The spectacular X-ray echo of a magnetar burst

The Anomalous X-ray Pulsar (AXP) 1E 1547.0-5408 reactivated in 2009 January with the emission of dozens of short bursts. Follow-up observations with Swift/XRT and XMM-Newton showed the presence of multiple expanding rings around the position of the AXP. These rings are due to scattering, by different layers of interstellar dust, of a very high fluence burst emitted by 1E 1547.0-5408 on 2009 January 22. Thanks to the exceptional brightness of the X-ray rings, we could carry out a detailed study of their spatial and spectral time evolution until 2009 February 4. This analysis gives the possibility to estimate the distance of 1E 1547.0-5408. We also derived constraints on the properties of the dust and of the burst responsible for this rare phenomenon.Comment: Proceedings of the conference X-Ray Astronomy 2009, Present Status, multiwavelength approach and future perspectives, September 7 - 11, 2009, Bologna, Ital

Numerical quadrature on the intersection of planar disks

We provide an algorithm that computes algebraic quadrature formulas with cardinality not exceeding the dimension of the exactness polynomial space, on the intersection of any number of planar disks with arbitrary radius. Applications arise for example in computational optics and in wireless networks analysis. By the inclusion-exclusion principle, we can also compute algebraic formulas for the union of a small number of disks. The algorithm is implemented in Matlab, via subperiodic trigonometric Gaussian quadrature and compression of discrete measures

Discrete norming inequalities on sections of sphere, ball and torus

By discrete trigonometric norming inequalities on subintervals of the period, we construct norming meshes with optimal cardinality growth for algebraic polynomials on sections of sphere, ball and torus

Behind the dust curtain: the spectacular case of GRB 160623A

We report on the X-ray dust-scattering features observed around the afterglow of the gamma ray burst GRB 160623A. With an XMM-Newton observation carried out ~2 days after the burst, we found evidence of at least six rings, with angular size expanding between ~2 and 9 arcmin, as expected for X-ray scattering of the prompt GRB emission by dust clouds in our Galaxy. From the expansion rate of the rings, we measured the distances of the dust layers with extraordinary precision: 528.1 +\- 1.2 pc, 679.2 +\- 1.9 pc, 789.0 +\- 2.8 pc, 952 +\- 5 pc, 1539 +\- 20 pc and 5079 +\- 64 pc. A spectral analysis of the ring spectra, based on an appropriate dust-scattering model (BARE-GR-B from Zubko et al. 2004}) and the estimated burst fluence, allowed us to derive the column density of the individual dust layers, which are in the range 7x10^20-1.5x10^22 cm^-2. The farthest dust-layer (i.e. the one responsible for the smallest ring) is also the one with the lowest column density and it is possibly very extended, indicating a diffuse dust region. The properties derived for the six dust-layers (distance, thickness, and optical depth) are generally in good agreement with independent information on the reddening along this line of sight and on the distribution of molecular and atomic gas.Comment: 9 pages, 10 figures, 1 table; accepted for publication in MNRA

Statistical model for intermittent plasma edge turbulence

The Probability Distribution Function of plasma density fluctuations at the edge of fusion devices is known to be skewed and strongly non-Gaussian. The causes of this peculiar behaviour are, up to now, largely unexplored. On the other hand, understanding the origin and the properties of edge turbulence is a key issue in magnetic fusion research. In this work we show that a stochastic fragmentation model, already successfully applied to fluid turbulence, is able to predict an asymmetric distribution that closely matches experimental data. The asymmetry is found to be a direct consequence of intermittency. A discussion of our results in terms of recently suggested BHP universal curve [S.T. Bramwell, P.C.W. Holdsworth, J.-F. Pinton, Nature (London) 396, 552 (1998)], that should hold for strongly correlated and critical systems, is also proposedComment: 13 pages. Physica Review E, accepte

Algebraic cubature on polygonal elements with a circular edge

We compute low-cardinality algebraic cubature formulas on convex or concave polygonal elements with a circular edge, by subdivision into circular quadrangles, blending formulas via subperiodic trigonometric Gaussian quadrature and final compression via Caratheodory\u2013Tchakaloff subsampling of discrete measures. We also discuss applications to the VEM (Virtual Element Method) in computational mechanics problems

Weakly Admissible Meshes and Discrete Extremal Sets

We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points. These provide new computational tools for polynomial least squares and interpolation on multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral and high-order methods for PDEs

About the parabolic relation existing between the skewness and the kurtosis in time series of experimental data

In this work we investigate the origin of the parabolic relation between skewness and kurtosis often encountered in the analysis of experimental time-series. We argue that the numerical values of the coefficients of the curve may provide informations about the specific physics of the system studied, whereas the analytical curve per se is a fairly general consequence of a few constraints expected to hold for most systems.Comment: To appear in Physica Script

On the Use of Compressed Polyhedral Quadrature Formulas in Embedded Interface Methods

The main idea of this paper is to apply a recent quadrature compression technique to algebraic quadrature formulas on complex polyhedra. The quadrature compression substantially reduces the number of integration points but preserves the accuracy of integration. The compression is easy to achieve since it is entirely based on the fundamental methods of numerical linear algebra. The resulting compressed formulas are applied in an embedded interface method to integrate the weak form of the Navier--Stokes equations. Simulations of flow past stationary and moving interface problems demonstrate that the compressed quadratures improve the efficiency of performing the weak form integration, while preserving accuracy and order of convergence

Massive data compression for parameter-dependent covariance matrices

We show how the massive data compression algorithm MOPED can be used to reduce, by orders of magnitude, the number of simulated data sets which are required to estimate the covariance matrix required for the analysis of Gaussian-distributed data. This is relevant when the covariance matrix cannot be calculated directly. The compression is especially valuable when the covariance matrix varies with the model parameters. In this case, it may be prohibitively expensive to run enough simulations to estimate the full covariance matrix throughout the parameter space. This compression may be particularly valuable for the next generation of weak lensing surveys, such as proposed for Euclid and Large Synoptic Survey Telescope, for which the number of summary data (such as band power or shear correlation estimates) is very large, ∼104, due to the large number of tomographic redshift bins which the data will be divided into. In the pessimistic case where the covariance matrix is estimated separately for all points in an Monte Carlo Markov Chain analysis, this may require an unfeasible 109 simulations. We show here that MOPED can reduce this number by a factor of 1000, or a factor of ∼106 if some regularity in the covariance matrix is assumed, reducing the number of simulations required to a manageable 103, making an otherwise intractable analysis feasible