Effective permittivity of porous media: a critical analysis of the complex refractive index model

The availability of reliable constitutive models linking the bulk electric properties of porous media to their inner structure is a key requirement for useful quantitative applications of noninvasive methods. This study focuses on the use of dielectric measurements to monitor fluid saturation changes in porous materials. A number of empirical, semi-empirical and theoretical relationships currently exists that link the bulk dielectric constant with volumetric water content. One such relationship, named complex refractive index model or Lichteneker-Rother model has been extensively applied in recent years. Here we first analyse the characteristics of this Lichteneker-Rother model by means of theoretical considerations. This theoretical analysis indicates that the Lichteneker-Rother exponent is dependent upon the geometrical properties of the porous structure, as well as the permittivity contrast between the different phases. Pore-scale modelling and experimental data further support this result. The parameter estimation robustness in presence of synthetic data error is also assessed. This demonstrates that Lichteneker-Rother parameters cannot, in general, be independently identified on the basis of bulk dielectric constant versus moisture content data.     

The primordial excitation and clearing of the asteroid belt—Revisited

We have performed new simulations of two different scenarios for the excitation and depletion of the primordial asteroid belt, assuming Jupiter and Saturn on initially circular orbits as predicted by the Nice Model of the evolution of the outer Solar System [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465]. First, we study the effects of sweeping secular resonances driven by the depletion of the solar nebula. We find that these sweeping secular resonances are incapable of giving sufficient dynamical excitation to the asteroids for nebula depletion timescales consistent with estimates for solar-type stars, and in addition cannot cause significant mass depletion in the asteroid belt or produce the observed radial mixing of different asteroid taxonomic types. Second, we study the effects of planetary embryos embedded in the primordial asteroid belt. These embedded planetary embryos, combined with the action of jovian and saturnian resonances, can lead to dynamical excitation and radial mixing comparable to the current asteroid belt. The mass depletion driven by embedded planetary embryos alone, even in the case of an eccentric Jupiter and Saturn, is roughly 10-20× less than necessary to explain the current mass of the main belt, and thus a secondary depletion event, such as that which occurs naturally in the Nice Model, is required. We discuss the implications of our new simulations for the dynamical and collisional evolution of the main belt.     

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.     

Fundamental physics and absolute positioning metrology with the MAGIA lunar orbiter

MAGIA is a mission approved by the Italian Space Agency (ASI) for Phase A study. Using a single large-diameter laser retroreflector, a large laser retroreflector array and an atomic clock onboard MAGIA we propose to perform several fundamental physics and absolute positioning metrology experiments: VESPUCCI, an improved test of the gravitational redshift in the Earth?CMoon system predicted by General Relativity; MoonLIGHT-P, a precursor test of a second generation Lunar Laser Ranging (LLR) payload for precision gravity and lunar science measurements under development for NASA, ASI and robotic missions of the proposed International Lunar Network (ILN); Selenocenter (the center of mass of the Moon), the determination of the position of the Moon center of mass with respect to the International Terrestrial Reference Frame/System (ITRF/ITRS); this will be compared to the one from Apollo and Lunokhod retroreflectors on the surface; MapRef, the absolute referencing of MAGIA??s lunar altimetry, gravity and geochemical maps with respect to the ITRF/ITRS. The absolute positioning of MAGIA will be achieved thanks to: (1) the laboratory characterization of the retroreflector performance at INFN-LNF; (2) the precision tracking by the International Laser Ranging Service (ILRS), which gives two fundamental contributions to the ITRF/ITRS, i.e. the metrological definition of the geocenter (the Earth center of mass) and of the scale of length; (3) the radio science and accelerometer payloads; (4) support by the ASI Space Geodesy Center in Matera, Italy. Future ILN geodetic nodes equipped with MoonLIGHT and the Apollo/Lunokhod retroreflectors will become the first realization of the International Moon Reference Frame (IMRF), the lunar analog of the ITRF.     

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.     

POLARIX: a pathfinder mission of X-ray polarimetry

Since the birth of X-ray astronomy, spectral, spatial and timing observation improved dramatically, procuring a wealth of information on the majority of the classes of the celestial sources. Polarimetry, instead, remained basically unprobed. X-ray polarimetry promises to provide additional information procuring two new observable quantities, the degree and the angle of polarization. Polarization from celestial X-ray sources may derive from emission mechanisms themselves such as cyclotron, synchrotron and non-thermal bremsstrahlung, from scattering in aspheric accreting plasmas, such as disks, blobs and columns and from the presence of extreme magnetic field by means of vacuum polarization and birefringence. Matter in strong gravity fields and Quantum Gravity effects can be studied by X-ray polarimetry, too. POLARIX is a mission dedicated to X-ray polarimetry. It exploits the polarimetric response of a Gas Pixel Detector, combined with position sensitivity, that, at the focus of a telescope, results in a huge increase of sensitivity. The heart of the detector is an Application-Specific Integrated Circuit (ASIC) chip with 105,600 pixels each one containing a full complete electronic chain to image the track produced by the photoelectron. Three Gas Pixel Detectors are coupled with three X-ray optics which are the heritage of JET-X mission. A filter wheel hosting calibration sources unpolarized and polarized is dedicated to each detector for periodic on-ground and in-flight calibration. POLARIX will measure time resolved X-ray polarization with an angular resolution of about 20 arcsec in a field of view of 15 × 15 arcmin and with an energy resolution of 20% at 6 keV. The Minimum Detectable Polarization is 12% for a source having a flux of 1 mCrab and 10⁵ s of observing time. The satellite will be placed in an equatorial orbit of 505 km of altitude by a Vega launcher. The telemetry down-link station will be Malindi. The pointing of POLARIX satellite will be gyroless and it will perform a double pointing during the earth occultation of one source, so maximizing the scientific return. POLARIX data are for 75% open to the community while 25% + SVP (Science Verification Phase, 1 month of operation) is dedicated to a core program activity open to the contribution of associated scientists. The planned duration of the mission is one year plus three months of commissioning and SVP, suitable to perform most of the basic science within the reach of this instrument. A nice to have idea is to use the same existing mandrels to build two additional telescopes of iridium with carbon coating plus two more detectors. The effective area in this case would be almost doubled.