Love numbers of a generalized Maxwell sphere

By elementary methods, we study the Love numbers of a homogeneous, incompressible, self-gravitating sphere characterized by a generalized Maxwell rheology, whose mechanical analogue is represented by a finite or infinite system of classical Maxwell elements disposed in parallel. Analytical, previously unknown forms of the complex shear modulus for the generalized Maxwell body are found by algebraic manipulation, and studied in the particular case of systems of springs and dashpots whose strength follows a power-law distribution. It will be shown that the sphere is asymptotically stable for any choice of the mechanical parameters that define the generalized Maxwell body and analytical forms of the Love numbers are always available for generalized bodies composed by less than five classical Maxwell bodies. For the homogeneous sphere, real Laplace inversion methods based on the Post-Widder formula can be applied without performing a numerical discretization of the n-th derivative, which can be computed in a closed-form with the aid of the Faà di Bruno formula.     

Modelling the long‐term deformation of the sedimentary substrate of Mt. Etna volcano (Italy)

This study investigates in detail the deformation events that have affected the sedimentary successions forming the substrate of Mt. Etna volcano (Italy). Based on the geometric reconstruction of a buried sedimentary marker, we have been able to identify and quantify the effects of three different mechanisms of deformation that have affected the area in the last 600 ka. Numerical results from Finite Element Method (FEM) applied to model viscoelastic deformation suggest the occurrence of a crustal doming process originating at the mantle‐crust transition (~16 km). We propose that the source of deformation is related to the diapiric uprise of hydrothermal material originating in altered ocean‐like crust and its emplacement at a shallower level in the crust. This process has great relevance in the volcanic system and should be considered for the full assessment of its origin and evolution.     

Intensity measures for response prediction of a torsional building subjected to bi-directional earthquake ground motion

In the framework of performance-based assessment of existing RC buildings, an important step is the definition of an intensity measure (IM) of the seismic action that be accurate and efficient in correlating with the engineering demand parameters (EDP) of interest and in reducing the variability in their prediction. Objective of this work is to assess five different IMs, when they are applied to an in-plan irregular three-dimensional building subjected to bi-directional earthquake motion. The objective is pursued through multiple regression of the results obtained from nonlinear dynamic analyses. The study shows that certain IMs are more suitable to evaluate EDPs when dealing with 3D structures subjected to 2D earthquakes.     

Observing cosmic microwave background polarization through ice

Ice crystal clouds in the upper troposphere can generate polarization signals at the μK level. This signal can seriously affect very sensitive ground-based searches for E and B modes of cosmic microwave background polarization. In this paper, we estimate this effect within the C_ℓOVER experiment observing bands (97, 150 and 220 GHz) for the selected observing site (Llano de Chajnantor, Atacama desert, Chile). The results show that the polarization signal from the clouds can be of the order of or even bigger than the cosmic microwave background expected polarization. Climatological data suggest that this signal is fairly constant over the whole year in Antarctica. On the other hand, the stronger seasonal variability in Atacama allows for a 50 per cent of clean observations during the dry season.     

Scaling improves stability of preconditioned CG‐like solvers for FE consolidation equations

Preconditioned projection (or conjugate gradient like) methods are increasingly used for the accurate and efficient solution to finite element (FE) coupled consolidation equations. Theory indicates that preliminary row/column scaling does not affect the eigenspectrum of the iteration matrix controlling convergence as long as the preconditioner relies on the incomplete factorization of the FE coefficient matrix. However, computational experience with mid‐large size problems shows that the above inexpensive operation can significantly accelerate the solver convergence, and to a minor extent also improve the final accuracy, as a result of a better solver stability to the accumulation and propagation of floating point round‐off errors. This is demonstrated with the aid of the least square logarithm (LSL) scaling algorithm on FE consolidation problems of increasing size up to more than 100 000. It is shown that a major source of numerical instability rests with the sub‐matrix which couples the structural to the fluid part of the underlying mathematical model. It is concluded that for mid‐large size, possibly difficult, FE consolidation problems left/right LSL scaling is to be always recommended when the incomplete factorization is used as a preconditioning technique. Copyright © 2003 John Wiley & Sons, Ltd.     

Three-dimensional experiments on landslide generated waves at a sloping coast

This paper describes new three dimensional experiments on water waves generated by landslides. The landslide is reproduced by a rigid elliptical body, sliding along an inclined plane (slope of 1/3, 1 vertical, 3 horizontal). The generated water waves are free to propagate both offshore and alongshore, since the plan dimensions of the used wave tank are of at least one order of magnitude larger than the width of the landslide, which can be considered to be a scale of the wave length. The experimental study has been carried out reproducing both subaerial and partially submerged landslides. The wave generation process is studied by means of video records of the near field flow and measurement of the landslide movement; the properties of the waves propagating along the coast are described on the basis of runup gauges. The waves observed during the experiments always present first a crest and then a trough; as the first wave propagates away from the generation area the crest tends to become smaller than the trough and the maximum runup along the coast is given by the second or by the third wave. An important feature is that the observed runup along the coast firstly grows with the distance from the generation area, it reaches a maximum value at about two times the width of the landslide, and then decreases. An estimate of the celerity at which the waves propagate along the coast is given on the basis of gauge measurements; it results that the crests propagate faster than the troughs, and the wave period increases.     

Galileo’s telescope: history, scientific analysis, and replicated observations

In the summer of 1609, Galileo Galilei started to improve upon the Dutch spyglass. Only a few months were needed to increase the magnifying power of the instrument up to 30 times. This transformation allowed Galileo to perform astronomical observations destined to change the traditional Universe. At present, the Institute and Museum of History of Science of Florence is conducting a research programme on the lenses of early telescopes. Historical research is combined with scientific analyses conducted by the National Institute of Applied Optics in Arcetri, the National Institute of Nuclear Physics in Florence, and the Glass Experimental Station in Murano. The shape and composition of the lenses are studied by applying different techniques. Moreover, the composition of early lenses and scientific glass objects are compared. Finally, Galileo’s observations are checked with an optical replica of Galileo’s telescope held at the Astrophysical Observatory in Arcetri.     

Chandra unveils a binary active galactic nucleus in Mrk 463

We analyse Chandra , XMM–Newton and Hubble Space Telescope ( HST ) data of the double-nucleus Ultraluminous Infrared Galaxy (ULIRG), Mrk 463. The Chandra detection of two luminous  ( L _2–10 keV= 1.5 × 10⁴³  and  3.8 × 10⁴² erg cm⁻² s⁻¹)  , unresolved nuclei in Mrk 463 indicates that this galaxy hosts a binary active galactic nucleus (AGN), with a projected separation of ≃3.8 kpc (  3.83 ± 0.01  arcsec). While the East nucleus was already known to be a type 2 Seyfert (and this is further confirmed by our Chandra detection of a neutral iron line), this is the first unambiguous evidence in favour of the AGN nature of the West nucleus. Mrk 463 is therefore the clearest case so far for a binary AGN, after NGC 6240.     

A semi-analytic theory for the motion of a lunar satellite

A semi-analytical solution to the problem of the motion of a satellite of the moon is presented. Perturbative effects which are considered include those due to the attraction of the moon, earth, and sun, the non-sphericity of the moon's gravitational field, coupling of lower-order terms, solar radiation pressure, and physical libration. Short-period terms and intermediate-period terms, terms with the period of the moon's longitude, are produced by means of von Zeipel's method; it is proposed to obtain the secular perturbations, and those depending only on the argument of perilune, by numerical integration of the equations of motions. The short-period terms and intermediate-period terms are developed up to second order, where first order is 10^–2. The secular perturbations and perturbations dependent on the argument of perilune are obtained to third order.