analytic approximations to the relation for the whole range delta from -1 to infinity. Our formula for voids accounts for the weak Omega_m-dependence of their maximal rate of expansion, which for Omega_m < 1 is slightly smaller that 3/2. For positive density contrasts, we find a simple relation div v = 3 H_0 (Omega_m)^(0.6) [ (1+delta)^(1/6) - (1+delta)^(1/2) ], that works very well up to the turn-around (i.e. up to delta ~ 13.5 for Omega_m = 0.25 and neglected Omega_Lambda). Having the same second-order expansion as the formula of Bernardeau, it can be regarded as an extension of the latter for higher density contrasts. Moreover, it gives a better fit to results of cosmological numerical simulations.
We present results of the investigations of the statistical properties of a joint density and velocity divergence probability distribution function (PDF) in the mildly non-linear regime. For that purpose we use both perturbation theory results, exten
We report a tight linear relation between the HI circular velocity measured at 6 $R_{rm e}$ and the stellar velocity dispersion measured within 1 $R_{rm e}$ for a sample of 16 early-type galaxies with stellar mass between $10^{10}$ and $10^{11}$ $mat
We investigate the relationship between the velocity dispersion of the gas and the SN rate and feedback efficiency in the ISM. We explore the constancy of the velocity dispersion profiles in the outer parts of galactic disks at~6-8 km s^-1, and the t
A fully microscopic model for the description of nuclear level density (NLD) in spherical nuclei is proposed. The model is derived by combining the partition function of the exact pairing solution plus the independent-particle model at finite tempera
We address the problem of evaluating the power spectrum of the velocity field of the ICM using only information on the plasma density fluctuations, which can be measured today by Chandra and XMM-Newton observatories. We argue that for relaxed cluster