Positive solutions of Schr\"odinger equations and fine regularity of boundary points

Given a Lipschitz domain $\Omega$ in ${\mathbb R} ^N$ and a nonnegative potential $V$ in $\Omega$ such that $V(x)\, d(x,\partial \Omega)^2$ is bounded in $\Omega$ we study the fine regularity of boundary points with respect to the Schr\"odinger operator $L_V:= \Delta -V$ in $\Omega$. Using potential theoretic methods, several conditions equivalent to the fine regularity of $z \in \partial \Omega$ are established. The main result is a simple (explicit if $\Omega$ is smooth) necessary and sufficient condition involving the size of $V$ for $z$ to be finely regular. An essential intermediate result consists in a majorization of $\int_A | {\frac {u} {d(.,\partial \Omega)}} | ^2\, dx$ for $u$ positive harmonic in $\Omega$ and $A \subset \Omega$. Conditions for almost everywhere regularity in a subset $A$ of $\partial \Omega$ are also given as well as an extension of the main results to a notion of fine ${\mathcal L}_1 | {\mathcal L}_0$-regularity, if ${\mathcal L}_j={\mathcal L}-V_j$, $V_0,\, V_1$ being two potentials, with $V_0 \leq V_1$ and ${\mathcal L}$ a second order elliptic operator.Comment: version 1. 23 pages version 3. 28 pages. Mainly a typo in Theorem 1.1 is correcte

New light on gamma-ray burst host galaxies with Herschel

Until recently, dust emission has been detected in very few host galaxies of gamma-ray bursts (GRBHs). With Herschel, we have now observed 17 GRBHs up to redshift z~3 and detected seven of them at infrared (IR) wavelengths. This relatively high detection rate (41%) may be due to the composition of our sample which at a median redshift of 1.1 is dominated by the hosts of dark GRBs. Although the numbers are small, statistics suggest that dark GRBs are more likely to be detected in the IR than their optically-bright counterparts. Combining our IR data with optical, near-infrared, and radio data from our own datasets and from the literature, we have constructed spectral energy distributions (SEDs) which span up to 6 orders of magnitude in wavelength. By fitting the SEDs, we have obtained stellar masses, dust masses, star-formation rate (SFR), and extinctions for our sample galaxies. We find that GRBHs are galaxies that tend to have a high specfic SFR (sSFR), and like other star-forming galaxies, their ratios of dust-to-stellar mass are well correlated with sSFR. We incorporate our Herschel sample into a larger compilation of GRBHs, and compare this combined sample to SFR-weighted median stellar masses of the widest, deepest galaxy survey to date. This is done in order to establish whether or not GRBs can be used as an unbiased tracer of cosmic comoving SFR density (SFRD) in the universe. In contrast with previous results, this comparison shows that GRBHs are medium-sized galaxies with relatively high sSFRs; stellar masses and sSFRs of GRBHs as a function of redshift are similar to what is expected for star-forming galaxy populations at similar redshifts. We conclude that there is no strong evidence that GRBs are biased tracers of SFRD; thus they should be able to reliably probe the SFRD to early epochs.Comment: 18 pages, 9 figures, accepted for publication in A&A. Revised to include Fig. 6, mistakenly omitted in origina

Turbulent ‘stopping plumes’ and plume pinch-off in uniform surroundings

Observations of turbulent convection in the environment are of variously sus- tained plume-like flows or intermittent thermal-like flows. At different times of the day the prevailing conditions may change and consequently the observed flow regimes may change. Understanding the link between these flows is of practical importance meteorologically, and here we focus our interest upon plume-like regimes that break up to form thermal-like regimes. It has been shown that when a plume rises from a boundary with low conductivity, such as arable land, the inability to maintain a rapid enough supply of buoyancy to the plume source can result in the turbulent base of the plume separating and rising away from the source. This plume ‘pinch-off’ marks the onset of the intermittent thermal-like behavior. The dynamics of turbulent plumes in a uniform environment are explored in order to investigate the phenomenon of plume pinch-off. The special case of a turbulent plume having its source completely removed, a ‘stopping plume’, is considered in particular. The effects of forcing a plume to pinch-off, by rapidly reducing the source buoyancy flux to zero, are shown experi- mentally. We release saline solution into a tank filled with fresh water generating downward propagating steady turbulent plumes. By rapidly closing the plume nozzle, the plumes are forced to pinch-off. The plumes are then observed to detach from the source and descend into the ambient. The unsteady buoyant region produced after pinch-off, cannot be described by the power-law behavior of either classical plumes or thermals, and so the terminology ‘stopping plume’ (analogous to a ‘starting plume’) is adopted for this type of flow. The propagation of the stopping plume is shown to be approximately linearly dependent on time, and we speculate therefore that the closure of the nozzle introduces some vorticity into the ambient, that may roll up to form a vortex ring dominating the dynamics of the base of a stopping plume

On the existence and structure of a mush at the inner core boundary of the Earth

It has been suggested about 20 years ago that the liquid close to the inner core boundary (ICB) is supercooled and that a sizable mushy layer has developed during the growth of the inner core. The morphological instability of the liquid-solid interface which usually results in the formation of a mushy zone has been intensively studied in metallurgy, but the freezing of the inner core occurs in very unusual conditions: the growth rate is very small, and the pressure gradient has a key role, the newly formed solid being hotter than the adjacent liquid. We investigate the linear stability of a solidification front under such conditions, pointing out the destabilizing role of the thermal and solutal fields, and the stabilizing role of the pressure gradient. The main consequence of the very small solidification rate is the importance of advective transport of solute in liquid, which tends to remove light solute from the vicinity of the ICB and to suppress supercooling, thus acting against the destabilization of the solidification front. For plausible phase diagrams of the core mixture, we nevertheless found that the ICB is likely to be morphologically unstable, and that a mushy zone might have developed at the ICB. The thermodynamic thickness of the resulting mushy zone can be significant, from $\sim100$ km to the entire inner core radius, depending on the phase diagram of the core mixture. However, such a thick mushy zone is predicted to collapse under its own weight, on a much smaller length scale ($\lesssim 1$ km). We estimate that the interdendritic spacing is probably smaller than a few tens of meter, and possibly only a few meters

Conformations of Linear DNA

We examine the conformations of a model for under- and overwound DNA. The molecule is represented as a cylindrically symmetric elastic string subjected to a stretching force and to constraints corresponding to a specification of the link number. We derive a fundamental relation between the Euler angles that describe the curve and the topological linking number. Analytical expressions for the spatial configurations of the molecule in the infinite- length limit were obtained. A unique configuraion minimizes the energy for a given set of physical conditions. An elastic model incorporating thermal fluctuations provides excellent agreement with experimental results on the plectonemic transition.Comment: 5 pages, RevTeX; 6 postscript figure

A quiescent galaxy at the position of the long GRB 050219A

Long-duration gamma-ray bursts (LGRBs) are produced by the collapse of very massive stars. Due to the short lifetime of their progenitors, LGRBs pinpoint star-forming galaxies. We present here a multi-band search for the host galaxy of the long dark GRB 050219A within the enhanced Swift/XRT error circle. We used spectroscopic observations acquired with VLT/X-shooter to determine the redshift and star-formation rate of the putative host galaxy. We compared the results with the optical/IR spectral energy distribution obtained with different facilities. Surprisingly, the host galaxy is a old and quiescent early-type galaxy at z = 0.211 characterised by an unprecedentedly low specific star-formation rate. It is the first LGRB host to be also an early-type post-starburst galaxy. This is further evidence that GRBs can explode in all kind of galaxies, with the only requirement being an episode of star-formation.Comment: 11 pages, 10 figures, 3 tables; accepted for publication in Astronomy & Astrophysic

Optical Images and Source Catalog of AKARI North Ecliptic Pole Wide Survey Field

We present the source catalog and the properties of the $B-, R-$, and $I-$band images obtained to support the {\it AKARI} North Ecliptic Pole Wide (NEP-Wide) survey. The NEP-Wide is an {\it AKARI} infrared imaging survey of the north ecliptic pole covering a 5.8 deg$^2$ area over 2.5 -- 6 \micron wavelengths. The optical imaging data were obtained at the Maidanak Observatory in Uzbekistan using the Seoul National University 4k $\times$ 4k Camera on the 1.5m telescope. These images cover 4.9 deg$^2$ where no deep optical imaging data are available. Our $B-, R-$, and $I-$band data reach the depths of $\sim$23.4, $\sim$23.1, and $\sim$22.3 mag (AB) at 5$\sigma$, respectively. The source catalog contains 96,460 objects in the $R-$band, and the astrometric accuracy is about 0.15\arcsec at 1$\sigma$ in each RA and Dec direction. These photometric data will be useful for many studies including identification of optical counterparts of the infrared sources detected by {\it AKARI}, analysis of their spectral energy distributions from optical through infrared, and the selection of interesting objects to understand the obscured galaxy evolution.Comment: 39 pages, 12 figure

The VVDS type-1 AGN sample: The faint end of the luminosity function

In a previous paper (Gavignaud et al. 2006), we presented the type-1 Active Galactic Nuclei (AGN) sample obtained from the first epoch data of the VIMOS-VLT Deep Survey (VVDS). The sample consists of 130 faint, broad-line AGN with redshift up to z=5 and 17.5< I <24.0, selected on the basis of their spectra. In this paper we present the measurement of the Optical Luminosity Function up to z=3.6 derived from this sample, we compare our results with previous results from brighter samples both at low and at high redshift. Our data, more than one magnitude fainter than previous optical surveys, allow us to constrain the faint part of the luminosity function up to high redshift. By combining our faint VVDS sample with the large sample of bright AGN extracted from the SDSS DR3 (Richards et al., 2006b) and testing a number of different evolutionary models, we find that the model which better represents the combined luminosity functions, over a wide range of redshift and luminosity, is a luminosity dependent density evolution (LDDE) model, similar to those derived from the major X-surveys. Such a parameterization allows the redshift of the AGN space density peak to change as a function of luminosity and explains the excess of faint AGN that we find at 1.0< z <1.5. On the basis of this model we find, for the first time from the analysis of optically selected samples, that the peak of the AGN space density shifts significantly towards lower redshift going to lower luminosity objects. This result, already found in a number of X-ray selected samples of AGN, is consistent with a scenario of "AGN cosmic downsizing", in which the density of more luminous AGN, possibly associated to more massive black holes, peaks earlier in the history of the Universe, than that of low luminosity ones.Comment: 13 pages, 10 figures, submitted to A&

Extensive dissolution of live pteropods in the Southern Ocean

The carbonate chemistry of the surface ocean is rapidly changing with ocean acidification, a result of human activities. In the upper layers of the Southern Ocean, aragonite—a metastable form of calcium carbonate with rapid dissolution kinetics—may become undersaturated by 2050 (ref. 2). Aragonite undersaturation is likely to affect aragonite-shelled organisms, which can dominate surface water communities in polar regions. Here we present analyses of specimens of the pteropod Limacina helicina antarctica that were extracted live from the Southern Ocean early in 2008. We sampled from the top 200m of the water column, where aragonite saturation levels were around 1, as upwelled deep water is mixed with surface water containing anthropogenic CO2. Comparing the shell structure with samples from aragonite-supersaturated regions elsewhere under a scanning electron microscope, we found severe levels of shell dissolution in the undersaturated region alone. According to laboratory incubations of intact samples with a range of aragonite saturation levels, eight days of incubation in aragonite saturation levels of 0.94– 1.12 produces equivalent levels of dissolution. As deep-water upwelling and CO2 absorption by surface waters is likely to increase as a result of human activities2,4, we conclude that upper ocean regions where aragonite-shelled organisms are affected by dissolution are likely to expand

The cause-specific morbidity and mortality, and referral patterns of all neonates admitted to a tertiary referral hospital in the northern provinces of Vietnam over a one year period.

OBJECTIVE: To describe the cause-specific morbidity and mortality, and referral patterns of all neonates admitted to a tertiary referral hospital in the northern provinces of Vietnam. DESIGN: A prospective hospital based observational study. SETTING: The Neonatal Department, National Hospital of Pediatrics, Hanoi, Vietnam. PATIENTS: All admissions to the Neonatal Department over a 12 month period. MAIN OUTCOME MEASURES: Cause-specific morbidity and mortality; deaths. RESULTS: There were 5064 admissions with the commonest discharge diagnoses being infection (32%) and prematurity (29%). The case fatality ratio (CFR) was 13.9% (n = 703). Infection (38%), cardio/respiratory disorders (27%), congenital abnormalities (20%) and neurological conditions (10%) were the main causes of death. Of all the deaths, 38% had an admission weight ≥2500g. Higher CFR were associated with lower admission weights. Very few deaths (3%) occurred in the first 24 hours of life. Most referrals and deaths came from Hanoi and neighbouring provincial hospitals, with few from the most distant provinces. Two distant referral provinces had the highest CFR. CONCLUSIONS: The CFR was high and few deaths occurred in neonates <24 hours old. The high rates of infection call for an improvement in infection control practices and peripartum antibiotic use at provincial and tertiary level. Understanding provincial hospital capacity and referral pathways is crucial to improving the outcomes at tertiary centres. A quality of care audit tool would enable more targeted interventions and monitoring of health outcomes