Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations

The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly) in time. In particular, in the case of an isochronous integrable part, the system can be cast in an exact normal form, regardless of the properties of the frequency vector. The general case is treated by a suitable adaptation of the finite order normalization techniques usually used for Nekhoroshev arguments. The key point is that the so called “geometric part” is not necessary in this case. As a consequence, no hypotheses on the integrable part are required, apart from analyticity. The work, based on two different perturbative approaches developed by Giorgilli et al., is a generalisation of the techniques used by the same authors to treat more specific aperiodically time-dependent problems.     

Onset of secular chaos in planetary systems: period doubling and strange attractors

As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are important, has not been thoroughly investigated. Here, we study the onset of stochastic motion in presence of dissipation, in the context of classical perturbation theory, and show that planetary systems approach chaos via a period-doubling route as dissipation is gradually reduced. Furthermore, we demonstrate that chaotic strange attractors can exist in mildly damped systems. The results presented here are of interest for understanding the early dynamical evolution of chaotic planetary systems, as they may have transitioned to chaos from a quasi-periodic state, dominated by dissipative interactions with the birth nebula.     

Buried pockmarks on the Top Chalk surface of the Danish North Sea and their potential significance for interpreting palaeocirculation patterns

Three-dimensional (3D) seismic data from the southern Danish North Sea were used to analyse the morphology and spatial distribution of depressions in the Danian Chalk deposit. Previously, these depressions were either interpreted as karst structures or pockmarks. The observed depressions occur in an interval from 25 ms below to 12 ms above the Top Chalk surface. Three types of depressions were differentiated based on their plan-view geometry and their degree of symmetry: Type 1, comprising sub-circular and symmetrical depressions, is the dominant group (ca. 70 %). Type 2, elongated and symmetrical depressions, represents only a small fraction (ca. 5 %). The elongated and asymmetrical depressions of Type 3 compose ca. 25 %. In cross section, each depression type can be either characterised by a V- or a U-shape. The maximum size of the depressions ranges from 50 to 580 m, with an average internal depth of 10 m. We interpret the depressions as pockmarks formed by the expulsion of biogenic or thermogenic fluids at the Danian seafloor. Likely, the initial form of the pockmarks has been circular (Type 1) and was subsequently modified for Types 2 and 3 to an elongated form by currents. The long axis of the pockmarks is interpreted to represent the effective current direction. The inferred direction is sub-parallel to the palaeobathymetric contours. The 3D seismic interpretation of pockmarks presented in this paper contributes to the understanding of fluid migration and palaeocirculation patterns during the sedimentation of the terminal Chalk Group in the southern Danish North Sea.     

Groundwater flow systems in turbidites of the Northern Apennines (Italy): natural discharge and high speed railway tunnel drainage

Turbidites crop out extensively in the Northern Apennine mountains (Italy). The huge amounts of groundwater drained by tunnels, built for the high speed railway connection between Bologna and Florence, demonstrate the aquifer-like behaviour of these units, up to now considered as aquitards. A conceptual model of groundwater flow systems (GFS) in fractured aquifers of turbidites is proposed, taking into account both system natural state and the perturbation induced by tunnel drainage. Analysis of hydrological data (springs, streams and tunnel discharge), collected over 10 years, was integrated with analysis of hydrochemical and isotopic data and a stream-tunnel tracer test. Hydrologic recession analysis of undisturbed conditions is a key tool in studying turbiditic aquifer hydrogeology, permitting the discrimination of GFS, the estimation of recharge relative to the upstream reach portion and the identification of springs most vulnerable to tunnel drainage impacts. The groundwater budgeting analysis provides evidence that the natural aquifer discharge was stream-focused through GFS, developed downslope or connected to main extensional tectonic lineaments intersecting stream beds; now tunnels drain mainly active recharge groundwater and so cause a relevant stream baseflow deplenishment (approximately two-thirds of the natural value), possibly resulting in adverse effects on local ecosystems.     

Filtering interpretation of acoustic inverse scattering undercoherent and incoherent insonification

The reconstruction process of two-dimensional and three-dimensional sound-soft obstacles from a set of scattered field measurements is formulated as a linear filtering problem. Under coherent and incoherent insonification, the impulse response of the equivalent filter completely characterizes the acoustical imaging process. An energy-based criterion is proposed to describe the impulse response features in both cases. Numerical simulations are also presented, showing the better performance of the incoherent insonification     

Shallow and deep reservoirs involved in magma supply of the 1944 eruption of Vesuvius

 During the 1944 eruption of Vesuvius a sudden change occurred in the dynamics of the eruptive events, linked to variations in magma composition. K-phonotephritic magmas were erupted during the effusive phase and the first lava fountain, whereas the emission of strongly porphyritic K-tephrites took place during the more intense fountain. Melt inclusion compositions (major and volatile elements) highlight that the magmas feeding the eruption underwent differentiation at different pressures. The K-tephritic volatile-rich melts (up to 3 wt.% H₂O, 3000 ppm CO₂, and 0.55 wt.% Cl) evolved to reach K-phonotephritic compositions by crystallization of diopside and forsteritic olivine at total fluid pressure higher than 300 MPa. These magmas fed a very shallow reservoir. The low-pressure differentiation of the volatile-poor K-phonotephritic magmas (H₂O<1 wt.%) involved mixing, open-system degassing, and crystallization of leucite, salite, and plagioclase. The eruption was triggered by intrusion of a volatile-rich magma batch that rose from a depth of 11–22 km into the shallow magma chamber. The first phase of the eruption represents the partial emptying of the shallow reservoir, the top of which is within the volcanic edifice. The newly arrived magma mixed with that resident in the shallow reservoir and forced the transition from the effusive to the lava fountain phase of the eruption. Received: 14 September 1998 / Accepted: 10 January 1999     

The XMM-Newton Bright Serendipitous Survey: First Extragalactic Results

We present here some initial results from the ongoing XMM-Newton bright serendipitous survey. The survey is aimed at selecting and spectroscopically identifying a large and statistically representative sample of bright (f _x ≳ 7× 10⁻¹⁴ c.g.s) serendipitous X-ray sources in the 0.5–4.5 keV energy band (BSS) and a complementary (smaller) sample in the 4.5–7.5 keV energy band (HBSS). The work is partly based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributors directly founded by ESA member states and the USA(NASA) and on observations collected at TNG. The TNG telescope is operated on the island of La Palma by the Centro Galileo Galilei of the INAF in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofísica de Canarias. On behalf of the XMM-Newton Survey Science Center.