Structural evolution of a 2M 1 phengite mica up to 11 GPa: an in situ single-crystal X-ray diffraction study

The structural evolution at high pressure of a natural 2M ₁-phengite [(K_0.98Na_0.02)_Σ=1.00(Al_1.55Mg_0.24Fe_0.21Ti_0.02)_Σ=2.01(Si_3.38Al_0.62)O₁₀(OH)₂; a = 5.228(2), b = 9.057(3), c = 19.971(6)Å, β = 95.76(2)°; space group: C2/c] from the metamorphic complex of Cima Pal (Sesia Zone, Western Alps, Italy) was studied by single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions up to ~11 GPa. A series of 12 structure refinements were performed at selected pressures within the P range investigated. The compressional behaviour of the same phengite sample was previously studied up to ~25 GPa by synchrotron X-ray powder diffraction, showing an irreversible transformation with a drastic decrease of the crystallinity at P > 15–17 GPa. The elastic behaviour between 0.0001 and 17 GPa was modelled by a third-order Birch–Murnaghan Equation of State (BM-EoS), yielding to K _T0 = 57.3(10) GPa and K′ = ?K _T0/?P = 6.97(24). The single-crystal structure refinements showed that the significant elastic anisotropy of the 2M ₁-phengite (with β(a):β(b):β(c) = 1:1.17:4.60) is mainly controlled by the anisotropic compression of the K-polyhedra. The evolution of the volume of the inter-layer K-polyhedron as a function of P shows a negative slope, Fitting the P–V(K-polyhedron) data with a truncated second-order BM-EoS we obtain a bulk modulus value of K _T0(K-polyhedron) = 26(1) GPa. Tetrahedra and octahedra are significantly stiffer than the K-polyhedron. Tetrahedra behave as quasi-rigid units within the P range investigated. In contrast, a monotonic decrease is observed for the octahedron volume, with K _T0 = 120(10) GPa derived by a BM-EoS. The anisotropic response to pressure of the K-polyhedron affects the P-induced deformation mechanism on the tetrahedral sheet, consisting in a cooperative rotation of the tetrahedra and producing a significant ditrigonalization of the six-membered rings. The volume of the K-polyhedron and the value of the ditrigonal rotation parameter (α) show a high negative correlation (about 93%), though a slight discontinuity is observed at P >8 GPa. α increases linearly with P up to 7–8 GPa (with ?α/?P ≈ 0.7°/GPa), whereas at higher Ps a “saturation plateau” is visible. A comparison between the main deformation mechanisms as a function of pressure observed in 2M ₁- and 3T-phengite is discussed.     

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of ≈ 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times ≈ 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.     

Weak stability boundary trajectories for the deployment of lunar spacecraft constellations

Suitable lunar constellation coverage can be obtained by separating the satellites in inclinations and node angles. It is shown in the paper that a relevant saving of velocity variation ΔV can be achieved using weak stability boundary trajectories. The weakly stable dynamics of such transfers allows the separation of the satellites from the nominal orbit to the required orbit planes with a small amount of ΔV. This paper also shows that only one different set of orbital parameters at Moon can be reached with the same ΔV manoeuvre starting from a nominal trajectory and ending at a fixed periselenium altitude. In fact, such a feature is proved to be common to other simpler dynamical systems, such as the two- and three-body problems.     

Irregular extrasolar systems and dynamical instability

The astrometric search for extrasolar planetary systems can regard, at least in the first stage, only systems with high mass ratio (10^–2) of the largest planets to the central star. The formation of such systems is probably a common occurrence in the galaxy, as indicated by various theoretical arguments; these systems could have evolved in a regular way (near-circular and coplanar orbits, Titius-Bode law, etc.) until the most massive accumulating protoplanet exceeded the critical value of the mass ratio corresponding to dynamical instability. This phenomenon has been extensively investigated in recent years, showing that a three- orN-body system becomes unstable (for relative separations similar to the planetary ones) for >10^–2. Therefore, it seems likely that observations of systems within this range of mass ratio will show the irregular end-products of processes related to the instability (close encounters or ejections), which affected drastically the orbital configuration in the last phase of the planet formation.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

The equilibrium of a rotating body of arbitrary density

This paper extends Clairaut's theory of rotational equilibrium to third order terms in a small parameter and is meant to be a sequel to a 1962 publication by the author bearing on the same topic. It has been feasible to obtain the Clairaut equation, which governs the deformation of the equipotential surfaces within a rapidly rotating mass in hydrostatic equilibrium, as an ordinary differential equation. This has been achieved by eliminating the two integral terms which appeared in the original formulation. It is expected that the numerical integration of this newly obtained equation will contribute toward a more precise solution of certain geophysical problems — e.g., the determination of the geoid to an accuracy of ±1 m, and the correction to the travel-time of seismic waves; it should also assist in some planetary questions like the determination of the exterior shape for the rapidly rotating planets Jupiter and Saturn.     

Implementation of the European Water Framework Directive: Natural variability associated with the CARLIT method on the rocky shores of the Ligurian Sea (Italy)

The Water Framework Directive (WFD) 2000/60/EC, adopted by the European Community in 2000 with the goal of maintaining and improving the aquatic environments, requires that member states achieve and maintain a good ecological status of all water bodies by 2015. In the marine context, the ecological status has to be quantified applying indexes based on appropriate key biological elements, which allow the categorization of water bodies into five Ecological Status (ES) classes. The CARLIT index is a cartographic monitoring tool enabling the Ecological Quality Ratio (EQR) to be calculated using macroalgae in coastal hard bottoms as a key biological element; at present it is being applied in Spain, France and Italy. To detect actual changes of water quality and, consequently, rely on the application of indexes for the assessment of the ecological status in the marine environment, it is necessary to evaluate their sensitivity to natural variability at different temporal and spatial scales. In this study we present a first quantification of natural (spatial and temporal) variability of EQR‐CARLIT quality assessment in 2006 and 2007 along the Ligurian coast (North‐Western Mediterranean, Italy). The EQR‐CARLIT values recorded along the Ligurian coastline show that natural variability of EQR‐CARLIT is low and that it does not affect the attribution of a given stretch of coast to a particular ES class, in agreement with the major human pressures acting in the area (urbanization, river load, sea‐farming). A small‐scale variability was detected, strengthening the use of cartography of the whole rocky shore, whenever possible, or, alternatively, the assessment of the ecological status for long stretches of coast, to encompass the small‐scale variability due to local factors.     

A parameterization of the wavelength of tidal dunes

The idealized model of Besio et al. (On the formation of sand waves and sand banks. Journal of Fluid Mechanics 2006; 557: 1–17) is used to predict the wavelength of tidal dunes (sand waves) generated by tidal currents in estuaries and shallow seas. The predictions are then analysed and a formula is proposed to estimate the wavelength of tidal dunes as a function of the parameters of the problem. The wavelength of the dunes is found to increase when the water depth is increased and/or the strength of the tidal current is decreased. On the other hand, the size of the bottom material (if medium sand is considered) and the tidal ellipticity are found to have a relatively small influence on the length of the bottom forms. The formula proposed provides results which are consistent with field observations of different authors. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic performance of masonry walls retrofitted with steel reinforced grout

An innovative solution for the seismic protection of existing masonry structures is proposed and investigated through shake table tests on a natural scale wall assemblage. After a former test series carried out without reinforcement, the specimen was retrofitted using Steel Reinforced Grout. The strengthening system comprises horizontal strips of ultra‐high strength steel cords, externally bonded to the masonry with hydraulic lime mortar, and connectors to transversal walls, applied within the thickness of the plaster layer. In order to assess the seismic performance of the retrofitted wall, natural accelerograms were applied with increasing intensity up to failure. Test results provide a deep understanding of the effectiveness of mortar‐based composites for improving the out‐of‐plane seismic capacity of masonry walls, in comparison with traditional reinforcements with steel tie‐bars. The structural implications of the proposed solution in terms of dynamic properties and damage development under earthquake loads are also discussed.Copyright © 2015 John Wiley & Sons, Ltd.