Generalized Tsen theorem and rationally connected Fano fibrations

We prove that a fibration X \to \Bbb P_1, the general fiber of which is a smooth Fano threefold, is rationally connected. The proof is based on a generalization of Tsen's classical theorem: a fibration X/C over a curve the general fiber of which is a Fano complete intersection in a product of weighted projective spaces has a section.Comment: LaTeX2e, 28 pages, modified proof of 4.

A decision support tool for landfill methane generation and gas collection

This study presents a decision support tool (DST) to enhance methane generation at individual landfill sites. To date there is no such tool available to provide landfill decision makers with clear and simplified information to evaluate biochemical processes within a landfill site, to assess performance of gas production and to identify potential remedies to any issues. The current lack in understanding stems from the complexity of the landfill waste degradation process. Two scoring sets for landfill gas production performance are calculated with the tool: (1) methane output score which measures the deviation of the actual methane output rate at each site which the prediction generated by the first order decay model LandGEM; and (2) landfill gas indicators’ score, which measures the deviation of the landfill gas indicators from their ideal ranges for optimal methane generation conditions. Landfill gas indicators include moisture content, temperature, alkalinity, pH, BOD, COD, BOD/COD ratio, ammonia, chloride, iron and zinc. A total landfill gas indicator score is provided using multi-criteria analysis to calculate the sum of weighted scores for each indicator. The weights for each indicator are calculated using an analytical hierarchical process. The tool is tested against five real scenarios for landfill sites in UK with a range of good, average and poor landfill methane generation over a one year period (2012). An interpretation of the results is given for each scenario and recommendations are highlighted for methane output rate enhancement. Results demonstrate how the tool can help landfill managers and operators to enhance their understanding of methane generation at a site-specific level, track landfill methane generation over time, compare and rank sites, and identify problems areas within a landfill site

The Clump Mass Function of the Dense Clouds in the Carina Nebula Complex

We want to characterize the properties of the cold dust clumps in the Carina Nebula Complex (CNC), which shows a very high level of massive star feedback. We derive the Clump Mass Function (ClMF), explore the reliability of different clump extraction algorithms, and investigate the influence of the temperatures within the clouds on the resulting shape of the ClMF. We analyze a 1.25x1.25 deg^2 wide-field sub-mm map obtained with LABOCA (APEX), which provides the first spatially complete survey of the clouds in the CNC. We use the three clump-finding algorithms CLUMPFIND (CF), GAUSSCLUMPS (GC) and SExtractor (SE) to identify individual clumps and determine their total fluxes. In addition to assuming a common `typical' temperature for all clouds, we also employ an empirical relation between cloud column densities and temperature to determine an estimate of the individual clump temperatures, and use this to determine individual clump masses. While the ClMF based on the CF extraction is very well described by a power-law, the ClMFs based on GC and SE are better represented by a log-normal distribution. We also find that the use of individual clump temperatures leads to a shallower ClMF slope than the assumption of a common temperature (e.g. 20 K) of all clumps. The power-law of dN/dM \propto M^-1.95 we find for the CF sample is in good agreement with ClMF slopes found in previous studies of other regions. The dependence of the ClMF shape (power-law vs. log-normal distribution) on the employed extraction method suggests that observational determinations of the ClMF shape yields only very limited information about the true structure of the cloud. Interpretations of log-normal ClMF shape as a signature of turbulent pre-stellar clouds vs. power-law ClMFs as a signature of star-forming clouds may be taken with caution for a single extraction algorithm without additional information.Comment: 8 pages, 7 figures, accepted by A&

Spectral interferometric polarised coherent anti-Stokes Raman spectroscopy

We have developed an interferometric implementation of coherent anti-Stokes Raman scattering (CARS) which enables broadband coherent Raman spectroscopy free from non-resonant background (NRB), with a signal strength proportional to concentration. Spectra encode mode symmetry information into the amplitude response which can be directly compared to polarised spontaneous Raman spectra. The method requires only passive polarisation optics and is suitable for a wide range of laser linewidths and pulse durationsComment: 5 pages, 3 figures, submitted to PR