96 research outputs found

    JIMWLK evolution in the Gaussian approximation

    Get PDF
    We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors Nc. This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it reproduces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite Nc. Any higher n-point function with n greater than or equal to 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.Comment: v2: 45 pages, 4 figures, various corrections, section 4.4 updated, to appear in JHE

    Modelled agroforestry outputs at field and farm scale to support biophysical and environmental assessments

    Get PDF
    This report, comprising Deliverable 6.17, in the AGFORWARD project brings together examples of modelled outputs at field and farm scale to support the biophysical, social, and environmental assessment of the innovations selected from work-packages 2 to 5.N/

    Agroforestry is paying off – Economic evaluation of ecosystem services in European landscapes with and without agroforestry systems

    Get PDF
    The study assessed the economic performance of marketable ecosystem services (ES) (biomass production) and non-marketable ecosystem services and dis-services (groundwater, nutrient loss, soil loss, carbon sequestration, pollination deficit) in 11 contrasting European landscapes dominated by agroforestry land use compared to business as usual agricultural practice. The productivity and profitability of the farming activities and the associated ES were quantified using environmental modelling and economic valuation. After accounting for labour and machinery costs the financial value of the outputs of Mediterranean agroforestry systems tended to be greater than the corresponding agricultural system; but in Atlantic and Continental regions the agricultural system tended to be more profitable. However, when economic values for the associated ES were included, the relative profitability of agroforestry increased. Agroforestry landscapes: (i) were associated to reduced externalities of pollution from nutrient and soil losses, and (ii) generated additional benefits from carbon capture and storage and thus generated an overall higher economic gain. Our findings underline how a market system that includes the values of broader ES would result in land use change favouring multifunctional agroforestry. Imposing penalties for dis-services or payments for services would reflect their real world prices and would make agroforestry a more financially profitable system

    Effective Rheology of Bubbles Moving in a Capillary Tube

    Full text link
    We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur
    corecore