Hamiltonian perturbation theory on a manifold

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.     

Rainfall induced debris flows in pyroclastic deposits, Campania (southern Italy)

A combination of empirical and physically based hydrological models has been used to analyze historical data on rainfall and debris-flow occurrence in western Campania, to examine the correlation between rainfall and debris-flow events.

Rainfall data from major storms recorded in recent decades in western Campania were compiled, including daily series from several rain gauges located inside landslide areas, supplemented by hourly rainfall data from some of the principal storms.

A two-phase approach is proposed. During phase 1, soil moisture levels have been modelled as the hydrological balance between precipitation and evapotranspiration, on a daily scale, using the method of Thornthwaite [Geograph. Rev. 38 (1948) 55].

Phase 2 is related to the accumulation of surplus moisture from intense rainfall, leading to the development of positive pore pressures. These interactions take place on an hourly time scale by the “leaky barrel” (LB) model described by Wilson and Wiezoreck [Env. Eng. Geoscience, 1 (1995) 11]. In combination with hourly rainfall records, the LB model has been used to compare hydrological effects of different storms. The critical level of retained rain water has been fixed by the timing of debris-flow activity, related to recorded storm events.

New rainfall intensity–duration thresholds for debris-flow initiation in western Campania are proposed. These thresholds are related to individual rain gauge and assume a previously satisfied field capacity condition. The new thresholds are somewhat higher than those plotted by previous authors, but are thought to be more accurate and thus need less conservatism.     

Thermal decay of carbonate dimension stones: fabric,physical and mechanical changes

This paper deals with the effects of thermal stresses on selected carbonate rocks used as dimension stones. They are Mesozoic calcareous and dolomitic rocks cropping out in Apulia (southern Italy) that, for their physico-mechanical and aesthetic properties, have always been finding a large application both as ornamental stones and as simple construction materials; their use is attested not only in Italy, in works of archaeological, historical and artistic interest too. The cause–effect relationships of thermal degradation were studied by means of an artificial accelerated ageing test, in order to provide a perspective about the decay of carbonate stones due to diurnal and seasonal temperature fluctuations, as well as thermal shocks during events of fire development. The stone samples were subjected to thermal cycles in a muffle furnace, ranging from 100 to 700 °C; after each cycle, several non-destructive and semi-destructive tests were carried out: mass and volume measurements, mercury intrusion porosimetry, sclerometer tests, ultrasonic tests, thin-section observations and determination of chromatic alterations through image analysis and Munsell charts method. In this way, the qualitative and quantitative modifications induced in fabric, physical and mechanical properties were discussed. The results highlight the fundamental role of depositional and diagenetic fabric that, together with mineralogical composition, represents the most significant discriminating factor in the response of the stone to thermal stresses.     

On estimating frequency-magnitude relations from heterogeneous catalogs

The paper studies the effect of magnitude errors on heterogeneous catalogs, by applying the apparent magnitude theory (seeTinti andMulargia, 1985a), which proves to be the most natural and rigorous approach to the problem. Heterogeneities in seismic catalogs are due to a number of various sources and affect both instrumental as well as noninstrumental earthquake compilations.The most frequent basis of heterogeneity is certainly that the recent instrumental records are to be combined with the historic and prehistoric event listings to secure a time coverage, considerably longer than the recurrence time of the major earthquakes. Therefore the case which attracts the greatest attention in the present analysis is that of a catalog consisting of a subset of higher quality data, generallyS ₁, spanning the interval T ₁ (the instrumental catalog), and of a second subset of more uncertain magnitude determination, generallyS ₂, covering a vastly longer interval T ₂ (the historic and/or the geologic catalog). The magnitude threshold of the subcatalogS ₁ is supposedly smaller than that ofS ₂, which, as we will see, is one of the major causes of discrepancy between the apparent magnitude and the true magnitude distributions. We will further suppose that true magnitude occurrences conform to theGutenberg-Richter (GR) law, because the assumption simplified the analysis without reducing the relevancy of our findings.The main results are: 1) the apparent occurrence rate exceeds the true occurrence rate from a certain magnitude onward, saym _GR; 2) the apparent occurrence rate shows two distinct GR regimes separated by an intermediate transition region. The offset between the two regimes is the essential outcome ofS ₁ being heterogeneous with respect toS ₂. The most important consequences of this study are that: 1) it provides a basis to infer the parameters of the true magnitude distribution, by correcting the bias deriving from heterogeneous magnitude errors; 2) it demonstrates that the double GR decay, that several authors have taken as the incontestable proof of the failure of the GR law and of the experimental evidence of the characteristic earthquake theory, is instead perfectly consistent with a GR-type seismicity.     

Chemical characterization of fine particulate matter during peak PM10 episodes in Apulia (South Italy)

Some peak PM10 episodes, occurred during PM monitoring campaigns performed on October 2005 and February and June 2006 in Bari town, have been characterized. Moreover back trajectories of air masses and Principal Component Analyses were applied. Three of the peak PM10 episodes investigated were related to local emissions of primary pollutants during poor atmospheric dispersion conditions. The other two peak PM10 episodes considered are related with long range transport air masses toward Apulia region: in one case the chemical characterization and the back trajectories analysis indicate that high PM10 value detected is due to the Saharan dust advection in the Apulia region; in the other case air masses with different origin give rise to high PM10 value.Moreover PM10 daily mean concentrations, presented in this paper collected from January 2005 to August 2007 and obtained by automatic device in six stations of air quality monitoring networks in Bari territory, do not show a seasonal trend for PM10 concentrations, contrary to the PM10 trend shown in the towns of North Italy. This can be explained mostly considering that our region presents generally meteo-climatic conditions that favour pollutants dispersion.     

Optical and X-Ray Observations of the Symbiotic System Ag Draconis During Quiescence and Outburst

We review the main characteristics of the symbiotic system AG Draconis, with special emphasis on its optical and X-ray variations. We also discuss the X-ray to visual energy distribution during quiescence and outburst and describe our spectroscopic and X-ray observations during the 2003 outburst. Based on X-ray observations collected with the XMM–Newton Observatory, on INES data from the IUE satellite, and on optical spectra collected with the Asiago–Cima Ekar, Bologna–Loiano and La Palma–Galileo Italian telescopes.     

ISA accelerometer onboard the Mercury Planetary Orbiter: error budget

We have estimated a preliminary error budget for the Italian Spring Accelerometer (ISA) that will be allocated onboard the Mercury Planetary Orbiter (MPO) of the European Space Agency (ESA) space mission to Mercury named BepiColombo. The role of the accelerometer is to remove from the list of unknowns the non-gravitational accelerations that perturb the gravitational trajectory followed by the MPO in the strong radiation environment that characterises the orbit of Mercury around the Sun. Such a role is of fundamental importance in the context of the very ambitious goals of the Radio Science Experiments (RSE) of the BepiColombo mission. We have subdivided the errors on the accelerometer measurements into two main families: (i) the pseudo-sinusoidal errors and (ii) the random errors. The former are characterised by a periodic behaviour with the frequency of the satellite mean anomaly and its higher order harmonic components, i.e., they are deterministic errors. The latter are characterised by an unknown frequency distribution and we assumed for them a noise-like spectrum, i.e., they are stochastic errors. Among the pseudo-sinusoidal errors, the main contribution is due to the effects of the gravity gradients and the inertial forces, while among the random-like errors the main disturbing effect is due to the MPO centre-of-mass displacements produced by the onboard High Gain Antenna (HGA) movements and by the fuel consumption and sloshing. Very subtle to be considered are also the random errors produced by the MPO attitude corrections necessary to guarantee the nadir pointing of the spacecraft. We have therefore formulated the ISA error budget and the requirements for the satellite in order to guarantee an orbit reconstruction for the MPO spacecraft with an along-track accuracy of about 1 m over the orbital period of the satellite around Mercury in such a way to satisfy the RSE requirements.