On the well-posedness of the stochastic Allen-Cahn equation in two dimensions

White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d \geq 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen-Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that a series of published numerical studies are problematic: shrinking the mesh size in these simulations does not lead to the recovery of a physically meaningful limit.Comment: 21 pages, 4 figures; accepted by Journal of Computational Physics (Dec 2011

An investigation of uniform expansions of large order Bessel functions in Gravitational Wave Signals from Pulsars

In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of applications, in particular the Fourier transform of the gravitational wave signal from a pulsar. The uniform expansion we consider here is found to be valid in the entire range of the argument

Interatomic potentials for atomistic simulations of the Ti-Al system

Semi-empirical interatomic potentials have been developed for Al, alpha-Ti, and gamma-TiAl within the embedded atomic method (EAM) by fitting to a large database of experimental as well as ab-initio data. The ab-initio calculations were performed by the linear augmented plane wave (LAPW) method within the density functional theory to obtain the equations of state for a number of crystal structures of the Ti-Al system. Some of the calculated LAPW energies were used for fitting the potentials while others for examining their quality. The potentials correctly predict the equilibrium crystal structures of the phases and accurately reproduce their basic lattice properties. The potentials are applied to calculate the energies of point defects, surfaces, planar faults in the equilibrium structures. Unlike earlier EAM potentials for the Ti-Al system, the proposed potentials provide reasonable description of the lattice thermal expansion, demonstrating their usefulness in the molecular dynamics or Monte Carlo studies at high temperatures. The energy along the tetragonal deformation path (Bain transformation) in gamma-TiAl calculated with the EAM potential is in a fairly good agreement with LAPW calculations. Equilibrium point defect concentrations in gamma-TiAl are studied using the EAM potential. It is found that antisite defects strongly dominate over vacancies at all compositions around stoichiometry, indicating that gamm-TiAl is an antisite disorder compound in agreement with experimental data.Comment: 46 pages, 6 figures (Physical Review B, in press

2,6-Dide­oxy-2,6-imino-l-glycero-d-ido-heptitol

The title mol­ecule, C7H15NO5, the major product from selective enzymatic oxidation followed by hydrogeno­lysis of the corresponding azido­heptitol, was found by X-ray crystallography to exisit in a chair conformation with three axial hydroxyl groups. One of the hydroxymethyl groups is disordered over two sets of sites in a 0.590 (3):0.410 (3) ratio. In the crystal, O—H⋯O, O—H⋯(O,O), O—H⋯N and N—H⋯O hydrogen bonding occurs

Performance studies of the Belle II Silicon Vertex Detector with data taken at the DESY test beam in April 2016

Belle II is a multipurpose detector currently under construction which will be operated at the next generation B-factory SuberKEKB in Japan. Its main devices for the vertex reconstruction are the Silicon Vertex Detector (SVD) and the Pixel Detector (PXD). In April 2016 a sector of the Belle II SVD and PXD have been tested in a beam of high energetic electrons at the test beam facility at DESY Hamburg (Germany). We report here the results for the hit efficiency estimation and the measurement of the resolution for the Belle II silicon vertex etector. We find that the hit efficiencies are on average above 99.5% and that the measured resolution is within the expectations

The Belle II SVD detector

The Silicon Vertex Detector (SVD) is one of the main detectors in the Belle II experiment at KEK, Japan. In combination with a pixel detector, the SVD determines precise decay vertex and low-momentum track reconstruction. The SVD ladders are being developed at several institutes. For the development of the tracking algorithm as well as the performance estimation of the ladders, beam tests for the ladders were performed. We report an overview of the SVD development, its performance measured in the beam test, and the prospect of its assembly and commissioning until installation

Performance studies of the Belle II Silicon Vertex Detector with data taken at the DESY test beam in April 2016

Belle II is a multipurpose detector currently under construction which will be operated at the next generation B-factory SuberKEKB in Japan. Its main devices for the vertex reconstruction are the Silicon Vertex Detector (SVD) and the Pixel Detector (PXD). In April 2016 a sector of the Belle II SVD and PXD have been tested in a beam of high energetic electrons at the test beam facility at DESY Hamburg (Germany). We report here the results for the hit efficiency estimation and the measurement of the resolution for the Belle II silicon vertex etector. We find that the hit efficiencies are on average above 99.5% and that the measured resolution is within the expectations

Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Kernel-based methods for combining information of several frame surveys

A sample selected from a single sampling frame may not represent adequatly the entire population. Multiple frame surveys are becoming increasingly used and popular among statistical agencies and private organizations, in particular in situations where several sampling frames may provide better coverage or can reduce sampling costs for estimating population quantities of interest. Auxiliary information available at the population level is often categorical in nature, so that incorporating categorical and continuous information can improve the efficiency of the method of estimation. Nonparametric regression methods represent a widely used and flexible estimation approach in the survey context. We propose a kernel regression estimator for dual frame surveys that can handle both continuous and categorical data. This methodology is extended to multiple frame surveys. We derive theoretical properties of the proposed methods and numerical experiments indicate that the proposed estimator perform well in practical settings under different scenarios.Ministerio de Economía y CompetitividadConsejería de Economía, Innovación, Ciencia y Emple

An Overview of the 2014 ALMA Long Baseline Campaign

A major goal of the Atacama Large Millimeter/submillimeter Array (ALMA) is to make accurate images with resolutions of tens of milliarcseconds, which at submillimeter (submm) wavelengths requires baselines up to ~15 km. To develop and test this capability, a Long Baseline Campaign (LBC) was carried out from September to late November 2014, culminating in end-to-end observations, calibrations, and imaging of selected Science Verification (SV) targets. This paper presents an overview of the campaign and its main results, including an investigation of the short-term coherence properties and systematic phase errors over the long baselines at the ALMA site, a summary of the SV targets and observations, and recommendations for science observing strategies at long baselines. Deep ALMA images of the quasar 3C138 at 97 and 241 GHz are also compared to VLA 43 GHz results, demonstrating an agreement at a level of a few percent. As a result of the extensive program of LBC testing, the highly successful SV imaging at long baselines achieved angular resolutions as fine as 19 mas at ~350 GHz. Observing with ALMA on baselines of up to 15 km is now possible, and opens up new parameter space for submm astronomy.Comment: 11 pages, 7 figures, 2 tables; accepted for publication in the Astrophysical Journal Letters; this version with small changes to affiliation