Isolated Boundary Singularities of Semilinear Elliptic Equations

Given a smooth domain \Omega\subset\RR^N such that $0 \in \partial\Omega$ and given a nonnegative smooth function $\zeta$ on $\partial\Omega$, we study the behavior near 0 of positive solutions of $-\Delta u=u^q$ in $\Omega$ such that $u = \zeta$ on $\partial\Omega\setminus\{0\}$. We prove that if $\frac{N+1}{N-1} < q < \frac{N+2}{N-2}$, then u(x)\leq C \abs{x}^{-\frac{2}{q-1}} and we compute the limit of \abs{x}^{\frac{2}{q-1}} u(x) as $x \to 0$. We also investigate the case $q= \frac{N+1}{N-1}$. The proofs rely on the existence and uniqueness of solutions of related equations on spherical domains

Retour d'expérience - Du projet de recherche AdaMont à la méthode, aux outils et aux services transférés aux territoires

The AdaMont project is part of a global problem of territorial adaptation change, based on the particular example of mountain territories facing to climate change. The Vercors Regional Nature Park quickly emerged as a a relevant territory in relation to the criteria for choosing the territories of application. It is under his double hat as a researcher from Irstea, the project leader, and as President of the Park's Scientific Council that François Véron gives us an overview of the project from the point of view of support for the actors.Le projet AdaMont s'inscrit dans une problématique globale d'adaptation des territoires au changement, en s'appuyant sur l'exemple particulier des territoires de montagne confrontés au changement climatique. Le Parc naturel régional du Vercors est rapidement apparu comme un territoire pertinent par rapport aux critères de choix des territoires d'application. C'est sous sa double casquette de chercheur d'Irstea, porteur du projet, et de Président du conseil scientifique du Parc que François Véron nous fait le bilan du projet vu sous l'angle de l'accompagnement des acteurs

The Double Quasar Q2138-431: Lensing by a Dark Galaxy?

We report the discovery of a new gravitational lens candidate Q2138-431AB, comprising two quasar images at a redshift of 1.641 separated by 4.5 arcsecs. The spectra of the two images are very similar, and the redshifts agree to better than 115 km.sec$^{-1}$. The two images have magnitudes $B_J = 19.8$ and $B_J = 21.0$, and in spite of a deep search and image subtraction procedure, no lensing galaxy has been found with $R < 23.8$. Modelling of the system configuration implies that the mass-to-light ratio of any lensing galaxy is likely to be around $1000 M_{\odot}/L_{\odot}$, with an absolute lower limit of $200 M_{\odot}/L_{\odot}$ for an Einstein-de Sitter universe. We conclude that the most likely explanation of the observations is gravitational lensing by a dark galaxy, although it is possible we are seeing a binary quasar.Comment: 17 pages (Latex), 8 postscript figures included, accepted by MNRA

Multi-wavelength study of the gravitational lens system RXS J1131-1231: III. Long slit spectroscopy: micro-lensing probes the QSO structure

(ABRIDGED) Aims: We discuss and characterize micro-lensing among the 3 brightest lensed images (A-B-C) of the gravitational lens system RXS J1131-1231 (a quadruply imaged AGN) by means of long slit optical and NIR spectroscopy. Qualitative constraints on the size of different emission regions are derived. Methods: We decompose the spectra into their individual emission components using a multi-component fitting approach. A complementary decomposition of the spectra enables us to isolate the macro-lensed fraction of the spectra independently of any spectral modelling. Results: -1. The data support micro-lensing de-amplification of images A and C. Not only is the continuum emission microlensed in those images but also a fraction of the Broad Line emitting Region (BLR).-2. Micro-lensing of a very broad component of MgII emission line suggests that the corresponding emission occurs in a region more compact than the other components of the emission line. -3. We find evidence that a large fraction of the FeII emission arises in the outer parts of the BLR. We also find very compact emitting region in the ranges 3080-3540 A and 4630-4800 A that is likely associated with FeII. -4. The OIII narrow emission line regions are partly spatially resolved. This enables us to put a lower limit of 110h^{-1} pc on their intrinsic size. -5. Analysis of MgII absorption found in the spectra indicates that the absorbing medium is intrinsic to the quasar, has a covering factor of 20%, and is constituted of small clouds homogeneously distributed in front of the continuum and BLRs. -6. Two neighbour galaxies are detected at redshifts z=0.10 and z=0.289. These galaxies are possible members of galaxy groups reported at those redshifts.Comment: Accepted by Astronomy and Astrophysics. Small modifications to match the final versio

Medium range structural order in amorphous tantala spatially resolved with changes to atomic structure by thermal annealing

Amorphous tantala (a-Ta2O5) is an important technological material that has wide ranging applications in electronics, optics and the biomedical industry. It is used as the high refractive index layers in the multi-layer dielectric mirror coatings in the latest generation of gravitational wave interferometers, as well as other precision interferometers. One of the current limitations in sensitivity of gravitational wave detectors is Brownian thermal noise that arises from the tantala mirror coatings. Measurements have shown differences in mechanical loss of the mirror coatings, which is directly related to Brownian thermal noise, in response to thermal annealing. We utilise scanning electron diffraction to perform Fluctuation Electron Microscopy (FEM) on Ion Beam Sputtered (IBS) amorphous tantala coatings, definitively showing an increase in the medium range order (MRO), as determined from the variance between the diffraction patterns in the scan, due to thermal annealing at increasing temperatures. Moreover, we employ Virtual Dark-Field Imaging (VDFi) to spatially resolve the FEM signal, enabling investigation of the persistence of the fragments responsible for the medium range order, as well as the extent of the ordering over nm length scales, and show ordered patches larger than 5 nm in the highest temperature annealed sample. These structural changes directly correlate with the observed changes in mechanical loss.Comment: 22 pages, 5 figure

Optically bright Active Galactic Nuclei in the ROSAT-Faint Source Catalogue

To build a large, optically bright, X-ray selected AGN sample we have correlated the ROSAT-FSC catalogue of X-ray sources with the USNO catalogue limited to objects brighter than O=16.5 and then with the APS database. Each of the 3,212 coincidences was classified using the slitless Hamburg spectra. 493 objects were found to be extended and 2,719 starlike. Using both the extended objects and the galaxies known from published catalogues we built up a sample of 185 galaxies with O_APS < 17.0 mag, which are high-probability counterparts of RASS-FSC X-ray sources. 130 galaxies have a redshift from the literature and for another 34 we obtained new spectra. The fraction of Seyfert galaxies in this sample is 20 %. To select a corresponding sample of 144 high-probability counterparts among the starlike sources we searched for very blue objects in an APS-based color-magnitude diagram. Forty-one were already known AGN and for another 91 objects we obtained new spectra, yielding 42 new AGN, increasing their number in the sample to 83. This confirms that surveys of bright QSOs are still significantly incomplete. On the other hand we find that, at a flux limit of 0.02 count /-1 and at this magnitude, only 40 % of all QSOs are detected by ROSAT.Comment: 17 pages, 16 figures, accepted by A&

How would farmers in the French Alps adapt their systems to different drought and socio-economic context scenarios?

International audienceThe French Alps are considered as an area that is particularly vulnerable to climate change. Several droughts have already occurred since 2003. In order to assess the ability of farming systems to adapt to future drought events, we developed prospective scenarios combining different climatic and socio-economic contexts. Four scenarios were defined based on (i) prospective studies conducted at national and international levels, and (ii) a participatory approach with various stakeholders to transcribe these scenarios at a local level. Farmers and shepherds in the Vercors and Oisans massifs were surveyed in order to understand how they had reacted to previous droughts, and how they would plan to react to our scenarios. Results show first that the farmers would strive to continue their activity in each scenario, taking advantage of the flexibility of their farming systems, as in previous years. However, in the most pessimistic climatic scenario, they would also decrease the size of their herds. Depending on the socio-economic hypothesis, they would adopt farm structural changes (farm processing activities, direct selling, etc.), or look for part-time non-agricultural jobs. Three types of strategies were identified, depending on the farmers' objectives and adjustments. Finally, public policies to accompany these changes are considered

Deep optical spectroscopy of extended Lyman alpha emission around three radio-quiet z=4.5 quasars

We report the first results of a spectroscopic search for Lyman alpha, envelopes around three z=4.5 radio-quiet quasars. Our observational strategy uses the FORS2 spectrograph attached to the UT1 of the Very Large Telescope (VLT) in the multi-slit mode. This allows us to observe simultaneously the quasars and several PSF stars. The spectra of the latter are used to remove the point-like quasar from the data, and to unveil the faint underlying Lyman alpha, envelopes associated with the quasars with unprecedented depth. We clearly detect an envelope around two of the three quasars. These envelopes measure respectively 10" and 13" in extent (i.e. 67 kpc and 87 kpc). This is 5 to 10 times larger than predicted by the models of Haiman & Rees (2001) and up to 100 times fainter. Our observations better agree with models involing a clumpy envelope as in Alam & Miralda-Escude (2002) or Chelouche et al. (2008). We find that the brighter quasars also have the brighter envelopes but that the extend of the envelopes does not depend on the quasar luminosity. Although our results are based on only two objects with a detected Lyman alpha, envelope, the quality of the spatial deblending of the spectra lends considerable hope to estimate the luminosity function and surface brightness profiles of high redshift Lyman alpha, envelopes down to F= 2-3 10^{-21} erg/s/cm^2/A. We find that the best strategy to carry out such a project is to obtain both narrow-band images and deep slit-spectra.Comment: 8 pages, 5 figures, submitted to A&

Astrometric suitability of optically-bright ICRF sources for the alignment with the future Gaia celestial reference frame

The ICRF, currently based on the position of 717 extragalactic radio sources observed by VLBI, is the fundamental celestial reference frame adopted by the IAU in 1997. Within the next 10 years, the European space astrometry mission Gaia, to be launched by 2011, will permit determination of the extragalactic reference frame directly in the visible for the first time. Aligning these two frames with the highest accuracy will therefore be very important in the future for ensuring consistency between the measured radio and optical positions. This paper is aimed at evaluating the current astrometric suitability of the individual ICRF radio sources which are considered appropriate for the alignment with the future Gaia frame. To this purpose, we cross-identified the ICRF and the optical catalog V\'eron-Cetty and V\'eron (2006), to identify the optically-bright ICRF sources that will be positioned with the highest accuracy with Gaia. Then we investigated the astrometric suitability of these sources by examining their VLBI brightness distribution. We identified 243 candidate ICRF sources for the alignment with the Gaia frame (with an optical counterpart brighter than the apparent magnitude 18), but only 70 of these (10% of the ICRF sources) are found to have the necessary high astrometric quality (i.e. a brightness distribution that is compact enough) for this link. Additionally, it was found that the QSOs that will have the most accurate positions in the Gaia frame tend to have less-accurate VLBI positions, most probably because of their physical structures. Altogether, this indicates that identifying other high-quality VLBI radio sources suitable for the alignment with the future Gaia frame is mandatory.Comment: To be published in A&A (2008)