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

Dirac-harmonic maps from index theory

We prove existence results for Dirac-harmonic maps using index theoretical tools. They are mainly interesting if the source manifold has dimension 1 or 2 modulo 8. Our solutions are uncoupled in the sense that the underlying map between the source and target manifolds is a harmonic map.Comment: 26 pages, no figur

Experimental evidence for the role of cantori as barriers in a quantum system

We investigate the effect of cantori on momentum diffusion in a quantum system. Ultracold caesium atoms are subjected to a specifically designed periodically pulsed standing wave. A cantorus separates two chaotic regions of the classical phase space. Diffusion through the cantorus is classically predicted. Quantum diffusion is only significant when the classical phase-space area escaping through the cantorus per period greatly exceeds Planck's constant. Experimental data and a quantum analysis confirm that the cantori act as barriers.Comment: 19 pages including 9 figures, Accepted for publication in Physical Review E in March 199

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<sub>3</sub>), an important removal reaction of nitrogen oxides in the marine boundary layer. The uptake of gaseous HNO<sub>3</sub> on deliquesced NaCl aerosol was measured in a flow reactor using HNO<sub>3</sub> labelled with the short-lived radioactive isotope <sup>13</sup>N. The uptake coefficient γ on pure deliquesced NaCl aerosol was γ=0.5±0.2 at 60% relative humidity and 30 ppb HNO<sub>3</sub>(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<sub>3</sub> uptake. It is concluded that it is the structure of the monolayers formed, which determines their resistance towards HNO<sub>3</sub> 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<sub>3</sub> 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<sub>3</sub> 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<sub>3</sub> uptake is smaller than that observed here for the C15 and C18 fatty acid monolayers

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

On a spin conformal invariant on manifolds with boundary

On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator under the chiral bag boundary condition. More precisely, we show that we can derive a spinorial analogue of Aubin's inequality.Comment: 26 page

Ammonia emission measurements of an intensively grazed pasture

The quantification of ammonia (NH3) emissions is still a challenge and the corresponding emission factor for grazed pastures is uncertain. This study presents NH3 emission measurements of two pasture systems in western Switzerland over the entire grazing season 2016. During the measurement campaign, each pasture system was grazed by 12 dairy cows in an intensive rotational management. The cow herds on the two pastures differed in the energy to protein balance of the diet. NH3 concentrations were measured upwind and downwind of a grazed subplot with line-integrating open path instruments that were able to retrieve small horizontal concentration differences (< 0.2 µg NH3 m−3). The NH3 emission fluxes were calculated by applying a backward Lagrangian stochastic (bLS) dispersion model to the difference of paired concentration measurements and ranged from 0 to 2.5 µg N–NH3 m−2 s−1. The fluxes increased steadily during a grazing interval from previous non-significant values to reach maximum emissions at the end of the grazing interval. Afterwards they decreased exponentially to near zero-values within 3–5 days. A default emission curve was calculated for each of the two systems and adopted to each rotation in order to account for missing data values and to estimate inflow disturbances due to grazing on upwind paddocks. Dung and cow location were monitored to account for the non-negligible inhomogeneity of cow excreta on the pasture. The average emission (± SD of individual rotation values) per grazing hour was calculated as 0.64±0.11 g N–NH3 cow−1 h−1 for the herd with the N-balanced diet (system M) and 1.07±0.06 g N–NH3 cow−1 h−1 for the herd with the protein-rich grass-only diet (system G). Surveys of feed intake, body weight and milk yield of the cow herds were used to estimate the nitrogen (N) excretion by an animal N budget model. Based on that, mean relative emission factors of 6.4±2.0 % and 8.7±2.7 % of the applied urine N were found for the systems M and G, respectively. The results can be used to validate the Swiss national emission inventory and demonstrate the positive effect of an N-balanced diet on pasture NH3 emissions

Solar signal in records and simulations of past climates

Abstract. Simulations with a fully coupled Climate System Model are used to show that a temporal fingerprint of solar influence on climate can be isolated. Smaller, rather than larger amplitudes of solar irradiance changes over the past Millennium generate a climate response in better agreement with proxy-based climate reconstructions. Summary The sun is the fundamental driver of the climate system. Radiative and dynamic processes in the Earth&apos;s atmosphere and other components (oceans, land surface, cryosphere) coupled into the climate system are continuously attempting to establish a radiative balance over the globe. In the absence of changes in the solar input and the overall composition of the atmosphere, the climate system could approach an equilibrium around which internal natural variability is occurring. However, the input from the sun is not constant. Variations happen from the shortest (minutes) to the longest (age of the solar system) time scales, and thus climate is in a constant state of adjustment. To establish a physical understanding of how these changes affect Earth, it is fundamental to identify and measure the response of the whole system to these changes. Depending on what time scales are being considered, it is important to focus on the relevant processes that dominate the solar forcing as well as the climate&apos;s response. Solar variations are not the only factor that can disturb the radiative balance of the planet. There are, for example, natural variations caused by explosive volcanism (short time scales) and changes in the Earth&apos;s orbit around the sun (longer time scales) that alter the amount of sunlight received over the planet. On geologic time scales, the changes in position of continents and mountain ranges are also affecting how energy is distributed and balanced. In most recent times, changes to the atmospheric composition and the Earths surface have been the result of human activity, imposing a large forcing on the energy balance of the planet. One of the most important challenges to the natural sciences is currently to detect and quantify the effect of our own influence on the climate system. In order to do this, we need to first understand what natural variations are occurring at the same time. Only when we can identify and subtract the natural effects can we isolate the human influence. The natural forcing from solar irradiance changes is still being considered a large uncertainty when evaluating the climate before and after the industrial revolution (IPCC 2001). Although significant irradiance change

A study of quantum decoherence in a system with Kolmogorov-Arnol'd-Moser tori

We present an experimental and numerical study of the effects of decoherence on a quantum system whose classical analogue has Kolmogorov-Arnol'd-Moser (KAM) tori in its phase space. Atoms are prepared in a caesium magneto-optical trap at temperatures and densities which necessitate a quantum description. This real quantum system is coupled to the environment via spontaneous emission. The degree of coupling is varied and the effects of this coupling on the quantum coherence of the system are studied. When the classical diffusion through a partially broken torus is < hbar, diffusion of quantum particles is inhibited. We find that increasing decoherence via spontaneous emission increases the transport of quantum particles through the boundary.Comment: 19 pages including 6 figure