Probability density functions are determined from new stellar parameters for the distance moduli of stars for which the RAdial Velocity Experiment (RAVE) has obtained spectra with S/N>=10. Single-Gaussian fits to the pdf in distance modulus suffice f
or roughly half the stars, with most of the other half having satisfactory two-Gaussian representations. As expected, early-type stars rarely require more than one Gaussian. The expectation value of distance is larger than the distance implied by the expectation of distance modulus; the latter is itself larger than the distance implied by the expectation value of the parallax. Our parallaxes of Hipparcos stars agree well with the values measured by Hipparcos, so the expectation of parallax is the most reliable distance indicator. The latter are improved by taking extinction into account. The effective temperature absolute-magnitude diagram of our stars is significantly improved when these pdfs are used to make the diagram. We use the method of kinematic corrections devised by Schoenrich, Binney & Asplund to check for systematic errors for general stars and confirm that the most reliable distance indicator is the expectation of parallax. For cool dwarfs and low-gravity giants <pi> tends to be larger than the true distance by up to 30 percent. The most satisfactory distances are for dwarfs hotter than 5500 K. We compare our distances to stars in 13 open clusters with cluster distances from the literature and find excellent agreement for the dwarfs and indications that we are over-estimating distances to giants, especially in young clusters.
Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used for coalesce
nce and fragmentation. Here we discuss how changes in these microscopic rules affect the macroscopic cluster-size distribution which emerges from the solution to the rate equation. More generally, our work elucidates the crucial role that the fragmentation rule can play in such dynamical grouping models. We focus on two well-known models whose fragmentation rules lie at opposite extremes setting the models within the broader context of binary coalescence-fragmentation models. Further, we provide a range of generalizations and new analytic results for a well-known model of social group formation [V. M. Eguiluz and M. G. Zimmermann, Phys. Rev. Lett. 85, 5659 (2000)]. We develop analytic perturbation treatment of the original model, and extend the mathematical to the treatment of growing and declining populations.
