Measurements and tests on FBK silicon sensors with an optimized electronic design for a CTA camera

In October 2013, the Italian Ministry approved the funding of a Research & Development (R&D) study, within the "Progetto Premiale TElescopi CHErenkov made in Italy (TECHE)", devoted to the development of a demonstrator for a camera for the Cherenkov Telescope Array (CTA) consortium. The demonstrator consists of a sensor plane based on the Silicon Photomultiplier (SiPM) technology and on an electronics designed for signal sampling. Preliminary tests on a matrix of sensors produced by the Fondazione Bruno Kessler (FBK-Trento, Italy) and on electronic prototypes produced by SITAEL S.p.A. will be presented. In particular, we used different designs of the electronics in order to optimize the output signals in terms of tail cancellation. This is crucial for applications where a high background is expected, as for the CTA experiment.Comment: 5 pages, 6 figures; Proceedings of the 10th Workshop on Science with the New Generation of High-Energy Gamma-ray experiments (SciNeGHE) - PoS(Scineghe2014)00

Internal alignment and position resolution of the silicon tracker of DAMPE determined with orbit data

The DArk Matter Particle Explorer (DAMPE) is a space-borne particle detector designed to probe electrons and gamma-rays in the few GeV to 10 TeV energy range, as well as cosmic-ray proton and nuclei components between 10 GeV and 100 TeV. The silicon-tungsten tracker-converter is a crucial component of DAMPE. It allows the direction of incoming photons converting into electron-positron pairs to be estimated, and the trajectory and charge (Z) of cosmic-ray particles to be identified. It consists of 768 silicon micro-strip sensors assembled in 6 double layers with a total active area of 6.6 m$^2$. Silicon planes are interleaved with three layers of tungsten plates, resulting in about one radiation length of material in the tracker. Internal alignment parameters of the tracker have been determined on orbit, with non-showering protons and helium nuclei. We describe the alignment procedure and present the position resolution and alignment stability measurements

Variable-order fractional calculus: A change of perspective

Several approaches to the formulation of a fractional theory of calculus of “variable order” have appeared in the literature over the years. Unfortunately, most of these proposals lack a rigorous mathematical framework. We consider an alternative view on the problem, originally proposed by G. Scarpi in the early seventies, based on a naive modification of the representation in the Laplace domain of standard kernels functions involved in (constant-order) fractional calculus. We frame Scarpi's ideas within recent theory of General Fractional Derivatives and Integrals, that mostly rely on the Sonine condition, and investigate the main properties of the emerging variable-order operators. Then, taking advantage of powerful and easy-to-use numerical methods for the inversion of Laplace transforms of functions defined in the Laplace domain, we discuss some practical applications of the variable-order Scarpi integral and derivative

Stability of systems of fractional-order differential equations with caputo derivatives

Systems of fractional-order differential equations present stability properties which differ in a substantial way from those of systems of integer order. In this paper, a detailed analysis of the stability of linear systems of fractional differential equations with Caputo derivative is proposed. Starting from the well-known Matignon’s results on stability of single-order systems, for which a different proof is provided together with a clarification of a limit case, the investigation is moved towards multi-order systems as well. Due to the key role of the Mittag–Leffler function played in representing the solution of linear systems of FDEs, a detailed analysis of the asymptotic behavior of this function and of its derivatives is also proposed. Some numerical experiments are presented to illustrate the main results

Good (and Not So Good) practices in computational methods for fractional calculus

The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach. In general, the numerical treatment of fractional differential equations is much more difficult than in the integer-order case, and very often non-specialist researchers are unaware of the specific difficulties. As a consequence, numerical methods are often applied in an incorrect way or unreliable methods are devised and proposed in the literature. In this paper we try to identify some common pitfalls in the use of numerical methods in fractional calculus, to explain their nature and to list some good practices that should be followed in order to obtain correct results

Efficient propagation of systematic uncertainties from calibration to analysis with the SnowStorm method in IceCube

Efficient treatment of systematic uncertainties that depend on a large number of nuisance parameters is a persistent difficulty in particle physics and astrophysics experiments. Where low-level effects are not amenable to simple parameterization or re-weighting, analyses often rely on discrete simulation sets to quantify the effects of nuisance parameters on key analysis observables. Such methods may become computationally untenable for analyses requiring high statistics Monte Carlo with a large number of nuisance degrees of freedom, especially in cases where these degrees of freedom parameterize the shape of a continuous distribution. In this paper we present a method for treating systematic uncertainties in a computationally efficient and comprehensive manner using a single simulation set with multiple and continuously varied nuisance parameters. This method is demonstrated for the case of the depth-dependent effective dust distribution within the IceCube Neutrino Telescope

On variable-order fractional linear viscoelasticity

We discuss a generalisation of fractional linear viscoelasticity based on Scarpi's approach to variable-order fractional calculus. After reviewing the general mathematical framework, we introduce the variable-order fractional Maxwell model as a simple example for our analysis. We then provide some physical considerations for the fractionalisation procedure and on the choice of the transition functions. Lastly, we compute the material functions for the considered model and evaluate them numerically for exponential-type and Mittag-Leffler-type order functions.Comment: 14 pages, 17 figure

Detection of the temporal variation of the sun's cosmic ray shadow with the IceCube detector

We report on the observation of a deficit in the cosmic ray flux from the directions of the Moon and Sun with five years of data taken by the IceCube Neutrino Observatory. Between 2010 May and 2011 May the IceCube detector operated with 79 strings deployed in the glacial ice at the South Pole, and with 86 strings between 2011 May and 2015 May. A binned analysis is used to measure the relative deficit and significance of the cosmic ray shadows. Both the cosmic ray Moon and Sun shadows are detected with high statistical significance (> 10 sigma) for each year. The results for the Moon shadow are consistent with previous analyses and verify the stability of the IceCube detector over time. This work represents the first observation of the Sun shadow with the IceCube detector. We show that the cosmic ray shadow of the Sun varies with time. These results make it possible to study cosmic ray transport near the Sun with future data from IceCube

Time-Integrated Neutrino Source Searches with 10 Years of IceCube Data.

This Letter presents the results from pointlike neutrino source searches using ten years of IceCube data collected between April 6, 2008 and July 10, 2018. We evaluate the significance of an astrophysical signal from a pointlike source looking for an excess of clustered neutrino events with energies typically above ∼1  TeV among the background of atmospheric muons and neutrinos. We perform a full-sky scan, a search within a selected source catalog, a catalog population study, and three stacked Galactic catalog searches. The most significant point in the northern hemisphere from scanning the sky is coincident with the Seyfert II galaxy NGC 1068, which was included in the source catalog search. The excess at the coordinates of NGC 1068 is inconsistent with background expectations at the level of 2.9σ after accounting for statistical trials from the entire catalog. The combination of this result along with excesses observed at the coordinates of three other sources, including TXS 0506+056, suggests that, collectively, correlations with sources in the northern catalog are inconsistent with background at 3.3σ significance. The southern catalog is consistent with background. These results, all based on searches for a cumulative neutrino signal integrated over the 10 years of available data, motivate further study of these and similar sources, including time-dependent analyses, multimessenger correlations, and the possibility of stronger evidence with coming upgrades to the detector

An analysis of solutions to fractional neutral differential equations with delay

This paper discusses some properties of solutions to fractional neutral delay differential equations. By combining a new weighted norm, the Banach fixed point theorem and an elegant technique for extending solutions, results on existence, uniqueness, and growth rate of global solutions under a mild Lipschitz continuous condition of the vector field are first established. Be means of the Laplace transform the solution of some delay fractional neutral differential equations are derived in terms of three-parameter Mittag–Leffler functions; their stability properties are hence studied by using use Rouché’s theorem to describe the position of poles of the characteristic polynomials and the final value theorem to detect the asymptotic behavior. By means of numerical simulations the theoretical findings on the asymptotic behavior are verified