The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

Regional and seasonal patterns of epipelagic fish assemblages from the central California Current

The coastal Pacific Ocean off northern and central California encompasses the strongest seasonal upwelling zone in the California Current ecosystem. Headlands and bays here generate complex circulation features and confer unusual oceanographic complexity. We sampled the coastal epipelagic fish community of this region with a surface trawl in the summer and fall of 2000–05 to assess patterns of spatial and temporal community structure. Fifty-three species of fish were captured in 218 hauls at 34 fixed stations, with clupeiform species dominating. To examine spatial patterns, samples were grouped by location relative to a prominent headland at Point Reyes and the resulting two regions, north coast and Gulf of the Farallones, were plotted by using nonmetric multidimensional scaling. Seasonal and interannual patterns were also examined, and representative species were identified for each distinct community. Seven oceanographic variables measured concurrently with trawling were plotted by principal components analysis and tested for correlation with biotic patterns. We found significant differences in community structure by region, year, and season, but no interaction among main effects. Significant differences in oceanographic conditions mirrored the biotic patterns, and a match between biotic and hydrographic structure was detected. Dissimilarity between assemblages was mostly the result of differences in abundance and frequency of occurrence of about twelve common species. Community patterns were best described by a subset of hydrographic variables, including water depth, distance from shore, and any one of several correlated variables associated with upwelling intensity. Rather than discrete communities with clear borders and distinct member species, we found gradients in community structure and identified stations with similar fish communities by region and by proximity to features such as the San Francisco Bay

The Dirac operator on generalized Taub-NUT spaces

We find sufficient conditions for the absence of harmonic $L^2$ spinors on spin manifolds constructed as cone bundles over a compact K\"ahler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page

Methanol exchange between grassland and the atmosphere

International audienceConcentrations and fluxes of methanol were measured above two differently managed grassland fields (intensive and extensive) in central Switzerland during summer 2004. The measurements were performed with a proton-transfer-reaction mass-spectrometer and fluxes were determined by the eddy covariance method. The observed methanol emission showed a distinct diurnal cycle and was strongly correlated with global radiation and water vapour flux. Mean and maximum daily emissions were found to depend on grassland species composition and, for the intensive field, also on the growing state. The extensive field with a more complex species composition had higher emissions than the graminoid-dominated intensive field, both on an area and on a biomass basis. A simple parameterisation depending on the water vapour flux and the leaf area index allowed a satisfying simulation of the temporal variation of methanol emissions over the growing phase. Accumulated carbon losses due to methanol emissions accounted for 0.024 and 0.048% of net primary productivity for the intensive and extensive field, respectively. The integral methanol emissions over the growing periods were more than one order of magnitude higher than the emissions related to cut and drying events

Regularity for eigenfunctions of Schr\"odinger operators

We prove a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator. More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0. Our result extends to the case when b_j and c_{ij} are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy

Invertible Dirac operators and handle attachments on manifolds with boundary

For spin manifolds with boundary we consider Riemannian metrics which are product near the boundary and are such that the corresponding Dirac operator is invertible when half-infinite cylinders are attached at the boundary. The main result of this paper is that these properties of a metric can be preserved when the metric is extended over a handle of codimension at least two attached at the boundary. Applications of this result include the construction of non-isotopic metrics with invertible Dirac operator, and a concordance existence and classification theorem.Comment: Accepted for publication in Journal of Topology and Analysi

The effect of fatty acid surfactants on the uptake of nitric acid to deliquesced NaCl aerosol

Surface active organic compounds have been observed in marine boundary layer aerosol. Here, we investigate the effect such surfactants have on the uptake of nitric acid (HNO&lt;sub&gt;3&lt;/sub&gt;), an important removal reaction of nitrogen oxides in the marine boundary layer. The uptake of gaseous HNO&lt;sub&gt;3&lt;/sub&gt; on deliquesced NaCl aerosol was measured in a flow reactor using HNO&lt;sub&gt;3&lt;/sub&gt; labelled with the short-lived radioactive isotope &lt;sup&gt;13&lt;/sup&gt;N. The uptake coefficient γ on pure deliquesced NaCl aerosol was γ=0.5&amp;plusmn;0.2 at 60% relative humidity and 30 ppb HNO&lt;sub&gt;3&lt;/sub&gt;(g). The uptake coefficient was reduced by a factor of 5–50 when the aerosol was coated with saturated linear fatty acids with carbon chain lengths of 18 and 15 atoms in monolayer quantities. In contrast, neither shorter saturated linear fatty acids with 12 and 9 carbon atoms, nor coatings with the unsaturated oleic acid (C18, cis-double bond) had a detectable effect on the rate of HNO&lt;sub&gt;3&lt;/sub&gt; uptake. It is concluded that it is the structure of the monolayers formed, which determines their resistance towards HNO&lt;sub&gt;3&lt;/sub&gt; uptake. Fatty acids (C18 and C15), which form a highly ordered film in the so-called liquid condensed state, represent a significant barrier towards HNO&lt;sub&gt;3&lt;/sub&gt; uptake, while monolayers of shorter-chain fatty acids (C9, C12) and of the unsaturated oleic acid form a less ordered film in the liquid expanded state and do not hinder the uptake. Similarly, high contents of humic acids in the aerosol, a structurally inhomogeneous, quite water soluble mixture of oxidised high molecular weight organic compounds did not affect HNO&lt;sub&gt;3&lt;/sub&gt; uptake. As surfactant films on naturally occurring aerosol are expected to be less structured due to their chemical inhomogeneity, it is likely that their inhibitory effect on HNO&lt;sub&gt;3&lt;/sub&gt; uptake is smaller than that observed here for the C15 and C18 fatty acid monolayers

Summertime elemental mercury exchange of temperate grasslands on an ecosystem-scale

In order to estimate the air-surface mercury exchange of grasslands in temperate climate regions, fluxes of gaseous elemental mercury (GEM) were measured at two sites in Switzerland and one in Austria during summer 2006. Two classic micrometeorological methods (aerodynamic and modified Bowen ratio) have been applied to estimate net GEM exchange rates and to determine the response of the GEM flux to changes in environmental conditions (e. g. heavy rain, summer ozone) on an ecosystem-scale. Both methods proved to be appropriate to estimate fluxes on time scales of a few hours and longer. Average dry deposition rates up to 4.3 ng m(-2) h(-1) and mean deposition velocities up to 0.10 cm s(-1) were measured, which indicates that during the active vegetation period temperate grasslands are a small net sink for atmospheric mercury. With increasing ozone concentrations depletion of GEM was observed, but could not be quantified from the flux signal. Night-time deposition fluxes of GEM were measured and seem to be the result of mercury co-deposition with condensing water. Effects of grass cuts could also be observed, but were of minor magnitude

The annual ammonia budget of fertilised cut grassland – Part 2: Seasonal variations and compensation point modeling

The net annual NH&lt;sub&gt;3&lt;/sub&gt; exchange budget of a fertilised, cut grassland in Central Switzerland is presented. The observation-based budget was computed from semi-continuous micrometeorological fluxes over a time period of 16 months and using a process-based gap-filling procedure. The data for emission peak events following the application of cattle slurry and for background exchange were analysed separately to distinguish short-term perturbations from longer-term ecosystem functioning. A canopy compensation point model of background exchange is parameterised on the basis of measured data and applied for the purposes of gap-filling. The data show that, outside fertilisation events, grassland behaves as a net sink for atmospheric NH&lt;sub&gt;3&lt;/sub&gt; with an annual dry deposition flux of &amp;minus;3.0 kg N ha&lt;sup&gt;&amp;minus;1&lt;/sup&gt; yr&lt;sup&gt;&amp;minus;1&lt;/sup&gt;, although small NH&lt;sub&gt;3&lt;/sub&gt; emissions by the canopy were measured in dry daytime conditions. The median &amp;Gamma;&lt;sub&gt;&lt;i&gt;s&lt;/i&gt;&lt;/sub&gt; ratio in the apoplast (=[NH&lt;sub&gt;4&lt;/sub&gt;&lt;sup&gt;+&lt;/sup&gt;]/[H&lt;sup&gt;+&lt;/sup&gt;]) estimated from micrometeorological measurements was 620, equivalent to a stomatal compensation point of 1.3 &amp;mu;g NH&lt;sub&gt;3&lt;/sub&gt; m&lt;sup&gt;&amp;minus;3&lt;/sup&gt; at 15 &amp;deg;C. Non-stomatal resistance to deposition &lt;i&gt;R&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt; was shown to increase with temperature and decrease with surface relative humidity, and &lt;i&gt;R&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt; values were among the highest published for European grasslands, consistent with a relatively high ratio of NH&lt;sub&gt;3&lt;/sub&gt; to acid gases in the boundary layer at this site. Since the gross annual NH&lt;sub&gt;3&lt;/sub&gt; emission by slurry spreading was of the order of +20 kg N ha&lt;sup&gt;&amp;minus;1&lt;/sup&gt; yr&lt;sup&gt;&amp;minus;1&lt;/sup&gt;, the fertilised grassland was a net NH&lt;sub&gt;3&lt;/sub&gt; source of +17 kg N ha&lt;sup&gt;&amp;minus;1&lt;/sup&gt; yr&lt;sup&gt;&amp;minus;1&lt;/sup&gt;. A comparison with the few other measurement-based budget values from the literature reveals considerable variability, demonstrating both the influence of soil, climate, management and grassland type on the NH&lt;sub&gt;3&lt;/sub&gt; budget and the difficulty of scaling up to the national level