52,249 research outputs found

    Analysis of astrometric catalogues with vector spherical harmonics

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    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

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    The qq-model, a random walk model rich in behaviour and applications, is investigated. We introduce and motivate the qq-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 qq-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 qq-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

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    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
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