165 research outputs found
Multiple-Images in the Cluster Lens Abell 2218: Constraining the Geometry of the Universe ?
In this Letter we present a detailed study of the lensing configuration in
the cluster Abell 2218. Four multiple-images systems with measured
spectroscopic redshifts have been identified in this cluster. These multiple
images are very useful to constrain accurately the mass distribution in the
cluster core, but they are also sensitive to the value of the geometrical
cosmological parameters of the Universe. Using a simplified maximum likelihood
analysis we find 0 < Omega_M < 0.30 assuming a flat Universe, and 0 < Omega_M <
0.33 and w < -0.85 for a flat Universe with dark energy. Interestingly, an
Einstein-de Sitter model is excluded at more than 4sigma. These constraints are
consistent with the current constraints derived with CMB anisotropies or
supernovae studies. The proposed method constitutes an independent test of the
geometrical cosmological parameters of the Universe and we discuss the limits
of this method and this particular application to Abell 2218. Application of
this method with more sophisticated tools and to a larger number of clusters or
with more multiple images constraints, will put stringent constraints on the
geometrical cosmological parameters.Comment: 5 pages, 3 figures. Accepted for publication by Astronomy &
Astrophysic
Pseudo Elliptical Lensing Mass Model: Application to the NFW Mass Distribution
We introduce analytical expressions for a pseudo fully analytical elliptical
projected Navarro, Frenk & White (NFW) mass profile to be used in lensing
equations. We propose a formalism that incorporates the ellipticity into the
expression for the lens potential, producing a pseudo-elliptical mass
distribution. This approach can be implemented to any circular mass profile for
which the projected mass profile Sigma(r) and the deflection angle profile
alpha(r) both have analytical expressions; however the potential does not
necessarily need to take an analytical form. We apply this new formalism to the
NFW mass distribution and study how well this pseudo-elliptical NFW model
describes an elliptical mass distribution. We conclude that the
pseudo-elliptical NFW model is a good description of elliptical mass
distributions provided that the ellipticity of the projected mass distribution
is <~ 0.4, although with a slightly boxy distribution.Comment: 7 pages, 8 figures. Revised versio
Homogenization of linear transport equations in a stationary ergodic setting
We study the homogenization of a linear kinetic equation which models the
evolution of the density of charged particles submitted to a highly oscillating
electric field. The electric field and the initial density are assumed to be
random and stationary. We identify the asymptotic microscopic and macroscopic
profiles of the density, and we derive formulas for these profiles when the
space dimension is equal to one.Comment: 24 page
A well-posedness theory in measures for some kinetic models of collective motion
We present existence, uniqueness and continuous dependence results for some
kinetic equations motivated by models for the collective behavior of large
groups of individuals. Models of this kind have been recently proposed to study
the behavior of large groups of animals, such as flocks of birds, swarms, or
schools of fish. Our aim is to give a well-posedness theory for general models
which possibly include a variety of effects: an interaction through a
potential, such as a short-range repulsion and long-range attraction; a
velocity-averaging effect where individuals try to adapt their own velocity to
that of other individuals in their surroundings; and self-propulsion effects,
which take into account effects on one individual that are independent of the
others. We develop our theory in a space of measures, using mass transportation
distances. As consequences of our theory we show also the convergence of
particle systems to their corresponding kinetic equations, and the
local-in-time convergence to the hydrodynamic limit for one of the models
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