An integrable multicomponent quad equation and its Lagrangian formulation

We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg-de Vries equation, and the lattice modified Boussinesq equation. The N-th member in the hierarchy is an N-component system defined on an elementary plaquette in the 2-dimensional lattice. The system is multidimensionally consistent and a Lagrangian which respects this feature, i.e., which has the desirable closure property, is obtained.Comment: 10 page

On the precision of chiral-dispersive calculations of ππ\pi\pi scattering

We calculate the combination $2a_0^{(0)}-5a_0^{(2)}$ (the Olsson sum rule) and the scattering lengths and effective ranges $a_1$, $a_2^{(I)}$ and $b_1$, $b_2^{(I)}$ dispersively (with the Froissart--Gribov representation) using, at low energy, the phase shifts for $\pi\pi$ scattering obtained by Colangelo, Gasser and Leutwyler (CGL) from the Roy equations and chiral perturbation theory, plus experiment and Regge behaviour at high energy, or directly, using the CGL parameters for $a$s and $b$s. We find mismatch, both among the CGL phases themselves and with the results obtained from the pion form factor. This reaches the level of several (2 to 5) standard deviations, and is essentially independent of the details of the intermediate energy region ($0.82\leq E\leq 1.42$ GeV) and, in some cases, of the high energy behaviour assumed. We discuss possible reasons for this mismatch, in particular in connection with an alternate set of phase shifts.Comment: Version to appear in Phys. Rev. D. Graphs and sum rule added. Plain TeX fil

Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schr\"odinger and Dirac particles. A central issue that should be carefully analyzed when functional series are applied is their convergence. In the present paper, we study the properties of the eigenfunction expansions appearing in nonrelativistic and relativistic $R$-matrix theories. In particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13, 491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761 (1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular formulation of the R-matrix theory for Dirac particles, the functional series fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical Physics, 21 pages, 1 figur

Life at the extreme:Plant-driven hotspots of soil nutrient cycling in the hyper-arid core of the Atacama Desert

The hyperarid core of the Atacama Desert represents one of the most intense environments on Earth, often being used as an analog for Mars regolith. The area is characterized by extremes in climate (e.g., temperature, humidity, UV irradiation) and edaphic factors (e.g., hyper-salinity, high pH, compaction, high perchlorates, and low moisture, phosphorus and organic matter). However, the halophytic C4 plant Distichlis spicata appears to be one of the few species on the planet that can thrive in this environment. Within this habitat it captures windblown sand leading to the formation of unique structures and the generation of above-ground phyllosphere soil. Using a combination of approaches (e.g., X-ray Computed Tomography, TXRF, δ13C/δ15N isotope profiling, microbial PLFAs, 14C turnover, phosphate sorption isotherms) we examined the factors regulating the biogeochemical cycling of nitrogen (N), phosphorus (P) and carbon (C) in both vegetated and unvegetated areas. Our results showed that D. spicata rhizomes with large aerenchyma were able to break through the highly cemented topsoil layer leading to root proliferation in the underlying soil. The presence of roots increased soil water content, P availability and induced a change in microbial community structure and promoted microbial growth and activity. In contrast, soil in the phyllosphere exhibited almost no biological activity. Organic C stocks and recent C4 plant derived input increased as follows: phyllosphere (1941 g C m−2; 85% recent) &gt; soils under plants (575–748 g C m−2; 55–60%) &gt; bare soils (491–642 g C m−2; 9–17%). Due to the high levels of nitrate in soil (&gt;2 t ha−1) and high rates of P sorption/precipitation, our data suggest that the microbial activity is both C and P, but not N limited. Root-mediated salt uptake combined with foliar excretion and dispersal of NaCl into the surrounding area indicated that D. spicata was responsible for actively removing ca. 55% of the salt from the rhizosphere. We also demonstrate that NH3 emissions may represent a major N loss pathway from these soil ecosystems during the processing of organic N. We attribute this to NH3 volatilization to the high pH of the soil and slow rates of nitrification. In conclusion, we demonstrate that the extremophile D. spicata physically, chemically and biologically reengineers the soil to create a highly bioactive hotspot within the climate-extreme of the Atacama Desert.</p

Discovery of Interstellar Hydrogen Fluoride

We report the first detection of interstellar hydrogen fluoride. Using the Long Wavelength Spectrometer (LWS) of the Infrared Space Observatory (ISO), we have detected the 121.6973 micron J = 2 - 1 line of HF in absorption toward the far-infrared continuum source Sagittarius B2. The detection is statistically significant at the 13 sigma level. On the basis of our model for the excitation of HF in Sgr B2, the observed line equivalent width of 1.0 nm implies a hydrogen fluoride abundance of 3E-10 relative to H2. If the elemental abundance of fluorine in Sgr B2 is the same as that in the solar system, then HF accounts for ~ 2% of the total number of fluorine nuclei. We expect hydrogen fluoride to be the dominant reservoir of gas-phase fluorine in Sgr B2, because it is formed rapidly in exothermic reactions of atomic fluorine with either water or molecular hydrogen; thus the measured HF abundance suggests a substantial depletion of fluorine onto dust grains. Similar conclusions regarding depletion have previously been reached for the case of chlorine in dense interstellar clouds. We also find evidence at a lower level of statistical significance (~ 5 sigma) for an emission feature at the expected position of the 4(3,2)-4(2,3) 121.7219 micron line of water. The emission line equivalent width of 0.5 nm for the water feature is consistent with the water abundance of 5E-6 relative to H2 that has been inferred previously from observations of the hot core of Sgr B2.Comment: 11 pages (AASTeX using aaspp4.sty) plus 2 figures; to appear in ApJ Letter

Experimental Designs for Binary Data in Switching Measurements on Superconducting Josephson Junctions

We study the optimal design of switching measurements of small Josephson junction circuits which operate in the macroscopic quantum tunnelling regime. Starting from the D-optimality criterion we derive the optimal design for the estimation of the unknown parameters of the underlying Gumbel type distribution. As a practical method for the measurements, we propose a sequential design that combines heuristic search for initial estimates and maximum likelihood estimation. The presented design has immediate applications in the area of superconducting electronics implying faster data acquisition. The presented experimental results confirm the usefulness of the method. KEY WORDS: optimal design, D-optimality, logistic regression, complementary log-log link, quantum physics, escape measurement

Representing time-dependent freezing behaviour in immersion mode ice nucleation

In order to understand the impact of ice formation in clouds, a quantitative understanding of ice nucleation is required, along with an accurate and efficient representation for use in cloud resolving models. Ice nucleation by atmospherically relevant particle types is complicated by interparticle variability in nucleating ability, as well as a stochastic, time-dependent, nature inherent to nucleation. Here we present a new and computationally efficient Framework for Reconciling Observable Stochastic Time-dependence (FROST) in immersion mode ice nucleation. This framework is underpinned by the finding that the temperature dependence of the nucleation-rate coefficient controls the residence-time and cooling-rate dependence of freezing. It is shown that this framework can be used to reconcile experimental data obtained on different timescales with different experimental systems, and it also provides a simple way of representing the complexities of ice nucleation in cloud resolving models. The routine testing and reporting of time-dependent behaviour in future experimental studies is recommended, along with the practice of presenting normalised data sets following the methods outlined here

The Relationship of Upwelling to Mussel Production in the Rias on the Western Coast of Spain

We have calculated an upwelling index for each month over a 17-year period (1969-1985) for a point off the western coast of Spain. We interpret April through September values of the index to indicate the flux of nitrate-rich water in the Spanish Rias. The index representing the 6-month upwelling series has been correlated with an index representing the conditions of mussels grown during that season on rafts in Ria de Arosa. Two seasons represent extreme upwelling conditions over the 17-year sampling period: 1977 when the upwelling index was the highest, and 1983 when it was the lowest. A comparison of the condition of mussels during these years showed that meat content was double in 1977. We suggest, by this study, that long range forecasts of synoptic scale weather patterns could be used to predict the potential nutritional value of mussels harvested in the rias of Spain

SU(2) Landau gluon propagator on a 140^3 lattice

We present a numerical study of the gluon propagator in lattice Landau gauge for three-dimensional pure-SU(2) lattice gauge theory at couplings beta = 4.2, 5.0, 6.0 and for lattice volumes V = 40^3, 80^3, 140^3. In the limit of large V we observe a decreasing gluon propagator for momenta smaller than p_{dec} = 350^{+ 100}_{- 50} MeV. Data are well fitted by Gribov-like formulae and seem to indicate an infra-red critical exponent kappa slightly above 0.6, in agreement with recent analytic results.Comment: 5 pages with 2 figures and 3 tables; added a paragraph on discretization effect