Towards the Amplituhedron Volume

21 pages; v2: version published in JHEPIt has been recently conjectured that scattering amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. In this paper we show some interesting connections between the tree-level amplituhedron and a special class of differential equations. In particular we demonstrate how the amplituhedron volume for NMHV amplitudes is determined by these differential equations. The new formulation allows for a straightforward geometric description, without any reference to triangulations. Finally we discuss possible implications for volumes related to generic N^kMHV amplitudes.Peer reviewe

Review of recent advances in local approaches applied to pre-stressed components under fatigue loading

Fatigue strength of mechanical components in the high cycle regime depends on both the applied loading and the intensity of any residual stress field induced by either non-homogeneous plastic deformation or the solidification of a local portion of material due to welding operations. In presence of geometric variations that are amenable to being modelled as a sharp V-notch, the residual stress distribution near the notch tip is singular and follows the same form as the solution obtained by Williams in 1952 where the intensity of the asymptotic stress field is quantified by the notch stress intensity factor (NSIF). However, the residual stress varies during fatigue loading and a stable value may be reached. Numerical models have been developed for the calculation of the residual NSIFs and their variation under fatigue loading. Taking advantage of these models, new local approaches have also been recently developed which are able to predict the fatigue strength of pre-stressed notched components. The present paper provides a brief review of such recent advances

Amplituhedron meets Jeffrey-Kirwan Residue

The tree amplituhedra A^(m)_n,k are mathematical objects generalising the notion of polytopes into the Grassmannian. Proposed for m=4 as a geometric construction encoding tree-level scattering amplitudes in planar N=4 super Yang-Mills theory, they are mathematically interesting for any m. In this paper we strengthen the relation between scattering amplitudes and geometry by linking the amplituhedron to the Jeffrey-Kirwan residue, a powerful concept in symplectic and algebraic geometry. We focus on a particular class of amplituhedra in any dimension, namely cyclic polytopes, and their even-dimensional conjugates. We show how the Jeffrey-Kirwan residue prescription allows to extract the correct amplituhedron volume functions in all these cases. Notably, this also naturally exposes the rich combinatorial and geometric structures of amplituhedra, such as their regular triangulations.Peer reviewedFinal Accepted Versio

The Momentum Amplituhedron

In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in N = 4 super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron M n,k is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted from the canonical form with logarithmic singularities on the boundaries of this geometry.Peer reviewedFinal Published versio

How to enhance crop production and nitrogen fluxes? A result-oriented scheme to evaluate best agri-environmental measures in Veneto Region, Italy

The cost-effectiveness of adopting agri-environmental measures (AEMs) in Europe, which combine agricultural productions with reduced N losses, is debated due to poorly targeted site-specific funding that is allocated regardless of local variability. An integrated DAYCENT model-GIS platform was developed combining pedo-climatic and agricultural systems information. The aim was to evaluate best strategies to improve N fluxes of agro-ecosystems within a perspective of sustainable intensification. Indicators of agronomic efficiency and environmental quality were considered. The results showed that agronomic benefits were observed with a continuous soil cover (conservation agriculture and cover crops), which enhanced nitrogen use efficiency (+17%) and crop yields (+34%), although in some cases these might be overestimated due to modelling limitations. An overall environmental improvement was found with continuous soil cover and long-term change from mineral to organic inputs (NLeach 45 Mg ha 121), which were effective in the sandy soils of western and eastern Veneto with low SOM, improving the soil-water balance and nutrients availability over time. Results suggest that AEM subsidies should be allocated at a site-specific level that includes pedo-climatic variability, following a result-oriented approach

Fourier Decomposition of RR Lyrae light curves and the SX Phe population in the central region of NGC 3201

CCD time-series observations of the central region of the globular cluster NGC~3201 were obtained with the aim of performing the Fourier decomposition of the light curves of the RR~Lyrae stars present in that field. This procedure gave the mean values, for the metallicity, of [Fe/H]$_{ZW}=-1.483 \pm 0.006$ (statistical) $\pm 0.090$ (systematical), and for the distance, $5.000 \pm 0.001$~kpc (statistical) $\pm 0.220$ (systematical). The values found from two RRc stars are consistent with those derived previously. The differential reddening of the cluster was investigated and individual reddenings for the RR Lyrae stars were estimated from their $V-I$ curves. We found an average value of $E(B-V)= 0.23 \pm 0.02$. An investigation of the light curves of stars in the {\it blue stragglers} region led to the discovery of three new SX~Phe stars. The period-luminosity relation of the SX~Phe stars was used for an independent determination of the distance to the cluster and of the individual reddenings. We found a distance of 5.0 kpcComment: To appear in Revista Mexicana de Astronom\'ia y Astrof\'isica, Octuber 2014 issue, Vol 50. 17 pages, 10 figure

Constraining the parameters of globular cluster NGC 1904 from its variable star population

We present the analysis of 11 nights of V and I time-series observations of the globular cluster NGC 1904 (M 79). Using this we searched for variable stars in this cluster and attempted to refine the periods of known variables, making use of a time baseline spanning almost 8 years. We use our data to derive the metallicity and distance of NGC 1904. We used difference imaging to reduce our data to obtain high-precision light curves of variable stars. We then estimated the cluster parameters by performing a Fourier decomposition of the light curves of RR Lyrae stars for which a good period estimate was possible. We also derive an estimate for the age of the cluster by fitting theoretical isochrones to our colour-magnitude diagram (CMD). Out of 13 stars previously classified as variables, we confirm that 10 are bona fide variables. We cannot detect variability in one other within the precision of our data, while there are two which are saturated in our data frames, but we do not find sufficient evidence in the literature to confirm their variability. We also detect a new RR Lyrae variable, giving a total number of confirmed variable stars in NGC 1904 of 11. Using the Fourier parameters, we find a cluster metallicity [Fe/H]_ZW=-1.63 +- 0.14, or [Fe/H]_UVES=-1.57 \pm 0.18, and a distance of 13.3 +- 0.4 kpc (using RR0 variables) or 12.9 kpc (using the one RR1 variable in our sample for which Fourier decomposition was possible).Comment: 14 pages, 11 figures, accepted for publication in A&

Quality interoperability within digital libraries: the DL.org perspective

Quality is the most dynamic aspect of DLs, and becomes even more complex with respect to interoperability. This paper formalizes the research motivations and hypotheses on quality interoperability conducted by the Quality Working Group within the EU-funded project DL.org (<a href="http://www.dlorg.eu">http://www.dlorg.eu/</a>). After providing a multi-level interoperability framework – adopted by DL.org - the authors illustrate key-research points and approaches on the way to the interoperability of DLs quality, grounding them in the DELOS Reference Model. By applying the DELOS Reference Model Quality Concept Map to their interoperability motivating scenario, the authors subsequently present the two main research outcomes of their investigation - the Quality Core Model and the Quality Interoperability Survey