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A. Gil

Publications and source records attributed to A. Gil.

At least 37 records · Page 2Linked to original sources
arXiv2017

Computation of asymptotic expansions of turning point problems via Cauchy's integral formula: Bessel functions

Linear second order differential equations having a large real parameter and turning point in the complex plane are considered. Classical asymptotic expansions for solutions involve the Airy function and its derivative, along with two infinite series, the coefficients of which are usually difficult to compute. By considering the series as asymptotic expansions for two explicitly defined analytic functions, Cauchy's integral formula is employed to compute the coefficient functions to high order of accuracy. The method employs a certain exponential form of Liouville-Green expansions for solutions of the differential equation, as well as for the Airy function. We illustrate the use of the method with the high accuracy computation of Airy-type expansions of Bessel functions of complex argument.

math.CA↗
arXiv2016

Analysis of Ground Level Enhancements (GLE): Extreme solar energetic particle events have hard spectra

Nearly 70 Ground Level Enhancements (GLEs) of cosmic rays have been recorded by the worldwide neutron monitor network since the 1950s depicting a big variety of energy spectra of solar energetic particles (SEP). Here we studied a statistical relation between the event-integrated intensity of GLEs (calculated as count-rate relative excess, averaged over all available polar neutron monitors, and expressed in percent-hours) and the hardness of the solar particle energy spectra. For each event the integral omnidirectional event-integrated fluences of particles with energy above 30 MeV ($F_{30}$) and above 200 MeV ($F_{200}$) were computed using the reconstructed spectra, and the ratio between the two fluences was considered as a simple index of the event's hardness. We also provided a justification of the spectrum estimate in the form of the Band-function, using direct PAMELA data for GLE 71 (17-May-2012). We found that, while there is no clear relation between the intensity and the hardness for weak events, all strong events with the intensity greater 100 \%*hr are characterized by a very hard spectrum. This implies that a hard spectrum can be securely assumed for all extreme GLE events, e.g., those studied using cosmogenic isotope data in the past.

physics.space-ph↗
arXiv2016

Efficient computation of Laguerre polynomials

An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials $L^{(α)}_n(z)$ are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for $n$ large and $α$ small, are used depending on the parameter region. Based on tests of contiguous relations in the parameter $α$ and the degree $n$ satisfied by the polynomials, we claim that a relative accuracy close or better than $10^{-12}$ can be obtained using the module LaguerrePol for computing the functions $L^{(α)}_n(z)$ in the parameter range $z \ge 0$, $-1 < α\le 5$, $n \ge 0$.

math.NA↗
arXiv2016

Computation of the incomplete gamma function for negative values of the argument

An algorithm for computing the incomplete gamma function $γ^*(a,z)$ for real values of the parameter $a$ and negative real values of the argument $z$ is presented. The algorithm combines the use of series expansions, Poincaré-type expansions, uniform asymptotic expansions and recurrence relations, depending on the parameter region. A relative accuracy $\sim 10^{-13}$ in the parameter region $(a,z) \in [-500,\,500] \times [-500,\,0)$ can be obtained when computing the function $γ^*(a,z)$ with the Fortran 90 module IncgamNEG implementing the algorithm.

cs.MS↗
arXiv2016

Efficient algorithms for the inversion of the cumulative central beta distribution

Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good non-local convergence properties (the Schwarzian-Newton method), asymptotic inversion methods and sharp bounds in the tails of the distribution function.

math.NA↗
arXiv2015

Study of the quasi-free $np \to np π^+π^-$ reaction with a deuterium beam at 1.25 GeV/nucleon

The tagged quasi-free $np \to npπ^+π^-$ reaction has been studied experimentally with the High Acceptance Di-Electron Spectrometer (HADES) at GSI at a deuteron incident beam energy of 1.25 GeV/nucleon ($\sqrt s \sim$ 2.42 GeV/c for the quasi-free collision). For the first time, differential distributions for $π^{+}π^{-}$ production in $np$ collisions have been collected in the region corresponding to the large transverse momenta of the secondary particles. The invariant mass and angular distributions for the $np\rightarrow npπ^{+}π^{-}$ reaction are compared with different models. This comparison confirms the dominance of the $t$-channel with $ΔΔ$ contribution. It also validates the changes previously introduced in the Valencia model to describe two-pion production data in other isospin channels, although some deviations are observed, especially for the $π^{+}π^{-}$ invariant mass spectrum. The extracted total cross section is also in much better agreement with this model. Our new measurement puts useful constraints for the existence of the conjectured dibaryon resonance at mass M$\sim$ 2.38 GeV and with width $Γ\sim$ 70 MeV.

nucl-ex↗
arXiv2015

Stochastic approach to the numerical solution of the non-stationary Parker's transport equation

We present the newly developed stochastic model of the galactic cosmic ray (GCR) particles transport in the heliosphere. Mathematically Parker transport equation (PTE) describing non-stationary transport of charged particles in the turbulent medium is the Fokker-Planck type. It is the second order parabolic time-dependent 4-dimensional (3 spatial coordinates and particles energy/rigidity) partial differential equation. It is worth to mention that, if we assume the stationary case it remains as the 3-D parabolic type problem with respect to the particles rigidity R. If we fix the energy it still remains as the 3-D parabolic type problem with respect to time. The proposed method of numerical solution is based on the solution of the system of stochastic differential equations (SDEs) being equivalent to the Parker's transport equation. We present the method of deriving from PTE the equivalent SDEs in the heliocentric spherical coordinate system for the backward approach. The obtained stochastic model of the Forbush decrease of the GCR intensity is in an agreement with the experimental data. The advantages and disadvantages of the forward and the backward solution of the PTE are discussed.

astro-ph.SR↗
arXiv2015

A stochastic method of solution of the Parker transport equation

We present the stochastic model of the galactic cosmic ray (GCR) particles transport in the heliosphere. Based on the solution of the Parker transport equation we developed models of the short-time variation of the GCR intensity, i.e. the Forbush decrease (Fd) and the 27-day variation of the GCR intensity. Parker transport equation being the Fokker-Planck type equation delineates non-stationary transport of charged particles in the turbulent medium. The presented approach of the numerical solution is grounded on solving of the set of equivalent stochastic differential equations (SDEs). We demonstrate the method of deriving from Parker transport equation the corresponding SDEs in the heliocentric spherical coordinate system for the backward approach. Features indicative the preeminence of the backward approach over the forward is stressed. We compare the outcomes of the stochastic model of the Fd and 27-day variation of the GCR intensity with our former models established by the finite difference method. Both models are in an agreement with the experimental data.

astro-ph.SR↗
arXiv2015

Computing the Kummer function U(a,b,z) for small values of the arguments

We describe methods for computing the Kummer function $U(a,b,z)$ for small values of $z$, with special attention to small values of $b$. For these values of $b$ the connection formula that represents $U(a,b,z)$ as a linear combination of two ${}_1F_1$-functions needs a limiting procedure. We use the power series of the ${}_1F_1$-functions and consider the terms for which this limiting procedure is needed. We give recursion relations for higher terms in the expansion, and we consider the derivative $U^\prime(a,b,z)$ as well. We also discuss the performance for small $\vert z\vert$ of an asymptotic approximation of the Kummer function in terms of modified Bessel functions.

math.CA↗
arXiv2015

GammaCHI: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)

A Fortran 90 module (GammaCHI) for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral) is presented. The main novelty of this package are the reliable and accurate inversion routines for the noncentral cumulative distribution functions. Additionally, the package also provides routines for computing the gamma function, the error function and other functions related to the gamma function. The module includes the routines cdfgamC, invcdfgamC, cdfgamNC, invcdfgamNC, errorfunction, inverfc, gamma, loggam, gamstar and quotgamm for the computation of the central gamma distribution function (and its complementary function), the inversion of the central gamma distribution function, the computation of the noncentral gamma distribution function (and its complementary function), the inversion of the noncentral gamma distribution function, the computation of the error function and its complementary function, the inversion of the complementary error function, the computation of: the gamma function, the logarithm of the gamma function, the regulated gamma function and the ratio of two gamma functions, respectively.

cs.MS↗
arXiv2014

Ionization and scintillation of nuclear recoils in gaseous xenon

Ionization and scintillation produced by nuclear recoils in gaseous xenon at approximately 14 bar have been simultaneously observed in an electroluminescent time projection chamber. Neutrons from radioisotope $α$-Be neutron sources were used to induce xenon nuclear recoils, and the observed recoil spectra were compared to a detailed Monte Carlo employing estimated ionization and scintillation yields for nuclear recoils. The ability to discriminate between electronic and nuclear recoils using the ratio of ionization to primary scintillation is demonstrated. These results encourage further investigation on the use of xenon in the gas phase as a detector medium in dark matter direct detection experiments.

physics.ins-det↗
arXiv2014

The asymptotic and numerical inversion of the Marcum $Q-$function

The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral gamma or the noncentral chi-squared cumulative distribution functions. In this paper we describe a new asymptotic method for inverting the generalized Marcum $Q-$function and for the complementary Marcum $P-$function. Also, we show how monotonicity and convexity properties of these functions can be used to find initial values for reliable Newton or secant methods to invert the function. We present details of numerical computations that show the reliability of the asymptotic approximations.

math.CA↗
arXiv2014

Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders

We consider the problem of computing satisfactory pairs of solutions of the differential equation for Legendre functions of non-negative integer order $μ$ and degree $-\frac12+iτ$, where $τ$ is a non-negative real parameter. Solutions of this equation are the conical functions ${\rm{P}}^μ_{-\frac12+iτ}(x)$ and ${Q}^μ_{-\frac12+iτ}(x)$, $x>-1$. An algorithm for computing a numerically satisfactory pair of solutions is already available when $-1 1$, the function $\Re\left\{e^{-iπμ} {Q}^μ_{-\frac{1}{2}+iτ}(x) \right\}$. The proposed algorithm allows the computation of the function on a large parameter domain without requiring the use of extended precision arithmetic.

math.CA↗
arXiv2014

Recent software developments for special functions in the Santander-Amsterdam project

We give an overview of published algorithms by our group and of current activities and future plans. In particular, we give details on methods for computing special functions and discuss in detail two current lines of research. Firstly, we describe the recent developments for the computation of central and non-central chi-square cumulative distributions (also called Marcum Q-functions), and we present a new quadrature method for computing them. Secondly, we describe the fourth-order methods for computing zeros of special functions recently developed, and we provide an explicit example for the computation of complex zeros of Bessel functions. We end with an overview of published software by our group for computing special functions.

math.CA↗
arXiv2013

Description and commissioning of NEXT-MM prototype: first results from operation in a Xenon-Trimethylamine gas mixture

A technical description of NEXT-MM and its commissioning and first performance is reported. Having an active volume of ~35 cm drift $\times$ 28 cm diameter, it constitutes the largest Micromegas-read TPC operated in Xenon ever constructed, made by a sectorial arrangement of the 4 largest single wafers manufactured with the Microbulk technique to date. It is equipped with a suitably pixelized readout and with a sufficiently large sensitive volume (~23 l) so as to contain long (~20 cm) electron tracks. First results obtained at 1 bar for Xenon and trimethylamine (Xe-(2 %)TMA) mixture are presented. The TPC can accurately reconstruct extended background tracks. An encouraging full-width half-maximum of 11.6 % was obtained for ~29 keV gammas without resorting to any data post-processing.

physics.ins-det↗
arXiv2013

Characterization of a medium size Xe/TMA TPC instrumented with microbulk Micromegas, using low-energy $γ$-rays

NEXT-MM is a general-purpose high pressure (10 bar, $\sim25$ l active volume) Xenon-based TPC, read out in charge mode with an 8 cm $\times$8 cm-segmented 700 cm$^2$ plane (1152 ch) of the latest microbulk-Micromegas technology. It has been recently commissioned at University of Zaragoza as part of the R&D of the NEXT $0νββ$ experiment, although the experiment's first stage is currently being built based on a SiPM/PMT-readout concept relying on electroluminescence. Around 2 million events were collected during the last months, stemming from the low energy $γ$-rays emitted by a $^{241}$Am source when interacting with the Xenon gas ($ε$ = 26, 30, 59.5 keV). The localized nature of such events above atmospheric pressure, the long drift times, as well as the possibility to determine their production time from the associated $α$ particle in coincidence, allow the extraction of primordial properties of the TPC filling gas, namely the drift velocity, diffusion and attachment coefficients. In this work we focus on the little explored combination of Xe and trimethylamine (TMA) for which, in particular, such properties are largely unknown. This gas mixture offers potential advantages over pure Xenon when aimed at Rare Event Searches, mainly due to its Penning characteristics, wave-length shifting properties and reduced diffusion, and it is being actively investigated by our collaboration. The chamber is currently operated at 2.7 bar, as an intermediate step towards the envisaged 10 bar. We report here its performance as well as a first implementation of the calibration procedures that have allowed the extension of the previously reported energy resolution to the whole readout plane (10.6%FWHM@30keV).

physics.ins-det↗
arXiv2013

Computation of the Marcum Q-function

Methods and an algorithm for computing the generalized Marcum $Q-$function ($Q_μ(x,y)$) and the complementary function ($P_μ(x,y)$) are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics and probability theory, where they are called the non-central chi-square or the non central gamma cumulative distribution functions. The algorithm for computing the Marcum functions combines different methods of evaluation in different regions: series expansions, integral representations, asymptotic expansions, and use of three-term homogeneous recurrence relations. A relative accuracy close to $10^{-12}$ can be obtained in the parameter region $(x,y,μ) \in [0,\,A]\times [0,\,A]\times [1,\,A]$, $A=200$, while for larger parameters the accuracy decreases (close to $10^{-11}$ for $A=1000$ and close to $5\times 10^{-11}$ for $A=10000$).

cs.MS↗