Calculations for deep inelastic scattering using fast interpolation grid techniques at NNLO in QCD and the extraction of $$\alpha _{\mathrm {s}}$$ from HERA data

The extension of interpolation-grid frameworks for perturbative QCD calculations at next-to-next-to-leading order (NNLO) is presented for deep inelastic scattering (DIS) processes. A fast and flexible evaluation of higher-order predictions for any a posteriori choice of parton distribution functions (PDFs) or value of the strong coupling constant is essential in iterative fitting procedures to extract PDFs and Standard Model parameters as well as for a detailed study of the scale dependence. The APPLfast project, described here, provides a generic interface between the parton-level Monte Carlo program NNLOjet and both the APPLgrid and fastNLO libraries for the production of interpolation grids at NNLO accuracy. Details of the interface for DIS processes are presented together with the required interpolation grids at NNLO, which are made available. They cover numerous inclusive jet measurements by the H1 and ZEUS experiments at HERA. An extraction of the strong coupling constant is performed as an application of the use of such grids and a best-fit value of $$\alpha _{\mathrm {s}} (M_{{\mathrm {Z}}}) = 0.1170\,(15)_\text {exp}\,(25)_\text {th}$$αs(MZ)=0.1170(15)exp(25)th is obtained using the HERA inclusive jet cross section data.

Mass-Conserving Remapping of Radar Data onto Two-Dimensional Cartesian Coordinates for Hydrologic Applications

Recent upgrades to operational radar-rainfall products in terms of quality and resolution call for reexamination of the factors that contribute to the uncertainty of radar-rainfall estimation. Remapping or regridding of radar observations onto Cartesian coordinates is implemented by practitioners when radar estimates are compared against rain gauge observations, in hydrologic applications, or for merging data from different radars. However, assuming perfect radar observations, many of the widely used remapping methodologies do not conserve mass for the rainfall rate field. The most popular remapping approaches used are those based on extracting information from radar bins whose centers fall within a certain distance from the center of the Cartesian grid. This paper develops a mass-conserving method for remapping, which is called “precise remapping,” which is compared against two other commonly used remapping methods. Results show that the choice of the remapping method can make a substantial difference in grid-averaged rainfall accumulations (up to more than 100%). Differences were quantified using observations from two radars, collected during a field experiment. The interpolation grid resolution was also found to affect interpolated rainfall estimates. Approximate remapping methods tend to be much more sensitive to the interpolation grid resolution than precise remapping. High-resolution radar data such as those from radars with short gate spacing or narrow beams, or the super-resolution Weather Surveillance Radar-1988 Doppler (WSR-88D) sampling format, are significantly more sensitive (by up to 100%) to the remapping method and the interpolation grid resolution than the legacy WSR-88D rainfall data resolution of 1° × 1 km.

Interpolation Grid for Local Area of Iasi City

Definitive transition to GNSS technology of achieving geodetic networks for cadastre implementation in cities and municipalities, enforce establishing a unique way of linking between current measurements and existing geodetic data, with a sufficient accuracy proper to urban cadastre standards. Regarding city of Iasi, is presented a different method of transformation which consist in an interpolation grid for heights system. The Romanian national height system is „Black Sea-1975” normal heights system. Founded in 1945 by Molodenski, this system uses the quasigeoid as reference surface, being in relation with the ellipsoid through the height anomalies sizes in each point. The unitary transformation between the ETRS- 89 ellipsoidal height system and the normal one, at national level is provided through the „TransdatRo” program developed by NACLR (National Agency for Cadastre and Land Registration).

Robust Gradient Estimation Schemes Using Radial Basis Functions

Utilization of Radial Basis Functions (RBFs) for gradient estimation is tested over various noisy flow fields. A novel mathematical formulation which minimizes the energy functional associated with the analytical surface fit for Gaussian (GA) and Generalized Multiquadratic (GMQ) RBFs is presented. Error analysis of the wall gradient estimation was performed at various resolutions, interpolation grid sizes, and noise levels in synthetically generated Poiseuille and Womersley flow fields for RBFs along with standard finite difference schemes. To test the effectiveness of the methods with DPIV (Digital Particle Image Velocimetry) data, the methods were compared using the velocities obtained by processing images generated from DNS data of an open turbulent channel. Random, bias and total error were computed in all cases. In the absence of noise all tested methods perform well, with error contained under 10% at all resolutions. In the presence of noise the RBFs perform robustly with a total error that can be contained under 10–15% even with 10% noise using various interpolation grid sizes, For turbulent flow data, although the total error is approximately 5% for finite difference schemes in the absence of noise, the error can go as high as 150% in the presence of as little as 1% noise. With DPIV processed data the error is 25–40% for TPS and MQ methods optimization of the fitting parameters that minimize the energy functional associated with the analytical surface using RBFs results in robust gradient estimators are obtained that are applicable to steady, unsteady and turbulent flow fields.