The distribution of pairwise peculiar velocities in the nonlinear regime

The distribution of pairwise, relative peculiar velocities, $f(u;r)$, on small nonlinear scales, $r$, is derived from the Press--Schechter approach. This derivation assumes that Press--Schechter clumps are virialized and isothermal. The virialized assumption requires that the circular velocity, $V_c \propto M^{1/3}$, where $M$ denotes the mass of the clump. The isothermal assumption means that the circular velocity is independent of radius. Further, it is assumed that the velocity distribution within a clump is Maxwellian, that the pairwise relative velocity distribution is isotropic, and that on nonlinear scales clump-clump motions are unimportant when calculating the distribution of velocity differences. Comparison with $N$-body simulations shows that, on small nonlinear scales, all these assumptions are accurate. For most power spectra of interest, the resulting line of sight, pairwise, relative velocity distribution, $f(u_{\rm r})$, is well approximated by an exponential, rather than a Gaussian distribution. This simple Press--Schechter model is also able to provide a natural explanation for the observed, non-Maxwellian shape of $f(v)$, the distribution of peculiar velocities.Comment: (MNRAS, in press) 16 pages, uuencode

Satellite Luminosities in Galaxy Groups

Halo model interpretations of the luminosity dependence of galaxy clustering assume that there is a central galaxy in every sufficiently massive halo, and that this central galaxy is very different from all the others in the halo. The halo model decomposition makes the remarkable prediction that the mean luminosity of the non-central galaxies in a halo should be almost independent of halo mass: the predicted increase is about 20% while the halo mass increases by a factor of more than 20. In contrast, the luminosity of the central object is predicted to increase approximately linearly with halo mass at low to intermediate masses, and logarithmically at high masses. We show that this weak, almost non-existent mass-dependence of the satellites is in excellent agreement with the satellite population in group catalogs constructed by two different collaborations. This is remarkable, because the halo model prediction was made without ever identifying groups and clusters. The halo model also predicts that the number of satellites in a halo is drawn from a Poisson distribution with mean which depends on halo mass. This, combined with the weak dependence of satellite luminosity on halo mass, suggests that the Scott effect, such that the luminosities of very bright galaxies are merely the statistically extreme values of a general luminosity distribution, may better apply to the most luminous satellite galaxy in a halo than to BCGs. If galaxies are identified with halo substructure at the present time, then central galaxies should be about 4 times more massive than satellite galaxies of the same luminosity, whereas the differences between the stellar M/L ratios should be smaller. Therefore, a comparison of the weak lensing signal from central and satellite galaxies should provide useful constraints. [abridged]Comment: 8 pages, 3 figures. Matches version accepted by MNRA

First-principles calculation of phase equilibrium of V-Nb, V-Ta, and Nb-Ta alloys

In this paper, we report the calculated phase diagrams of V-Nb, V-Ta, and Nb-Ta alloys computed by combining the total energies of 40–50 configurations for each system (obtained using density functional theory) with the cluster expansion and Monte Carlo techniques. For V-Nb alloys, the phase diagram computed with conventional cluster expansion shows a miscibility gap with consolute temperature T_c=1250 K. Including the constituent strain to the cluster expansion Hamiltonian does not alter the consolute temperature significantly, although it appears to influence the solubility of V- and Nb-rich alloys. The phonon contribution to the free energy lowers T_c to 950 K (about 25%). Our calculations thus predicts an appreciable miscibility gap for V-Nb alloys. For bcc V-Ta alloy, this calculation predicts a miscibility gap with T_c=1100 K. For this alloy, both the constituent strain and phonon contributions are found to be significant. The constituent strain increases the miscibility gap while the phonon entropy counteracts the effect of the constituent strain. In V-Ta alloys, an ordering transition occurs at 1583 K from bcc solid solution phase to the V_(2)Ta Laves phase due to the dominant chemical interaction associated with the relatively large electronegativity difference. Since the current cluster expansion ignores the V_(2)Ta phase, the associated chemical interaction appears to manifest in making the solid solution phase remain stable down to 1100 K. For the size-matched Nb-Ta alloys, our calculation predicts complete miscibility in agreement with experiment

Cluster expansion Monte Carlo study of phase stability of vanadium nitrides

Phase stability of stable and metastable vanadium nitrides is studied using density functional theory (DFT) based total-energy calculations combined with cluster expansion Monte Carlo simulation and supercell methods. We have computed the formation enthalpy of the various stable and metastable vanadium nitride phases considering the available structural models and found that the formation enthalpies of the different phases decrease in the same order as they appear in the experimental aging sequence. DFT calculations are known to show stoichiometric V2N to be polymorphic in ϵ-Fe_2N and ζ-Fe2_N structures within a few meV and VN to be more stable in WC(B_h) phase than in the experimentally observed NaCl(B1) structure. As these nitrides are known to be generally nonstoichiometric due to presence of nitrogen vacancies, we used cluster expansion and supercell methods for examining the effect of nitrogen vacancies on the phase stability. It is found that nitrogen vacancies, represented by ◻, stabilize ϵ-Fe_2N phase of V_2N_(1−x◻x) and NaCl(B1) phase of VN_(1−x◻x) compared to ζ-Fe_2N and WC(B_h) phases respectively, rendering the computed phase stability scenario to be in agreement with experiments. Analysis of supercell calculated electronic density of states (DOS) of VN_(1−x◻x) with varying x, shows that the nitrogen vacancies increase the DOS at Fermi level in WC phase, whereas they decrease the DOS in NaCl phase. And this serves as the mechanism of enhancement of the stability of the NaCl phase. Monte Carlo simulations were used for computing the finite temperature formation enthalpies of these phases as a function of nitrogen-vacancy concentration and found close agreement for NaCl(B1) phase of VN_(1−x◻x) for which measured values are available

Estimation and Determinants of Chronic Poverty in India : An Alternative Approach

The paper conceptualizes chronic poverty by using the spaces of income and nutrition and estimates its incidence among states and social groups. It also aims to improve our understanding of the determinant of chronic poverty by considering economic, demographic and social factors. It attempts to answer the following questions : How important a determinant of chronic poverty is household income? What factors inhibit escape from chronic poverty? How different are the other poor from chronic poor? The analysis uses the unit level NSS and NFHS data.Chrinic Poverty, India

Estimation and determinants of chronic poverty in India: An Alternative approach

The paper conceptualizes chronic poverty by using the spaces of income and nutrition and estimates its incidence among states and social groups. It also aims to improve our understanding of the determinant of chronic poverty by considering economic, demographic and social factors. It attempts to answer the following questions: How important a determinant of chronic poverty is household income? What factors inhibit escape from chronic poverty? How different are the other poor from chronic poor? The analysis uses the unit level NSS and NFHS data.