Elastic scattering cross section of photons by water: limits for the free atom approximation

Several papers can be found in the literature in which elastic and inelastic experimental scattering cross sections of photons by water with energies in the keV range are measured. Usually, the authors use some kind of normalization with theoretical values, because of the difficulties in obtaining some parameters necessary to obtain absolute cross sections from the measurements. A reasonable range of momentum transfer has been covered, but nevertheless, inconsistencies and gaps still remain. In this work, we address the problem performing absolute cross section measurements in the high momentum transfer region (0.33 Å^?1 ≤ x ≤ 4.5 Å^?1), where no structure effects can be observed. We compare the results with theory to validate it in an intermediary region (0.33 Å^?1 ≤ x ≤ 1.72 Å^?1) and then use the experimental values to normalize data in the low‐energy region (0.078 Å^?1 ≤ x ≤ 1.72 Å^?1) to obtain the experimental cross section in that region. From the comparison, we concluded that for momentum transfers, x between 0.7 and 4.5 Å^?1 the scattering can be considered as being due to free atoms in free molecules. Therefore, the scattering cross sections may be considered as a sum of those from free atoms. Theoretically, the scattering cross sections can be obtained from the form factors as well as from the second‐order perturbation theory (S‐matrix) because there is no significant difference between both. On the other hand, for x ≤ 0.7 Å^?1, interference between the photon‐scattered amplitudes due to liquid structure generates oscillations in the cross section values. Copyright © 2014 John Wiley & Sons, Ltd.     

Properties of the Zeros of the Polynomials Belonging to the Askey Scheme

In this paper, we provide properties—which are, to the best of our knowledge, new—of the zeros of the polynomials belonging to the Askey scheme. These findings include Diophantine relations satisfied by these zeros when the parameters characterizing these polynomials are appropriately restricted.     

Light absorption in Ge nanoclusters embedded in SiO2: comparison between magnetron sputtering and sol–gel synthesis

SiGeO films have been produced by a sol–gel derived approach and by magnetron sputtering deposition. Post-thermal annealing of SiGeO films in forming gas or nitrogen atmosphere between 600 and 900 °C ensured the phase separation of the SiGeO films and synthesis and growth of Ge nanoclusters (NCs) embedded in SiO₂. Rutherford backscattering spectrometry analysis evidenced a similar Ge concentration (~12 %), but a different Ge out-diffusion after annealing between the two types of techniques with the formation of a pure SiO₂ surface layer (~30 nm thick) in sol–gel samples. The thermal evolution of Ge NCs has been followed by transmission electron microscopy and Raman analysis. In both samples, Ge NCs form with similar size increase (from ~3 up to ~7 nm) and with a concomitant amorphous to crystalline transition in the 600–800 °C temperature range. Despite a similar Ge concentration, a significant lower NCs density is observed in sol–gel samples attributed to an incomplete precipitation of Ge, which probably remains still dispersed in the matrix. The optical absorption of Ge NCs has been measured by spectrophotometry analyses. Ge NCs produced by the sol–gel method evidence an optical band gap of around 2 eV, larger than that of NCs produced by sputtering (~1.5 eV). These data are presented and discussed also considering the promising implications of a low-cost sol–gel based technique towards the fabrication of light harvesting devices based on Ge nanostructures.     

Bayesian prediction of crack growth based on a hierarchical diffusion model

A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide predictions for crack propagation in an early stage of the growth process. To improve the prediction, the information of other crack growth processes is used in a hierarchical (mixed‐effects) model. Two stochastic versions of a deterministic growth model are compared. One is a nonlinear regression setup where the trajectory is assumed to be the solution of an ordinary differential equation with additive errors. The other is a diffusion model defined by a stochastic differential equation where increments have additive errors. While Bayesian prediction is known for hierarchical models based on nonlinear regression, we propose a new Bayesian prediction method for hierarchical diffusion models. Six growth models for each of the two approaches are compared with respect to their ability to predict the crack propagation in a large data example. Surprisingly, the stochastic differential equation approach has no advantage concerning the prediction compared with the nonlinear regression setup, although the diffusion model seems more appropriate for crack growth. Copyright © 2016 John Wiley & Sons, Ltd.     

Exact and heuristic approaches for the set cover with pairs problem

This work deals with the set cover with pairs problem (SCPP) which is a generalization of the set cover problem (SCP). In the SCPP the elements have to be covered by specific pairs of objects, instead of a single object. We propose a new mathematical formulation using extended variables that is capable of consistently solve instances with up to 500 elements and 500 objects. We also developed an ILS heuristic which was capable of finding better solutions for several tested instances in less computational time.     

Thermal analysis of the RFX-mod2 operating conditions for the design of the temperature measurement system

Journal of Thermal Analysis and Calorimetry - The laminar two-dimensional mixed convection in a trapezoidal enclosure with a rotating inner circular cylinder and a sinusoidal bottom wall is studied...     

A defect model for the optical and EPR activity of the T-center in yttrium-stabilized zirconia

Abstract

Direct quantitative correlations have been recently observed between the T-centre EPR signal and an optical absorption band at 370 nm, in X-irradiated YSZ, suggesting that the colour centre and the paramagnetic centre might be the same entity. In order to confirm this hypothesis, theoretical modeling was undertaken, where by appropriate refinement the known electronic structure of the T-centre is shown to be compatible with an optical transition, having an oscillator strength of the correct magnitude.     

Algebraic entropy of amenable group actions

Mathematische Zeitschrift - Let R be a ring, let G be an amenable group and let $$R{*}G$$ be a crossed product. The goal of this paper is to construct, starting with a suitable additive function L...