Regions of stability in rotational dynamics

We investigate the rotational dynamics of a triaxial planet moving on a Keplerian orbit around its star. The dynamics is ruled by several parameters, like the eccentricity, the obliquity, the non-principal rotation, the angular momentum, etc. We consider two specific cases in which the planet is symmetric or asymmetric, according to whether two moments of inertia coincide or differs from each other. We study the dynamics by constructing maps of dynamical stability based on the computation of the maximum Lyapunov characteristic number versus some typical parameters. The results show that only specific resonances appear in the symmetric case, while the asymmetric case shows a much richer phenomenology.     

Flooding scenarios due to land subsidence and sea‐level rise: a case study for Lipari Island (Italy)

Archaeological and instrumental data indicate that the southern sector of the volcanic island of Lipari has been subsiding for the last 2100 years due to isostatic and tectonic factors, at variable rates of up to ~11 mm a^?1. Based on this data, a detailed marine flooding scenario for 2100 AD is provided for the bay of Marina Lunga in the eastern part of the island from (1) an ultra‐high‐resolution Digital Terrain and Marine Model (DTMM) generated from multibeam bathymetry (MB) and Unmanned Aerial Vehicles (UAV), (2) the rate of land subsidence from Global Positioning System (GPS) data and (3) the regional sea‐level projections of the International Panel on Climate Change (IPCC). When land subsidence is considered, the upper bound of sea‐level rise is estimated at 1.36 m and 1.60 m for RCP4.5 and RCP8.5 climate change scenarios, respectively. Here, we show the expected impact of marine flooding at Lipari for the next 85 years and discuss the hazard implications for the population living along the shore.     

Seismic reliability of traditional and innovative concentrically braced frames

Structural engineering problems are always affected by many sources of uncertainty, such as aleatory of material properties, applied loads and earthquake intensity, therefore, seismic assessment of structures should be based on probabilistic methods. Since PBSD (Performance‐based Seismic Design) philosophy was formulated, many researches have been conducted in this field in order to develop simple and accurate procedures for evaluating structural reliability. An important contribution has been provided by Jalayer and Cornell, who have developed a closed‐form expression to evaluate the mean annual frequency of exceeding a defined limit state. In this paper, by assuming the record‐to‐record variability as the only source of uncertainty, the seismic reliability of concentrically braced frames designed according to traditional and innovative methodologies is investigated, and a comparison between their performances is presented. In particular, two design methodologies have been applied: Eurocode 8 provisions and a new design methodology based on a rigorous application of ‘capacity design’ criteria. The innovative reduced section solution strategy, based on the reduction of cross sections at bracing member ends, has also been analysed. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimation of mean spectral directions in random seas

A method for obtaining the directional spectrum, on assuming that the frequencies of the elementary waves are all different from one another, is re-proposed in a form suitable for applications to sea states near a coast. The method is applied to an interval of 10 h during which the sea state remained basically steady state off the beach at Reggio Calabria (east coast of the Straits of Messina). It is shown that the directional spectrum converges as the length of the time series data grows. A numerical simulation of a 10 h sea state confirms that the directional spectrum converges as the length of the time series grows, and the convergence is onto the known directional spectrum used to make the numerical simulation. Through the numerical simulation, it is proved that the method, generally, is suitable for applications even with short time series of wind waves (duration of about 100T_p). Finally, it is shown that the method is not necessarily inadequate even with short records of multimodal sea states with different modal directions, modal amplitude ratios and intermodal distances.     

An application of the Nekhoroshev theorem to the restricted three-body problem

We studied the stability of the restricted circular three-body problem. We introduced a model Hamiltonian in action-angle Delaunay variables. which is nearly-integrable with the perturbing parameter representing the mass ratio of the primaries. We performed a normal form reduction to remove the perturbation in the initial Hamiltonian to higher orders in the perturbing parameter. Next we applied a result on the Nekhoroshev theorem proved by Pöschel [13] to obtain the confinement in phase space of the action variables (related to the elliptic elements of the minor body) for an exponentially long time. As a concrete application. we selected the Sun-Ceres-Jupiter case, obtaining (after the proper normal form reduction) a stability result for a time comparable to the age of the solar system (i.e., 4.9 · 10⁹ years) and for a mass ratio of the primaries less or equal than 10^–6.     

Dependence on the observational time intervals and domain of convergence of orbital determination methods

In the framework of the orbital determination methods, we study some properties related to the algorithms developed by Gauss, Laplace and Mossotti. In particular, we investigate the dependence of such methods upon the size of the intervals between successive observations, encompassing also the case of two nearby observations performed within the same night. Moreover we study the convergence of Gauss algorithm by computing the maximal eigenvalue of the jacobian matrix associated to the Gauss map. Applications to asteroids and Kuiper belt objects are considered.     

On the stability of the lagrangian points in the spatial restricted problem of three bodies

The problem of stability of the Lagrangian equilibrium point of the circular restricted problem of three bodies is investigated in the light of Nekhoroshev-like theory. Looking for stability over a time interval of the order of the estimated age of the universe, we find a physically relevant stability region. An application of the method to the Sun-Jupiter and the Earth-Moon systems is made. Moreover, we try to compare the size of our stability region with that of the region where the Trojan asteroids are actually found; the result in such case is negative, thus leaving open the problem of the stability of these asteroids.     

Slope dynamics of Lake Albano (Rome,Italy): insights from high resolution bathymetry

New detailed data about the morphology of the submerged slopes of Lake Albano (Rome, Italy) have been collected by a sonar multibeam survey financed by the Italian Department of Civil Protection. These data allow for investigation of the subaqueous slope dynamics of the lake, which partially fills a volcanic depression, and the elucidation of the relationships between subaqueous and subaerial slope processes. Subaerial, submerged and combined subaerial/submerged landslide‐related morphologies were detected around the inner slopes of the lake. In the submerged slopes, several gravity‐induced landforms were recognized: landslide scar areas, landslide accumulations, erosional chutes and channels, block fields, isolated blocks, scarps and slope breaks. An attempt to evaluate the state of activity of the submerged slopes was carried out by taking into consideration the relative freshness of some selected landforms. Interpretation of bathymetric data, as well as direct surveys of the subaerial slopes, was used to assess the morphometric features and interpret the type of movement of the landslides. We propose a comprehensive classification based on the landslide's size and type of movement. We recognized rock fall/topples, debris flows, rock slides and slump, complex rock slides/channelled flows and debris slide and slump. The volume of the main landslides ranged between 10¹ and 10³ m³, while a few rock and debris slides have volumes ranging between 10³ and 10⁵ m³. Two large palaeo‐landslides with volumes on the order of 10⁶ m³ were identified in the southern and northern part of the lake, respectively. Velocities of the recognized landslides range from rapid to extremely rapid. Two main landslide hazard scenarios have been depicted from the results of the integrated analysis of both subaerial and submerged gravity‐induced landforms. The most hazardous scenario involves extremely rapid large volume events (>10⁶ m³) that could, if they interacted with water, induce catastrophic tsunamis. Copyright © 2009 John Wiley & Sons, Ltd.     

Effects on geodetic VLBI measurements due to polarization leakage in S/X receivers

Geodetic very long baseline interferometry (VLBI) delivers time series of station positions and Earth orientation parameters. These series offer a viable and precise way to study Earth crustal and core dynamics and to support space navigation. Their accuracy is degraded by instrumental errors, of which polarization leakage is considered to be one of the largest that is not yet being addressed. Its effect on the data can be corrected, provided one knows the leakage characteristics of the receivers. For this purpose, we designed a VLBI session to measure the polarization leakage at 15 geodetic and very long baseline array stations over the frequency range from 8,212.99 to 8,932.99 MHz. We describe the polarization leakage measurements and the algorithm that was implemented to correct for its effect on the geodetic delay observables. Subsequently, we applied the correction for polarization leakage to the same data that were used to determine the leakage and checked for the resulting improvement. From the measured leakage terms, one would expect polarization leakage to affect the group delay measurements in 90% of the cases by 1.6 ps or less. This proved to be below the statistical noise in our single VLBI session, and hence, an improvement from the correction could not be detected. Applying this analysis in the context of VLBI2010, we provide a specification for the allowable polarization leakage to achieve the target submillimetre accuracy.