Improved Leap—Frog Symplectic Integrators for Orbits of Small Eccentricity in the Perturbed Kepler Problem

I have improved the precision of the leap–frog symplectic integrators for perturbed Kepler problems at small eccentricities, without significant loss of CPU time. The integration scheme proposed is competitive, in some situations, with the so-called mixed variable integrators.     

Analysis of the Chaotic Behaviour of Orbits Diffusing along the Arnold Web

In a previous work [Guzzo et al. DCDS B 5, 687–698 (2005)] we have provided numerical evidence of global diffusion occurring in slightly perturbed integrable Hamiltonian systems and symplectic maps. We have shown that even if a system is sufficiently close to be integrable, global diffusion occurs on a set with peculiar topology, the so-called Arnold web, and is qualitatively different from Chirikov diffusion, occurring in more perturbed systems. In the present work we study in more detail the chaotic behaviour of a set of 90 orbits which diffuse on the Arnold web. We find that the largest Lyapunov exponent does not seem to converge for the individual orbits while the mean Lyapunov exponent on the set of 90 orbits does converge. In other words, a kind of average mixing characterizes the diffusion. Moreover, the Local Lyapunov Characteristic Numbers (LLCNs), on individual orbits appear to reflect the different zones of the Arnold web revealed by the Fast Lyapunov Indicator. Finally, using the LLCNs we study the ergodicity of the chaotic part of the Arnold web.     

Sun–Earth L_{1} and L_{2} to Moon transfers exploiting natural dynamics

This paper examines the design of transfers from the Sun–Earth libration orbits, at the \(L_{1}\) and \(L_{2}\) points, towards the Moon using natural dynamics in order to assess the feasibility of future disposal or lifetime extension operations. With an eye to the probably small quantity of propellant left when its operational life has ended, the spacecraft leaves the libration point orbit on an unstable invariant manifold to bring itself closer to the Earth and Moon. The total trajectory is modeled in the coupled circular restricted three-body problem, and some preliminary study of the use of solar radiation pressure is also provided. The concept of survivability and event maps is introduced to obtain suitable conditions that can be targeted such that the spacecraft impacts, or is weakly captured by, the Moon. Weak capture at the Moon is studied by method of these maps. Some results for planar Lyapunov orbits at \(L_{1}\) and \(L_{2}\) are given, as well as some results for the operational orbit of SOHO.     

Scaling improves stability of preconditioned CG‐like solvers for FE consolidation equations

Preconditioned projection (or conjugate gradient like) methods are increasingly used for the accurate and efficient solution to finite element (FE) coupled consolidation equations. Theory indicates that preliminary row/column scaling does not affect the eigenspectrum of the iteration matrix controlling convergence as long as the preconditioner relies on the incomplete factorization of the FE coefficient matrix. However, computational experience with mid‐large size problems shows that the above inexpensive operation can significantly accelerate the solver convergence, and to a minor extent also improve the final accuracy, as a result of a better solver stability to the accumulation and propagation of floating point round‐off errors. This is demonstrated with the aid of the least square logarithm (LSL) scaling algorithm on FE consolidation problems of increasing size up to more than 100 000. It is shown that a major source of numerical instability rests with the sub‐matrix which couples the structural to the fluid part of the underlying mathematical model. It is concluded that for mid‐large size, possibly difficult, FE consolidation problems left/right LSL scaling is to be always recommended when the incomplete factorization is used as a preconditioning technique. Copyright © 2003 John Wiley & Sons, Ltd.     

High-resolution spectrometer for atmospheric studies

A high-resolution spectrometer (0.0014 nm at 313 nm) has been developed at the University of L’Aquila (Italy) for atmospheric spectroscopic studies. The layout, optics and software for the instrument control are described. Measurements of the mercury low-pressure lamp lines from 200 to 600 nm show the high performances of the spectrometer. Laboratory measurements of OH and NO₂ spectrums demonstrate that the system could be used for cross-section measurements and to detect these species in the atmosphere. The first atmospheric application of the system was the observation of direct solar and sky spectrums that shows a filling-in of the sky lines due to rotational Raman scattering. The measurements have been done with clear and cloudy sky and in both there was a strong dependence of the filling-in from the solar zenith angle whereas no dependence from the wavelengths was evident at low solar zenith angles (less than 85°).     

Evidence of a full West Antarctic Ice Sheet back to the early Oligocene: insight from double dating of detrital apatites in Ross Sea sediments.

The West Antarctic Ice Sheet is the most unstable component of the Antarctic cryosphere. Its fluctuations are well documented since the Pliocene, but its behaviour over the last 35 Ma is more controversial, particularly during periods of past high global pCO₂ values similar to those predicted in future global climate scenarios. Here, we present new U–Pb dating of detrital apatite grains (previously dated by the fission‐track method) from Cape Roberts Project Oligocene to Pliocene marine sediments in the Ross Sea. Two past ice‐flow patterns were identified: one formed by outlet glaciers sourcing short‐travelled apatites and one, northerly directed, bringing far‐travelled apatite grains. The latter provides the first robust physical evidence for the presence and repeated expansion of an Oligocene West Antarctic Ice Sheet.     

Evidence-based robust design of deflection actions for near Earth objects

This paper presents a novel approach to the robust design of deflection actions for near Earth objects (NEO). In particular, the case of deflection by means of solar-pumped laser ablation is studied here in detail. The basic idea behind laser ablation is that of inducing a sublimation of the NEO surface, which produces a low thrust thereby slowly deviating the asteroid from its initial Earth threatening trajectory. This work investigates the integrated design of the space-based laser system and the deflection action generated by laser ablation under uncertainty. The integrated design is formulated as a multi-objective optimisation problem in which the deviation is maximised and the total system mass is minimised. Both the model for the estimation of the thrust produced by surface laser ablation and the spacecraft system model are assumed to be affected by epistemic uncertainties (partial or complete lack of knowledge). Evidence Theory is used to quantify these uncertainties and introduce them in the optimisation process. The propagation of the trajectory of the NEO under the laser-ablation action is performed with a novel approach based on an approximated analytical solution of Gauss’ variational equations. An example of design of the deflection of asteroid Apophis with a swarm of spacecraft is presented.