52,249 research outputs found
Analysis of astrometric catalogues with vector spherical harmonics
Comparison of stellar catalogues with position and proper motion components
using a decomposition on a set of orthogonal vector spherical harmonics. We
show the theoretical and practical advantages of this technique as a result of
invariance properties and the independence of the decomposition from a prior
model. We describe the mathematical principles used to perform the spectral
decomposition, evaluate the level of significance of the multipolar components
and examine the transformation properties under space rotation. The principles
are illustrated with a characterisation of the systematic effects in the FK5
catalogue compared to Hipparcos and with an application to the extraction of
the rotation and dipole acceleration in the astrometric solution of QSOs
expected from Gaia.Comment: accepted for publication in Astronomy & Astrophysic
Dynamics and Critical Behaviour of the q-model
The -model, a random walk model rich in behaviour and applications, is
investigated. We introduce and motivate the -model via its application
proposed by Coppersmith {\em et al.} to the flow of stress through granular
matter at rest. For a special value of its parameters the -model has a
critical point that we analyse. To characterise the critical point we imagine
that a uniform load has been applied to the top of the granular medium and we
study the evolution with depth of fluctuations in the distribution of load.
Close to the critical point explicit calculation reveals that the evolution of
load exhibits scaling behaviour analogous to thermodynamic critical phenomena.
The critical behaviour is remarkably tractable: the harvest of analytic results
includes scaling functions that describe the evolution of the variance of the
load distribution close to the critical point and of the entire load
distribution right at the critical point, values of the associated critical
exponents, and determination of the upper critical dimension. These results are
of intrinsic interest as a tractable example of a random critical point. Of the
many applications of the q-model, the critical behaviour is particularly
relevant to network models of river basins, as we briefly discuss. Finally we
discuss circumstances under which quantum network models that describe the
surface electronic states of a quantum Hall multilayer can be mapped onto the
classical -model. For mesoscopic multilayers of finite circumference the
mapping fails; instead a mapping to a ferromagnetic supersymmetric spin chain
has proved fruitful. We discuss aspects of the superspin mapping and give a new
elementary derivation of it making use of operator rather than functional
methods.Comment: 34 pages, Revtex, typo correcte
Density and Velocity Fields from the PSCz Survey
We present the results for the predicted density and peculiar velocity fields
and the dipole from the PSCz survey of 15,000 IRAS galaxies over 84% of the
sky. We find a significant component to the dipole arising between 6000 and
15,000 km/s, but no significant component from greater distances. The
misalignment with the CMB is 20 degrees. The most remarkable feature of the
PSCz model velocity field is a coherent large-scale flow along the baseline
connecting Perseus-Pisces, the Local Supercluster, Great Attractor and the
Shapley Concentration. We have measured the parameter beta using the amplitude
of the dipole, bulk flow and point by point comparisons between the individual
velocities of galaxies in the MarkIII and SFI datasets, and the large-scale
clustering distortion in redshift space.All our results are consistent with
beta = 0.6 +- 0.1.Comment: 8 pages, 8 figures. To appear in 'Towards an Understanding of Cosmic
Flows', Victoria, July 1999, eds Courteau,S., Strauss,M., Willick,J. PAS
- …