On the precision of chiral-dispersive calculations of ππ\pi\pi scattering

We calculate the combination $2a_0^{(0)}-5a_0^{(2)}$ (the Olsson sum rule) and the scattering lengths and effective ranges $a_1$, $a_2^{(I)}$ and $b_1$, $b_2^{(I)}$ dispersively (with the Froissart--Gribov representation) using, at low energy, the phase shifts for $\pi\pi$ scattering obtained by Colangelo, Gasser and Leutwyler (CGL) from the Roy equations and chiral perturbation theory, plus experiment and Regge behaviour at high energy, or directly, using the CGL parameters for $a$s and $b$s. We find mismatch, both among the CGL phases themselves and with the results obtained from the pion form factor. This reaches the level of several (2 to 5) standard deviations, and is essentially independent of the details of the intermediate energy region ($0.82\leq E\leq 1.42$ GeV) and, in some cases, of the high energy behaviour assumed. We discuss possible reasons for this mismatch, in particular in connection with an alternate set of phase shifts.Comment: Version to appear in Phys. Rev. D. Graphs and sum rule added. Plain TeX fil

Neural Network-Based Equations for Predicting PGA and PGV in Texas, Oklahoma, and Kansas

Parts of Texas, Oklahoma, and Kansas have experienced increased rates of seismicity in recent years, providing new datasets of earthquake recordings to develop ground motion prediction models for this particular region of the Central and Eastern North America (CENA). This paper outlines a framework for using Artificial Neural Networks (ANNs) to develop attenuation models from the ground motion recordings in this region. While attenuation models exist for the CENA, concerns over the increased rate of seismicity in this region necessitate investigation of ground motions prediction models particular to these states. To do so, an ANN-based framework is proposed to predict peak ground acceleration (PGA) and peak ground velocity (PGV) given magnitude, earthquake source-to-site distance, and shear wave velocity. In this framework, approximately 4,500 ground motions with magnitude greater than 3.0 recorded in these three states (Texas, Oklahoma, and Kansas) since 2005 are considered. Results from this study suggest that existing ground motion prediction models developed for CENA do not accurately predict the ground motion intensity measures for earthquakes in this region, especially for those with low source-to-site distances or on very soft soil conditions. The proposed ANN models provide much more accurate prediction of the ground motion intensity measures at all distances and magnitudes. The proposed ANN models are also converted to relatively simple mathematical equations so that engineers can easily use them to predict the ground motion intensity measures for future events. Finally, through a sensitivity analysis, the contributions of the predictive parameters to the prediction of the considered intensity measures are investigated.Comment: 5th Geotechnical Earthquake Engineering and Soil Dynamics Conference, Austin, TX, USA, June 10-13. (2018

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Fast atom diffraction inside a molecular beam epitaxy chamber, a rich combination

Two aspects of the contribution of grazing incidence fast atom diffraction (GIFAD) to molecular beam epitaxy (MBE) are reviewed here: the ability of GIFAD to provide \emph{in-situ} a precise description of the atomic-scale surface topology, and its ability to follow larger-scale changes in surface roughness during layer-by-layer growth. Recent experimental and theoretical results obtained for the He atom beam incident along the highly corrugated $[ 1\bar{1}0 ]$ direction of the $\beta_{2}$(2$\times$4) reconstructed GaAs(001) surface are summarized and complemented by the measurements and calculations for the beam incidence along the weakly corrugated [010] direction where a periodicity twice smaller as expected is observed. The combination of the experiment, quantum scattering matrix calculations, and semiclassical analysis allows in this case to reveal structural characteristics of the surface. For the in situ measurements of GIFAD during molecular beam epitaxy of GaAs on GaAs surface we analyse the change in elastic and inelastic contributions in the scattered beam, and the variation of the diffraction pattern in polar angle scattering. This analysis outlines the robustness, the simplicity and the richness of the GIFAD as a technique to monitor the layer-by-layer epitaxial growth

Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem in low dimensions

We consider the classical Brezis-Nirenberg problem in the unit ball of $\mathbb{R}^N$, $N\geq 3$ and analyze the asymptotic behavior of nodal radial solutions in the low dimensions $N=3,4,5,6$ as the parameter converges to some limit value which naturally arises from the study of the associated ordinary differential equation

An integrable multicomponent quad equation and its Lagrangian formulation

We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg-de Vries equation, and the lattice modified Boussinesq equation. The N-th member in the hierarchy is an N-component system defined on an elementary plaquette in the 2-dimensional lattice. The system is multidimensionally consistent and a Lagrangian which respects this feature, i.e., which has the desirable closure property, is obtained.Comment: 10 page

Improved fidelity of triggered entangled photons from single quantum dots

We demonstrate the on-demand emission of polarisation-entangled photon pairs from the biexciton cascade of a single InAs quantum dot embedded in a GaAs/AlAs planar microcavity. Improvements in the sample design blue shifts the wetting layer to reduce the contribution of background light in the measurements. Results presented show that >70% of the detected photon pairs are entangled. The high fidelity of the (|HxxHx>+|VxxVx>)/2^0.5 state that we determine is sufficient to satisfy numerous tests for entanglement. The improved quality of entanglement represents a significant step towards the realisation of a practical quantum dot source compatible with applications in quantum information.Comment: 9 pages. Paper is available free of charge at http://www.iop.org/EJ/abstract/1367-2630/8/2/029/, see also 'A semiconductor source of triggered entangled photon pairs', R. M. Stevenson et al., Nature 439, 179 (2006

On the criticality of inferred models

Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to a phase transition. On one side, we show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher Information) is directly related to the model's susceptibility. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. On the other, this region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time-scales naturally yield models which are close to criticality.Comment: 6 pages, 2 figures, version to appear in JSTA