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Hamilton-Jacobi Equations and Distance Functions on Riemannian Manifolds
The paper is concerned with the properties of the distance function from a
closed subset of a Riemannian manifold, with particular attention to the set of
singularities
Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity
Connes' formula defines a distance in loop quantum gravity, via the spinfoam
Dirac operator. A simple notion of spectral distance on a graph can be extended
do the discrete Lorentzian context, providing a physically natural example of
Lorentzian spectral geometry, with a neat space of Dirac operators. The Hilbert
structure of the fermion space is Lorentz covariant rather than invariant.Comment: 4 page
The special growth history of central galaxies in groups and clusters
Central galaxies (CGs) in galaxy groups and clusters are believed to form and
assemble a good portion of their stellar mass at early times, but they also
accrete significant mass at late times via galactic cannibalism, that is
merging with companion group or cluster galaxies that experience dynamical
friction against the common host dark-matter halo. The effect of these mergers
on the structure and kinematics of the CG depends not only on the properties of
the accreted satellites, but also on the orbital parameters of the encounters.
Here we present the results of numerical simulations aimed at estimating the
distribution of merging orbital parameters of satellites cannibalized by the
CGs in groups and clusters. As a consequence of dynamical friction, the
satellites' orbits evolve losing energy and angular momentum, with no clear
trend towards orbit circularization. The distributions of the orbital
parameters of the central-satellite encounters are markedly different from the
distributions found for halo-halo mergers in cosmological simulations. The
orbits of satellites accreted by the CGs are on average less bound and less
eccentric than those of cosmological halo-halo encounters. We provide fits to
the distributions of the central-satellite merging orbital parameters that can
be used to study the merger-driven evolution of the scaling relations of CGs.Comment: 14 pages, 11 figures, accepted for publication in MNRAS. Minor
changes with respect to previous versio
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