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.     

Earthquake-induced reactivation of landslides under variable hydrostatic conditions: evaluation at regional scale and implications for risk assessment

Landslides - Earthquake-induced landslides represent a significant seismic hazard since they can largely increase the damage and losses due to a seismic event, an issue that must be considered in...     

Weighting of Parts in Compositional Data Analysis: Advances and Applications

Mathematical Geosciences - It often occurs in practice that it is sensible to give different weights to the variables involved in a multivariate data analysis—and the same holds for...     

The contrasting geochemical message from the New Caledonia gabbronorites: insights on depletion and contamination processes of the sub-arc mantle in a nascent arc setting

The New Caledonia ophiolite hosts one of the rare examples of crust-mantle sections built in a nascent arc environment, providing the unique opportunity to investigate the first stages of arc magmatism in a subduction setting. The sequence consists of refractory harzburgites, overlain by ultramafic (dunites and wehrlites) and mafic lithologies (gabbronorites). The gabbronorites occur in the upper part of the sequence as decimetre to metre-size sills. They are mainly formed (??55 to 70 vol%) of Ca-rich plagioclase (An up to 96 mol%) and high Mg# (88–92), Al₂O₃-poor (1.5–2.4 wt%) clinopyroxene (8–20 vol%), often rimmed by interstitial or poikilitic orthopyroxene (6–27 vol%). Mg-rich olivine (3–15 vol%, Fo?=?87–89 mol%) occurs as anhedral, resorbed crystals. Whole rock (WR) compositions exhibit high Mg# (86–92) and strikingly low trace element contents. They own LREE-depleted patterns, with nearly flat (0.82?≤?Dy_N/Yb_N?≤?1.00) and low HREE (Yb_N?=?0.2–0.9) and positive Eu anomalies. Clinopyroxene trace element chemistry mirrors the extreme depletion of the WR. By contrast, FME enrichments are observed for WR and clinopyroxene. Geochemical models show that the gabbronorites crystallized from primitive, ultra-depleted melts bearing evidence of fluid contamination processes, but with significantly different geochemical signatures compared to boninitic rocks worldwide, i.e. lower LREE-MREE, and absence of Nb depletion and Zr–Hf enrichments. Nd isotopes (+?8.2?≤?εNd_i?≤?+?13.1), together with radiogenic Pb isotopic ratios, support an origin from a DMM source variably modified by slab fluids. We propose that the geochemical signature of the New Caledonia gabbronorites reflect emplacement of primitive, non-aggregated, magma batches in the lower fore-arc crust, during the first phases of arc formation.     

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.     

A facies of Kophobelemnon (Cnidaria,Octocorallia) from Santa Maria di Leuca coral province (Mediterranean Sea)

During a research cruise carried out in April 2010, aimed at updating the knowledge on the biodiversity of the Santa Maria di Leuca (SML) cold‐water coral province (Mediterranean Sea), a facies of the sea pen Kophobelemnon stelliferum (Muller, 1776) was found on mud‐dominated bottoms. This finding represents a new species and a new habitat record from the SML coral province as well as a new bathyal facies in the whole Central Mediterranean Sea. The colonies were collected using an epi‐benthic sledge, at depths between 400 and 470 m. A significant positive relationship between polyp number and colony length was detected. Density of the colonies ranged from 0.003 to 0.038 N·m^?2. Differences and affinities between Mediterranean and Atlantic occurrences of K. stelliferum are discussed.     

Some results on the global dynamics of the regularized restricted three-body problem with dissipation

We perform an analysis of the dynamics of the circular, restricted, planar three-body problem under the effect of different kinds of dissipation (linear, Stokes and Poynting–Robertson drags). Since the problem is singular, we implement a regularization technique in the style of Levi–Civita. The effect of the dissipation is often to decrease the semi-major axis; as a consequence the minor body collides with one of the primaries. In general, it is quite difficult to find non-collision orbits using random initial conditions. However, by means of the computation of the Fast Lyapunov Indicators (FLI), we obtain a global view of the dynamics. Precisely, we detect the regions of the phase space potentially belonging to basins of attraction. This investigation provides information on the different regions of the phase space, showing both collision and non-collision trajectories. Moreover, we find periodic orbit attractors for the case of linear and Stokes drags, while in the case of the Poynting–Robertson effect no other attractors are found beside the primaries, unless a fourth body is added to counterbalance the dissipative effect.