Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region

Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities

Affine actions on non-archimedean trees

We initiate the study of affine actions of groups on $\Lambda$-trees for a general ordered abelian group $\Lambda$; these are actions by dilations rather than isometries. This gives a common generalisation of isometric action on a $\Lambda$-tree, and affine action on an $\R$-tree as studied by I. Liousse. The duality between based length functions and actions on $\Lambda$-trees is generalised to this setting. We are led to consider a new class of groups: those that admit a free affine action on a $\Lambda$-tree for some $\Lambda$. Examples of such groups are presented, including soluble Baumslag-Solitar groups and the discrete Heisenberg group.Comment: 27 pages. Section 1.4 expanded, typos corrected from previous versio

Spectral properties of the narrow-line region in Seyfert galaxies selected from the SDSS-DR7

Although the properties of the narrow-line region (NLR) of active galactic nuclei(AGN) have been deeply studied by many authors in the past three decades, many questions are still open. The main goal of this work is to explore the NLR of Seyfert galaxies by collecting a large statistical spectroscopic sample of Seyfert 2 and Intermediate-type Seyfert galaxies having a high signal-to-noise ratio in order to take advantage of a high number of emission-lines to be accurately measured. 2153 Seyfert 2 and 521 Intermediate-type Seyfert spectra were selected from Sloan Digital Sky Survey - Data Release 7 (SDSS-DR7) with a diagnostic diagram based on the oxygen emission-line ratios. All the emission-lines, broad components included, were measured by means of a self-developed code, after the subtraction of the stellar component. Physical parameters, such as internal reddening, ionization parameter, temperature, density, gas and stellar velocity dispersion were determined for each object. Furthermore, we estimated mass and radius of the NLR, kinetic energy of the ionized gas, and black-hole accretion rate. From the emission-line analysis and the estimated physical properties, it appears that the NLR is similar in Seyfert 2 and Intermediate-Seyfert galaxies. The only differences, lower extinction, gas kinematics in general not dominated by the host galaxy gravitational potential and higher percentage of [O III]5007 blue asymmetries in Intermediate-Seyfert can be ascribed to an effect of inclination of our line of sight with respect to the torus axis.Comment: Accepted for publication in MNRA

Optical Emission Lines and the X-Ray Properties of Type 1 Seyfert Galaxies

In this contribution we report on the study of the optical emission lines and X-ray spectra of a sample of Type 1 AGNs, collected at the Sloan Digital Sky Survey database and observed by the XMM Newton satellite. Exploiting the different instruments carried onboard XMM, we identify the spectral components of the soft and hard energy bands (in the range from 0.3 keV up to 10 keV). The properties of the X-ray continuum and of the Fe Kalpha line feature are investigated in relation to the optical broad emission line profiles and intensity ratios. The resulting picture of emission, absorption and reflection processes is interpreted by means of a BLR structural model that was developed on the basis of independent optical and radio observations.Comment: 6 pages, 3 figures, Proceedings of the VIII Serbian Conference on Spectral Line Shapes in Astrophysics, accepted for publication on Baltic Astronomy. Corrected typos in V

The Relation between Nuclear Activity and Stellar Mass in Galaxies

The existence of correlations between nuclear properties of galaxies, such as the mass of their central black holes, and larger scale features, like the bulge mass and luminosity, represent a fundamental constraint on galaxy evolution. Although the actual reasons for these relations have not yet been identified, it is widely believed that they could stem from a connection between the processes that lead to black hole growth and stellar mass assembly. The problem of understanding how the processes of nuclear activity and star formation can affect each other became known to the literature as the Starburst-AGN connection. Despite years of investigation, the physical mechanisms which lie at the basis of this relation are known only in part. In this work, we analyze the problem of star formation and nuclear activity in a large sample of galaxies. We study the relations between the properties of the nuclear environments and of their host galaxies. We find that the mass of the stellar component within the galaxies of our sample is a critical parameter, that we have to consider in an evolutionary sequence, which provides further insight in the connection between AGN and star formation processes.Comment: 13 pages, 10 figures, accepted for publication on MNRAS. Reference to the mass derivation procedure correcte

A spectroscopic analysis of a sample of narrow-line Seyfert 1 galaxies selected from the Sloan Digital Sky Survey

We revisited the spectroscopic characteristics of narrow-line Seyfert 1 galaxies (NLS1s) by analysing a homogeneous sample of 296 NLS1s at redshift between 0.028 and 0.345, extracted from the Sloan Digital Sky Survey (SDSS-DR7) public archive. We confirm that NLS1s are mostly characterized by Balmer lines with Lorentzian profiles, lower black hole masses and higher Eddington ratios than classic broad-line Seyfert 1 (BLS1s), but they also appear to be active galactic nuclei (AGNs) contiguous with BLS1s and sharing with them common properties. Strong Fe II emission does not seem to be a distinctive property of NLS1s, as low values of Fe II/H$\beta$ are equally observed in these AGNs. Our data indicate that Fe II and Ca II kinematics are consistent with the one of H$\beta$. On the contrary, O I $\lambda$8446 seems to be systematically narrower and it is likely emitted by gas of the broad-line region more distant from the ionizing source and showing different physical properties. Finally, almost all NLS1s of our sample show radial motions of the narrow-line region highly-ionised gas. The mechanism responsible for this effect is not yet clear, but there are hints that very fast outflows require high continuum luminosities (> $10^{44}$ erg/s) or high Eddington ratios (log(L$_{\rm bol}$/L$_{\rm Edd}$) > -0.1).Comment: 27 pages, 31 figures, 4 tables, accepted for publication in MNRA

[O III] line properties in two samples of radio-emitting narrow-line Seyfert 1 galaxies

The [O III] $\lambda\lambda$ 4959,5007 lines are a useful proxy to test the kinematic of the narrow-line region (NLR) in active galactic nuclei (AGN). In AGN, and particularly in narrow-line Seyfert 1 galaxies (NLS1s) these lines often show few peculiar features, such as blue wings, often interpreted as outflowing component, and a shift $-$ typically toward lower wavelengths $-$ of the whole spectroscopic feature in some exceptional sources, the so-called blue outliers, which are often associated to strong winds. We investigated the incidence of these peculiarities in two samples of radio-emitting NLS1s, one radio-loud and one radio-quiet. We also studied a few correlations between the observational properties of the [O III] lines and those of the AGN. Our aim was to understand the difference between radio-quiet and radio-loud NLS1s, which may in turn provide useful information on the jet formation mechanism. We find that the NLR gas is much more perturbed in radio-loud than in radio-quiet NLS1s. In particular the NLR dynamics in $\gamma$-ray emitting NLS1s appears to be highly disturbed, and this might be a consequence of interaction with the relativistic jet. The less frequently perturbed NLR in radio-quiet NLS1s suggests instead that these sources likely do not harbor a fully developed relativistic jet. Nonetheless blue-outliers in radio-quiet NLS1s are observed, and we interpret them as a product of strong winds.Comment: 16 pages, 13 figures, 7 tables, accepted for publication on Astronomy & Astrophysic

Experimental investigation on crack propagation paths in spur gears

Spur gears subjected to bending fatigue may nucleate cracks at the tooth root fillet. In thin rim gears these cracks may propagate in a safe way (through the tooth) or in catastrophic way (through the rim). Crack propagation direction is mainly influenced by both wheel geometry parameters and crack initiation point, as already pointed out by theoretical and numerical results available in literature. Aim of this work is to set up an experimental activity in order to verify the onset of the bending crack and its propagation path in spur gears with different geometries. In particular, a special device connected to a standard fatigue machine was realized to perform bending tests for both standard and thin rim gears. During bending tests, an IR thermocamera was utilized to monitor the surface thermal profile in the tooth root fillet zone

Are Boltzmann Plots of Hydrogen Balmer lines a tool for identifying a subclass of S1 AGN?

It is becoming clear that we can define two different types of nearby AGN belonging to the Seyfert 1 class (S1), on the basis of the match of the intensities of their Broad Balmer Lines (BBL) with the Boltzmann Plots (BP). These two types of S1 galaxies, that we call BP-S1 and NoBP-S1, are characterized, in first approximation, by Broad Line Regions (BLR) with different structural and physical properties. In this communication, we show that these features can be well pointed out by a multi-wavelength analysis of the continuum and of the broad recombination Hydrogen lines, that we carry out on a sample of objects detected at optical and X-ray frequencies. The investigation is addressed to verify whether BP-S1 are the ideal candidates for the study of the kinematical and structural properties of the BLR, in order to derive reliable estimates of the mass of their central engine and to constrain the properties of their nuclear continuum spectrum.Comment: 26 pages, 4 figures (1 multi-paged). Accepted for publication on Advances in Space Research. Contribution to the IX SCSLS

Effective Elastic Moduli in Solids with High Crack Density

We investigate the weakening of elastic materials through randomly distributed circles and cracks numerically and compare the results to predictions from homogenization theories. We find a good agreement for the case of randomly oriented cracks of equal length in an isotropic plane-strain medium for lower crack densities; for higher densities the material is weaker than predicted due to precursors of percolation. For a parallel alignment of cracks, where percolation does not occur, we analytically predict a power law decay of the effective elastic constants for high crack densities, and confirm this result numerically.Comment: 8 page