arXiv subjects

Paolo Saracco

Publications and source records attributed to Paolo Saracco.

At least 55 records · Page 3Linked to original sources

arXiv2020

Towards differentiation and integration between Hopf algebroids and Lie algebroids

In this paper we set up the foundations around the notions of formal differentiation and formal integration in the context of commutative Hopf algebroids and Lie-Rinehart algebras. Specifically, we construct a contravariant functor from the category of commutative Hopf algebroids with a fixed base algebra to that of Lie-Rinehart algebras over the same algebra, the differentiation functor, which can be seen as an algebraic counterpart to the differentiation process from Lie groupoids to Lie algebroids. The other way around, we provide two interrelated contravariant functors form the category of Lie-Rinehart algebras to that of commutative Hopf algebroids, the integration functors. One of them yields a contravariant adjunction together with the differentiation functor. Under mild conditions, essentially on the base algebra, the other integration functor only induces an adjunction at the level of Galois Hopf algebroids. By employing the differentiation functor, we also analyse the geometric separability of a given morphism of Hopf algebroids. Several examples and applications are presented along the exposition.

math.RA↗

arXiv2020

Partial and global representations of finite groups

Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case where H is trivial), we develop further an effective theory that allows explicit computations. As a case study, we apply our theory to the symmetric group and its subgroup of permutations fixing 1: this provides a natural extension of the classical representation theory of the symmetric group.

math.RT↗

arXiv2020

The Hopf algebroid structure of differentially recursive sequences

A differentially recursive sequence over a differential field is a sequence of elements satisfying a homogeneous differential equation with non-constant coefficients (namely, Taylor expansions of elements of the field) in the differential algebra of Hurwitz series. The main aim of this paper is to explore the space of all differentially recursive sequences over a given field with a non-zero differential. We show that these sequences form a two-sided vector space that admits, in a canonical way, a structure of Hopf algebroid over the subfield of constant elements. We prove that it is the direct limit, as a left comodule, of all spaces of formal solutions of linear differential equations and that it satisfies, as Hopf algebroid, an additional universal property. When the differential on the base field is zero, we recover the Hopf algebra structure of linearly recursive sequences.

math.AG↗

arXiv2020

Evolutions in photoelectric cross section calculations and their validation

This paper updates and complements a previously published evaluation of computational methods for total and partial cross sections, relevant to modeling the photoelectric effect in Monte Carlo particle transport. It examines calculation methods that have become available since the publication of the previous paper, some of which claim improvements over previous calculations; it tests them with statistical methods against the same sample of experimental data collected for the previous evaluation. No statistically significant improvements are observed with respect to the calculation method identified in the previous paper as the state of the art for the intended purpose, encoded in the EPDL97 data library. Some of the more recent computational methods exhibit significantly lower capability to reproduce experimental measurements than the existing alternatives.

physics.comp-ph↗

arXiv2020

Electromagnetic Data Libraries: recent evolutions and new perspectives

This paper summarizes the current status of the electromagnetic data libraries, reviews recent experimental validation results, highlights open issues and introduces new perspectives for the future of these data libraries taking shape in the context of INFN research. Special emphasis is given to the characteristics of reliability, transparency and openness, along with opportunities for the improvement and the extension of the physics content.

physics.comp-ph↗

arXiv2019

On the boundary conditions for the neutron transport equation

The solution of the linear transport equation used for the study of neutral particle fields requires the imposition of appropriate boundary conditions. The choice of the conditions to impose for an infinite medium is not straightforward. The question has been given different formulations in the literature with various justifications based on some physical reasoning. Some aspects of the question are here analysed, from both the mathematical and the physical point of view. It is concluded that the inspiring golden rule should be the establishment of conditions that do not require any reference to the properties of the specific medium being considered for their justification.

nucl-th↗

arXiv2019

An Extremely Massive Quiescent Galaxy at $z=3.493$: Evidence of Insufficiently Rapid Quenching Mechanisms in Theoretical Models

We present spectra of the most massive quiescent galaxy yet discovered at $z>3$, spectroscopically confirmed via the detection of Balmer absorption features in the $H-$ and $K-$bands of Keck/MOSFIRE. The spectra confirm a galaxy with no significant ongoing star formation, consistent with the lack of rest-frame UV flux and overall photometric spectral energy distribution. With a stellar mass of $3.1^{+0.1}_{-0.2} \times 10^{11} ~\rm{M}_\odot$ at $z = 3.493$, this galaxy is nearly three times more massive than the highest redshift spectroscopically confirmed absorption-line identified galaxy known. The star-formation history of this quiescent galaxy implies that it formed $>1000 ~\rm{M}_\odot$/yr for almost 0.5 Gyr beginning at $z\sim7.2$, strongly suggestive that it is the descendant of massive dusty star-forming galaxies at $5<z<7$ recently observed with ALMA. While galaxies with similarly extreme stellar masses are reproduced in some simulations at early times, such a lack of ongoing star formation is not seen there. This suggests the need for a more rapid quenching process than is currently prescribed, challenging our current understanding of how ultra-massive galaxies form and evolve in the early Universe.

astro-ph.GA↗

arXiv2018

Complete IRAC mapping of the CFHTLS-DEEP, MUSYC AND NMBS-II FIELDS

The IRAC mapping of the NMBS-II fields program is an imaging survey at 3.6 and 4.5$μ$m with the Spitzer Infrared Array Camera (IRAC). The observations cover three Canada-France-Hawaii Telescope Legacy Survey Deep (CFHTLS-D) fields, including one also imaged by AEGIS, and two MUSYC fields. These are then combined with archival data from all previous programs into deep mosaics. The resulting imaging covers a combined area of about 3 $deg^2$, with at least $\sim$2 hr integration time for each field. In this work, we present our data reduction techniques and document the resulting coverage maps at 3.6 and 4.5$μ$m. All of the images are W-registered to the reference image, which is either the z-band stack image of the 25\% best seeing images from the CFHTLS-D for CFHTLS-D1, CFHTLS-D3, and CFHTLS-D4, or the K-band images obtained at the Blanco 4-m telescope at CTIO for MUSYC1030 and MUSYC1255. We make all images and coverage maps described herein publicly available via the Spitzer Science Center.

astro-ph.GA↗

arXiv2018

Coquasi-bialgebras with preantipode and rigid monoidal categories

By a theorem of Majid, every monoidal category with a neutral quasi-monoidal functor to finitely-generated and projective $\Bbbk$-modules gives rise to a coquasi-bialgebra. We prove that if the category is also rigid, then the associated coquasi-bialgebra admits a preantipode, providing in this way an analogue for coquasi-bialgebras of Ulbrich's reconstruction theorem for Hopf algebras. When $\Bbbk$ is field, this allows us to characterize coquasi-Hopf algebras as well in terms of rigidity of finite-dimensional corepresentations.

math.QA↗

arXiv2018

Topological tensor product of bimodules, complete Hopf Algebroids and convolution algebras

Given a finitely generated and projective Lie-Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between the completion of the finite dual of its universal enveloping Hopf algebroid and the associated convolution algebra. The topological Hopf algebroid structure of this convolution algebra is here clarified, by providing an explicit description of its topological antipode as well as of its other structure maps. Conditions under which that homomorphism becomes an homeomorphism are also discussed. These results, in particular, apply to the smooth global sections of any Lie algebroid over a smooth (connected) manifold and they lead a new formal groupoid scheme to enter into the picture. In the Appendix we develop the necessary machinery behind complete Hopf algebroid constructions, which involves also the topological tensor product of filtered bimodules over filtered rings.

math.AC↗

arXiv2017

$PBW$-deformations of graded rings

We prove in a very general framework several versions of the classical Poincaré-Birkhoff-Witt Theorem, which extend results from [BeGi, BrGa, CS, HvOZ, WW]. Applications and examples are discussed in the last part of the paper.

math.QA↗

arXiv2017

Comparing topologies on linearly recursive sequences

The space of linearly recursive sequences of complex numbers admits two distinguished topologies. Namely, the adic topology induced by the ideal of those sequences whose first term is $0$ and the topology induced from the Krull topology on the space of complex power series via a suitable embedding. We show that these topologies are not equivalent.

math.AC↗

arXiv2017

Colour gradients in cluster ellipticals at z~1.4: the hidden content of the galaxy central regions

We present F775W-F850LP (rest-frame UV-U) and F850LP-F160W (rest-frame U-R) colour gradients for a sample of 17 elliptical galaxies morphologically selected in the cluster XMMU J2235.3-2557 at $z$=1.39. We detected significant negative (redder inwards) U-R colour gradients in $\sim$70 per cent of the galaxies and flat gradients for the remaining ones. On the other hand, the UV-U gradients are significant positive (bluer inwards) for $\sim$80 per cent of the galaxies and flat for the remaining ones. Using stellar population synthesis models, we found that the behaviour of the two colour gradients cannot be simultaneously explained by a radial variation of age, metallicity and/or dust. The observed U-R gradients are consistent with a metallicity gradient (mean value $\nabla_{Z} =-0.4$) in agreement with the one observed in the local elliptical galaxies. The positive UV-U gradients cannot be explained with age or metallicity variations and imply an excess of UV emission towards the galaxies' central regions.This excess calls into question mechanisms able to efficiently produce UV emission. The data require either steady weak star formation (< 1 M$_\odot$ yr$^{-1}$) or an He-rich population in the cores of these galaxies in order to simultaneously reproduce both the colour gradients. On the contrary, the presence of a QSO cannot account for the observed UV excess on its own. We discuss these hypotheses on the basis of current observations and available models.

astro-ph.GA↗

arXiv2016

Influence of reflector materials and core coolant on the characteristics of accelerator driven systems

In this paper we simulated the behavior of a simple ADS model, based on MOX fuel embedded in solid lead, in terms of multiplication coefficient keff, thermal power and absolute neutron spectra. In the first part of the paper, we report on the results obtained when modifying the reflector surrounding the fission core, by replacing pure lead with a layered graphite/lead structure. We found that, by appropriately choosing position and thickness of the graphite and lead layers, it is possible to obtain a hybrid system where the neutron spectrum in the core still exhibits a fast character, while the spectrum in the graphite layer is considerably softer, becoming thermal in the most peripheral positions. In order to obtain such a modulation of the neutron spectra from the center of the system to the periphery, a careful choice of the materials has to be made in order to avoid large variations of the local power at the core boundary. However, the smoothness of the power distribution is obtained at the expense of lower values of keff and the total power of the system. In the second part of the paper, we explored the option of adopting light water as coolant, instead of the helium gas assumed in the initial design. We found that this produces an increase in keff and thermal power, without significantly perturbing the fast character of the system and without introducing spatial power excursions in any place within the core. The characteristics obtained may allow to design a system where fast, mixed and thermal spectra can be used to expand the use of the ADS as an irradiation facility.

physics.comp-ph↗

arXiv2016

Quantitative Test of the Evolution of Geant4 Electron Backscattering Simulation

Evolutions of Geant4 code have affected the simulation of electron backscattering with respect to previously published results. Their effects are quantified by analyzing the compatibility of the simulated electron backscattering fraction with a large collection of experimental data for a wide set of physics configuration options available in Geant4. Special emphasis is placed on two electron scattering implementations first released in Geant4 version 10.2: the Goudsmit-Saunderson multiple scattering model and a single Coulomb scattering model based on Mott cross section calculation. The new Goudsmit-Saunderson multiple scattering model appears to perform equally or less accurately than the model implemented in previous Geant4 versions, depending on the electron energy. The new Coulomb scattering model was flawed from a physics point of view, but computationally fast in Geant4 version 10.2; the physics correction released in Geant4 version 10.2p01 severely degrades its computational performance. Evolutions in the Geant4 geometry domain have addressed physics problems observed in electron backscattering simulation in previous publications.

physics.comp-ph↗

arXiv2016

The adjoint neutron transport equation and the statistical approach for its solution

The adjoint equation was introduced in the early days of neutron transport and its solution, the neutron importance, has ben used for several applications in neutronics. The work presents at first a critical review of the adjoint neutron transport equation. Afterwards, the adjont model is constructed for a reference physical situation, for which an analytical approach is viable, i.e. an infinite homogeneous scattering medium. This problem leads to an equation that is the adjoint of the slowing-down equation that is well-known in nuclear reactor physics. A general closed-form analytical solution to such adjoint equation is obtained by a procedure that can be used also to derive the classical Placzek functions. This solution constitutes a benchmark for any statistical or numerical approach to the adjoint equation. A sampling technique to evaluate the adjoint flux for the transport equation is then proposed and physically interpreted as a transport model for pseudo-particles. This can be done by introducing appropriate kernels describing the transfer of the pseudo-particles in phase space. This technique allows estimating the importance function by a standard Monte Carlo approach. The sampling scheme is validated by comparison with the analytical results previously obtained.

nucl-th↗

arXiv2016

An alternative observable to estimate keff in fast ADS

In this paper we examine an alternative method for determining the neutron multiplication factor keff in fast subcritical reactors, based on the observable obtained by calculating the ratio between the ``fast`` component of the neutron flux (in this case by fast we mean neutrons with kinetic energy above 0.5 MeV) and the whole flux at all energies. The assumption behind the present study was that the above mentioned observable would be only sensitive to keff, provided a peripheral fuel rod is considered (i.e. far from the neutron source in subcritical systems) and keff is sufficiently high. Indeed, our results show that, for keff> 0.7, the ratio calculated for LFR or GFR models turns out to show a quite similar trend well approximated by a straight line, while a different slope is observed for a sodium reactor. In our opinion, the results obtained show that such observable, after appropriate calibrations on the real systems under consideration, may be used for determining keff in all operational conditions, in particular for subcritical systems with different types of neutron source and different values of the beam current.

physics.ins-det↗

arXiv2016

Validation of cross sections for Monte Carlo simulation of the photoelectric effect

Several total and partial photoionization cross section calculations, based on both theoretical and empirical approaches, are quantitatively evaluated with statistical analyses using a large collection of experimental data retrieved from the literature to identify the state of the art for modeling the photoelectric effect in Monte Carlo particle transport. Some of the examined cross section models are available in general purpose Monte Carlo systems, while others have been implemented and subjected to validation tests for the first time to estimate whether they could improve the accuracy of particle transport codes. The validation process identifies Scofield's 1973 non-relativistic calculations, tabulated in the Evaluated Photon Data Library(EPDL), as the one best reproducing experimental measurements of total cross sections. Specialized total cross section models, some of which derive from more recent calculations, do not provide significant improvements. Scofield's non-relativistic calculations are not surpassed regarding the compatibility with experiment of K and L shell photoionization cross sections either, although in a few test cases Ebel's parameterization produces more accurate results close to absorption edges. Modifications to Biggs and Lighthill's parameterization implemented in Geant4 significantly reduce the accuracy of total cross sections at low energies with respect to its original formulation. The scarcity of suitable experimental data hinders a similar extensive analysis for the simulation of the photoelectron angular distribution, which is limited to a qualitative appraisal.

physics.comp-ph↗