Normal forms for the epicyclic approximations of the perturbed Kepler problem

We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward.     

A simplified vulnerability model for the extensive liquefaction risk assessment of buildings

Bulletin of Earthquake Engineering - The quantitative assessment of natural risks offers a rational strategy to protect communities, undertake cost effective mitigation and plan the organic and...     

Thermal convection in ice-I shells of Titan and Enceladus

Cassini-Huygens observations have shown that Titan and Enceladus are geologically active icy satellites. Mitri and Showman [Mitri, G., Showman, A.P., 2005. Icarus 177, 447-460] and McKinnon [McKinnon, W.B., 2006. Icarus 183, 435-450] investigated the dynamics of an ice shell overlying a pure liquid-water ocean and showed that transitions from a conductive state to a convective state have major implications for the surface tectonics. We extend this analysis to the case of ice shells overlying ammonia-water oceans. We explore the thermal state of Titan and Enceladus ice-I shells, and also we investigate the consequences of the ice-I shell conductive-convective switch for the geology. We show that thermal convection can occur, under a range of conditions, in the ice-I shells of Titan and Enceladus. Because the Rayleigh number Ra scales with δ³/ηb, where δ is the thickness of the ice shell and ηb is the viscosity at the base of the ice-I shell, and because ammonia in the liquid layer (if any) strongly depresses the melting temperature of the water ice, Ra equals its critical value for two ice-I shell thicknesses: for relatively thin ice shell with warm, low-viscosity base (Onset I) and for thick ice shell with cold, high-viscosity base (Onset II). At Onset I, for a range of heat fluxes, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. Switches between these states can cause large, rapid changes in the ice-shell thickness. For Enceladus, we demonstrate that an Onset I transition can produce tectonic stress of ∼500 bars and fractures of several tens of km depth. At Onset II, in contrast, we demonstrate that zero equilibrium states exist for a range of heat fluxes. For a mean heat flux within this range, the satellite experiences oscillations in surface heat flux and satellite volume with periods of ∼50-800 Myr even when the interior heat production is constant or monotonically declining in time; these oscillations in the thermal state of the ice-I shell would cause repeated episodes of extensional and compressional tectonism.     

Mechanical interpretation of dry granular masses impacting on rigid obstacles

Acta Geotechnica - The evaluation of impact forces exerted by flowing granular masses on rigid obstacles is of fundamental importance for the assessment of the associated risk and for the design of...     

Possibilita' di applicazione dei metodi geoelettrici di prospezione alla registrazione dei movimenti del magma entro i condotti vulcanici

Riassunto Dopo avere accennato all'importanza della registrazione dei movimenti del magma nel condotto vulcanico ai fini scientifici, viene mostrata, attraverso alcune esperienze, la possibilità di una utile registrazione e che tale possibilità può raggiungersi più facilmente mediante l'impiego dei seguenti metodi usati nella prospezione del sottosuolo: metodo di Wenner, metodo della misura diretta della resistenza, metodo induttivo.

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Zusammenfassung Nach Hervorhebung der Wichtigkeit die Bewegungen des Magmas im innern eines Vulkans registrieren zu können, wird gezeigt, auf Grund einiger Experimente, wie diese Registrierung möglich ist und zwar durch die Anwendung der geoelektrischen Bodenforschungs-Verfahren, nähmlich: di Wenner-Methode, die Methode der direkten Widerstands-Messung, Induktions-Verfahren.

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Résumé Après avoir fait allusion à l'importance scientifique de l'enregistrement des mouvements du magna dans le conduit d'un volcan, on démontre, avec quelques expériences, la possibilité d'un enregistrement convenable qu'on peut obtenir d'ailleurs plus aisément en enployant une des méthodes suivantes utilisées dans la prospection du sous-sol: méthode de Wenner, méthode de la mésure directe de la résistance, méthode inductive.

     

Geodynamic Evolution of Northeastern Tunisia During the Maastrichtian–Paleocene Time: Insights from Integrated Seismic Stratigraphic Analysis

The Maastrichtian–Paleocene El Haria formation was studied and defined in Tunisia on the basis of outcrops and borehole data; few studies were interested in its three-dimensional extent. In this paper, the El Haria formation is reviewed in the context of a tectono-stratigraphic interval using an integrated seismic stratigraphic analysis based on borehole lithology logs, electrical well logging, well shots, vertical seismic profiles and post-stack surface data. Seismic analysis benefits from appropriate calibration with borehole data, conventional interpretation, velocity mapping, seismic attributes and post-stack model-based inversion. The applied methodology proved to be powerful for charactering the marly Maastrichtian–Paleocene interval of the El Haria formation. Migrated seismic sections together with borehole measurements are used to detail the three-dimensional changes in thickness, facies and depositional environment in the Cap Bon and Gulf of Hammamet regions during the Maastrichtian–Paleocene time. Furthermore, dating based on their microfossil content divulges local and multiple internal hiatuses within the El Haria formation which are related to the geodynamic evolution of the depositional floor since the Campanian stage. Interpreted seismic sections display concordance, unconformities, pinchouts, sedimentary gaps, incised valleys and syn-sedimentary normal faulting. Based on the seismic reflection geometry and terminations, seven sequences are delineated. These sequences are related to base-level changes as the combination of depositional floor paleo-topography, tectonic forces, subsidence and the developed accommodation space. These factors controlled the occurrence of the various parts of the Maastrichtian–Paleocene interval. Detailed examinations of these deposits together with the analysis of the structural deformation at different time periods allowed us to obtain a better understanding of the sediment architecture in depth and the delineation of the geodynamic evolution of the region.     

A direct scaling analysis for the sea level rise

The estimation of long-term sea level variability is of primary importance for a climate change assessment. Despite the value of the subject, no scientific consensus has yet been reached on the existing acceleration in observed values. The existence of this acceleration is crucial for coastal protection planning purposes. The absence of the acceleration would enhance the debate on the general validity of current future projections. Methodologically, the evaluation of the acceleration is a controversial and still open discussion, reported in a number of review articles, which illustrate the state-of-art in the field of sea level research. In the present paper, the well-proven direct scaling analysis approach is proposed in order to describe the long-term sea level variability at 12 worldwide-selected tide gauge stations. For each of the stations, it has been shown that the long-term sea level variability exhibits a trimodal scaling behaviour, which can be modelled by a power law with three different pairs of shape and scale parameters. Compared to alternative methods in literature, which take into account multiple correlated factors, this simple method allows to reduce the uncertainties on the sea level rise parameters estimation.     

Deep tunnel fronts in cohesive soils under undrained conditions: a displacement-based approach for the design of fibreglass reinforcements

The fronts of tunnels excavated under particularly difficult ground conditions by employing conventional tunnelling methods are commonly supported: the stabilization is usually achieved either by improving the mechanical properties of the soil (injections, jet grouting, soil freezing, etc.) or by introducing linear inclusions. This last technique, consisting in the introduction of pipes (usually made of fibreglass reinforced polymers) in the front, is particularly popular since it is very simple to adapt the reinforcement geometry, length and number to the different conditions encountered during the excavation. The design of this reinforcement technique is nowadays based on very simplified approaches: on either empirical formula or the limit equilibrium method. In a previous paper, the authors numerically studied the mechanical response of unreinforced fronts in cohesive soils and defined a non-dimensional front characteristic curve. In this paper, the authors intend to take into consideration the role of reinforcements by following the same approach. A procedure allowing the definition of the reinforced non-dimensional front characteristic curve, once the reinforcement pattern is assigned, is introduced. The practical use of this curve is described.

     

Magnesite growth rates as a function of temperature and saturation state

Magnesite growth rates and step velocities have been measured systematically as a function of temperature from 80 to 105 °C and saturation state in 0.1 M NaCl solutions using hydrothermal atomic force microscopy (HAFM). The observations indicate that at these conditions magnesite precipitation is dominated by the coupling of step generation via spiral growth at screw dislocations and step advancement away from these dislocations. As these two processes occur in series the slowest of these dominates precipitation rates. At 100 °C magnesite growth rates (r) determined by HAFM are consistent with

r=k(Ω-1)²,