Twisted cohomology of arrangements of lines and Milnor fibers

Let \A be an arrangement of affine lines in \C^2, with complement \M(\A). The (co)homo-logy of \M(\A) with twisted coefficients is strictly related to the cohomology of the Milnor fibre associated to the conified arrangement, endowed with the geometric monodromy. Although several partial results are known, even the first Betti number of the Milnor fiber is not understood. We give here a vanishing conjecture for the first homology, which is of a different nature with respect to the known results. Let $\Gamma$ be the graph of \emph{double points} of \A: we conjecture that if $\Gamma$ is connected then the geometric monodromy acts trivially on the first homology of the Milnor fiber (so the first Betti number is combinatorially determined in this case). This conjecture depends only on the combinatorics of \A. We prove it in some cases with stronger hypotheses. In the final parts, we introduce a new description in terms of the group given by the quotient ot the commutator subgroup of \pi_1(\M(\A)) by the commutator of its \emph{length zero subgroup.} We use that to deduce some new interesting cases of a-monodromicity, including a proof of the conjecture under some extra conditions.Comment: 2 m pages, 7 figure

The genus of the configuration spaces for Artin groups of affine type

Let $(W,S)$ be a Coxeter system, $S$ finite, and let $G_{W}$ be the associated Artin group. One has configuration spaces $Y,\ Y_{W},$ where $G_{W}=\pi_1(Y_{W}),$ and a natural $W$-covering $f_{W}:\ Y\to Y_{W}.$ The Schwarz genus $g(f_{W})$ is a natural topological invariant to consider. In this paper we generalize this result by computing the Schwarz genus for a class of Artin groups, which includes the affine-type Artin groups. Let $K=K(W,S)$ be the simplicial scheme of all subsets $J\subset S$ such that the parabolic group $W_J$ is finite. We introduce the class of groups for which $dim(K)$ equals the homological dimension of $K,$ and we show that $g(f_{W})$ is always the maximum possible for such class of groups. For affine Artin groups, such maximum reduces to the rank of the group. In general, it is given by $dim(X_{W})+1,$ where $X_{ W}\subset Y_{ W}$ is a well-known $CW$-complex which has the same homotopy type as $Y_{ W}.$Comment: To appear in Atti Accad. Naz. Lincei Rend. Lincei Mat. App

Some issues concerning Large-Eddy Simulation of inertial particle dispersion in turbulent bounded flows

The problem of an accurate Eulerian-Lagrangian modeling of inertial particle dispersion in Large Eddy Simulation (LES) of turbulent wall-bounded flows is addressed. We run Direct Numerical Simulation (DNS) for turbulent channel flow at shear Reynolds numbers equal to 150 and 300 and corresponding a-priori and a-posteriori LES on differently coarse grids. We then tracked swarms of different inertia particles and we examined the influence of filtering and of Sub-Grid Scale (SGS) modeling for the fluid phase on particle velocity and concentration statistics. We also focused on how particle preferential segregation is predicted by LES. Results show that even ``well-resolved'' LES is unable to reproduce the physics as demonstrated by DNS, both for particle accumulation at the wall and for particle preferential segregation. Inaccurate prediction is observed for the entire range of particles considered in this study, even when the particle response time is much larger than the flow timescales not resolved in LES. Both a-priori and a-posteriori tests indicate that recovering the level of fluid and particle velocity fluctuations is not enough to have accurate prediction of near-wall accumulation and local segregation. This may suggest that reintroducing the correct amount of higher-order moments of the velocity fluctuations is also a key point for SGS closure models for the particle equation. Another important issue is the presence of possible flow Reynolds number effects on particle dispersion. Our results show that, in small Reynolds number turbulence and in the case of heavy particles, the shear fluid velocity is a suitable scaling parameter to quantify these effects

Some computations on the characteristic variety of a line arrangement

We find monodromy formulas for line arrangements which are fibered with respect to the projection from one point. We use them to find $0$-dimensional translated components in the first characteristic variety of the arrangement $\mathcal R(2n)$ determined by a regular $n$-polygon and its diagonals.Comment: 17 pages, 4 figure

Investigation on numerical schemes in the simulation of barotropic cavitating flows

A numerical methodology for the simulation of cavitating flows is considered. A homogeneous-flow cavitation model, accounting for thermal effects and active nuclei concentration, is considered, which leads to a barotropic state law. The continuity and momentum equations for compressible inviscid flows are discretized through a finite-volume approach, applicable to unstructured grids. The numerical fluxes are computed by shockcapturing schemes and adhoc preconditioning is used to avoid accuracy problems in the low-Mach regime. Second-order accuracy in space is obtained through MUSCL reconstruction. Time advancing is carried out by an implicit linearized scheme. Two different numerical fluxes are investigated here, viz. the Roe and the Rusanov schemes. For the Rusanov flux two different time linearizations are proposed; in the first one the upwind part of the flux function is frozen in time, while in the second one its time variation is taken into account, although in an approximated manner. The different schemes and the different linearizations are appraised for the quasi 1D-flow in a nozzle through comparison against exact solutions and for the flow around a hydrofoil mounted in a wind tunnel through comparison against experimental data. Non-cavitating and cavitating conditions are simulated. It is shown that, for cavitating conditions, the Rusanov scheme together with the more complete time linearization allows time steps much larger than for the Roe scheme to be used. Finally, the results obtained with this scheme are in good agreement with the exact solutions or the experimental data for all the considered test cases.http://deepblue.lib.umich.edu/bitstream/2027.42/84242/1/CAV2009-final42.pd

Blazar Flaring Patterns (B-FlaP): Classifying Blazar Candidates of Uncertain type in the third Fermi-LAT catalog by Artificial Neural Networks

The Fermi Large Area Telescope (LAT) is currently the most important facility for investigating the GeV $\gamma$-ray sky. With Fermi LAT more than three thousand $\gamma$-ray sources have been discovered so far. 1144 ($\sim40\%$) of the sources are active galaxies of the blazar class, and 573 ($\sim20\%$) are listed as Blazar Candidate of Uncertain type (BCU), or sources without a conclusive classification. We use the Empirical Cumulative Distribution Functions (ECDF) and the Artificial Neural Networks (ANN) for a fast method of screening and classification for BCUs based on data collected at $\gamma$-ray energies only, when rigorous multiwavelength analysis is not available. Based on our method, we classify 342 BCUs as BL Lacs and 154 as FSRQs, while 77 objects remain uncertain. Moreover, radio analysis and direct observations in ground-based optical observatories are used as counterparts to the statistical classifications to validate the method. This approach is of interest because of the increasing number of unclassified sources in Fermi catalogs and because blazars and in particular their subclass High Synchrotron Peak (HSP) objects are the main targets of atmospheric Cherenkov telescopes.Comment: 18 pages, 17 figures, accepted for publication on MNRA

Classification and Ranking of Fermi LAT Gamma-ray Sources from the 3FGL Catalog using Machine Learning Techniques

We apply a number of statistical and machine learning techniques to classify and rank gamma-ray sources from the Third Fermi Large Area Telescope (LAT) Source Catalog (3FGL), according to their likelihood of falling into the two major classes of gamma-ray emitters: pulsars (PSR) or Active Galactic Nuclei (AGN). Using 1904 3FGL sources that have been identified/associated with AGN (1738) and PSR (166), we train (using 70% of our sample) and test (using 30%) our algorithms and find that the best overall accuracy (>96%) is obtained with the Random Forest (RF) technique, while using a logistic regression (LR) algorithm results in only marginally lower accuracy. We apply the same techniques on a sub-sample of 142 known gamma-ray pulsars to classify them into two major subcategories: young (YNG) and millisecond pulsars (MSP). Once more, the RF algorithm has the best overall accuracy (~90%), while a boosted LR analysis comes a close second. We apply our two best models (RF and LR) to the entire 3FGL catalog, providing predictions on the likely nature of {\it unassociated} sources, including the likely type of pulsar (YNG or MSP). We also use our predictions to shed light on the possible nature of some gamma-ray sources with known associations (e.g. binaries, SNR/PWN). Finally, we provide a list of plausible X-ray counterparts for some pulsar candidates, obtained using Swift, Chandra, and XMM. The results of our study will be of interest for both in-depth follow-up searches (e.g. pulsar) at various wavelengths, as well as for broader population studies.Comment: Accepted by Ap

Optical counterparts of undetermined type γ\gamma-ray Active Galactic Nuclei with blazar-like Spectral Energy Distributions

During its first four years of scientific observations, the Fermi Large Area Telescope (Fermi-LAT) detected 3033 $\gamma$-ray sources above a 4$\sigma$ significance level. Although most of the extra-Galactic sources are active galactic nuclei (AGN) of the blazar class, other families of AGNs are observed too, while a still high fraction of detections ($\sim 30\%$) remains with uncertain association or classification. According to the currently accepted interpretation, the AGN $\gamma$-ray emission arises from inverse Compton (IC) scattering of low energy photons by relativistic particles confined in a jet that, in the case of blazars, is oriented very close to our line of sight. Taking advantage of data from radio and X-ray wavelengths, which we expect to be produced together with $\gamma$-rays, providing a much better source localization potential, we focused our attention on a sample of $\gamma$-ray Blazar Candidates of Undetermined Type (BCUs), starting a campaign of optical spectroscopic observations. The main aims of our investigation include a census of the AGN families that contribute to $\gamma$-ray emission and a study of their redshift distribution, with the subsequent implications on the intrinsic source power. We furthermore analyze which $\gamma$-ray properties can better constrain the nature of the source, thus helping in the study of objects not yet associated with a reliable low frequency counterpart. In this communication we report on the instruments and techniques used to identify the optical counterparts of $\gamma$-ray sources, we give an overview on the status of our work, and we discuss the implications of a large scale study of $\gamma$-ray emitting AGNs.Comment: 9 pages, 2 figures, proceedings of the 10th Serbian Conference on Spectral Line Shapes in Astrophysics. JOAA, accepte

Radio-quiet and radio-loud pulsars: similar in Gamma-rays but different in X-rays

We present new Chandra and XMM-Newton observations of a sample of eight radio-quiet Gamma-ray pulsars detected by the Fermi Large Area Telescope. For all eight pulsars we identify the X-ray counterpart, based on the X-ray source localization and the best position obtained from Gamma-ray pulsar timing. For PSR J2030+4415 we found evidence for an about 10 arcsec-long pulsar wind nebula. Our new results consolidate the work from Marelli et al. 2011 and confirm that, on average, the Gamma-ray--to--X-ray flux ratios (Fgamma/Fx) of radio-quiet pulsars are higher than for the radio-loud ones. Furthermore, while the Fgamma/Fx distribution features a single peak for the radio-quiet pulsars, the distribution is more dispersed for the radio-loud ones, possibly showing two peaks. We discuss possible implications of these different distributions based on current models for pulsar X-ray emission.Comment: Accepted for publication in The Astrophysical Journal; 12 pages, 3 figures, 2 table