On dimension and existence of local bases for multivariate spline spaces

AbstractWe consider spaces of splines in k variables of smoothness r and degree d defined on a polytope in Rk which has been divided into simplices. Bernstein-Bézier methods are used to develop a framework for analyzing dimension and basis questions. Dimension formulae and local bases are found for the case r = 0 and general k. The main result of the paper shows the existence of local bases for spaces of trivariate splines (where k = 3) whenever d > 8r

Extracting forward strong amplitudes from elastic differential cross sections

The feasibility of a model-independent extraction of the forward strong amplitude from elastic nuclear cross section data in the Coulomb-nuclear interference region is assessed for $\pi$ and $K^+$ scattering at intermediate energies. Theoretically-generated "data" are analyzed to provide criteria for optimally designing experiments to measure these amplitudes, whose energy dependence (particularly that of the real parts) is needed for disentangling various sources of medium modifications of the projectile-nucleon interaction. The issues considered include determining the angular region over which to make the measurements, the role of the most forward angles measured, and the effects of statistical and systematic errors. We find that there is a region near the forward direction where Coulomb-nuclear interference allows reliable extraction of the strong forward amplitude for both pions and the $K^+$ from .3 to 1 GeV/c.Comment: 16 pages plus 12 separate postscript figure

Labour efficiency on-farm

End of project reportImprovements in milking efficiency have a greater influence than any other aspect of the dairy farmers work on overall farm labour inputs (Whipp, 1992). In order to facilitate the examination of milking process labour inputs, the milking process may be divided into the following three components: herding pre and post milking (transfer of cows to and from the milking parlour); milking (milking tasks / work routines within the parlour); and washing (washing of milking machine and yard). Meanwhile, within milking specifically, the number of cows milked per operator per hour is the best measure of both the performance of the operator and the milking installation (Clough, 1978). This is affected by the following three factors: the milking times of the cows, the number and arrangement of the milking units, and the operator’s work routine (Whipp, 1992). The addition of extra milking units will only increase milking performance if the operator has idle time during milking (Hansen, 1999)

Consistently Simulating a Wide Range of Atmospheric Scenarios for K2-18b with a Flexible Radiative Transfer Module

The atmospheres of small, potentially rocky exoplanets are expected to cover a diverse range in composition and mass. Studying such objects therefore requires flexible and wide-ranging modeling capabilities. We present in this work the essential development steps that lead to our flexible radiative transfer module, REDFOX, and validate REDFOX for the Solar system planets Earth, Venus and Mars, as well as for steam atmospheres. REDFOX is a k-distribution model using the correlated-k approach with random overlap method for the calculation of opacities used in the $\delta$-two-stream approximation for radiative transfer. Opacity contributions from Rayleigh scattering, UV / visible cross sections and continua can be added selectively. With the improved capabilities of our new model, we calculate various atmospheric scenarios for K2-18b, a super-Earth / sub-Neptune with $\sim$8 M$_\oplus$ orbiting in the temperate zone around an M-star, with recently observed H$_2$O spectral features in the infrared. We model Earth-like, Venus-like, as well as H$_2$-He primary atmospheres of different Solar metallicity and show resulting climates and spectral characteristics, compared to observed data. Our results suggest that K2-18b has an H$_2$-He atmosphere with limited amounts of H$_2$O and CH$_4$. Results do not support the possibility of K2-18b having a water reservoir directly exposed to the atmosphere, which would reduce atmospheric scale heights, hence too the amplitudes of spectral features inconsistent with the observations. We also performed tests for H$_2$-He atmospheres up to 50 times Solar metallicity, all compatible with the observations.Comment: 28 pages, 13 figures, accepted for publication in Ap

Initial State Interactions for K−K^--Proton Radiative Capture

The effects of the initial state interactions on the $K^--p$ radiative capture branching ratios are examined and found to be quite sizable. A general coupled-channel formalism for both strong and electromagnetic channels using a particle basis is presented, and applied to all the low energy $K^--p$ data with the exception of the {\it 1s} atomic level shift. Satisfactory fits are obtained using vertex coupling constants for the electromagnetic channels that are close to their expected SU(3) values.Comment: 16 pages, uses revte

A Fast Infrared Radiative Transfer Model for Overlapping Clouds

A fast infrared radiative transfer model (FIRTM2) appropriate for application to both single-layered and overlapping cloud situations is developed for simulating the outgoing infrared spectral radiance at the top of the atmosphere (TOA). In FIRTM2 a pre-computed library of cloud reflectance and transmittance values is employed to account for one or two cloud layers, whereas the background atmospheric optical thickness due to gaseous absorption can be computed from a clear-sky radiative transfer model. FIRTM2 is applicable to three atmospheric conditions: 1) clear-sky, 2) single-layered ice or water cloud, and 3) two simultaneous cloud layers in a column (e.g., ice cloud overlying water cloud). Moreover, FIRTM2 outputs the derivatives (i.e., Jacobians) of the TOA brightness temperature with respect to cloud optical thickness and effective particle size. Sensitivity analyses have been carried out to assess the performance of FIRTM2 for two spectral regions, namely the longwave (LW) band (587.3 - 1179.5/cm) and the short-to-medium wave (SMW) band (1180.1 - 2228.9/cm). The assessment is carried out in terms of brightness temperature differences (BTD) between FIRTM2 and the well-known discrete ordinates radiative transfer model (DISORT), henceforth referred to as BTD (F-D). The BTD (F-D) values for single-layered clouds are generally less than 0.8 K. For the case of two cloud layers (specifically ice cloud over water cloud), the BTD(F-D) values are also generally less than 0.8 K except for the SMW band for the case of a very high altitude (>15 km) cloud comprised of small ice particles. Note that for clear-sky atmospheres, FIRTM2 reduces to the clear-sky radiative transfer model that is incorporated into FIRTM2, and the errors in this case are essentially those of the clear-sky radiative transfer model