Cross-entropy optimizer: a new tool to study precession in astrophysical jets

Evidence of jet precession in many galactic and extragalactic sources has been reported in the literature. Much of this evidence is based on studies of the kinematics of the jet knots, which depends on the correct identification of the components to determine their respective proper motions and position angles on the plane of the sky. Identification problems related to fitting procedures, as well as observations poorly sampled in time, may influence the follow-up of the components in time, which consequently might contribute to a misinterpretation of the data. In order to deal with these limitations, we introduce a very powerful statistical tool to analyse jet precession: the cross-entropy method for continuous multi-extremal optimization. Only based on the raw data of the jet components (right ascension and declination offsets from the core), the cross-entropy method searches for the precession model parameters that better represent the data. In this work we present a large number of tests to validate this technique, using synthetic precessing jets built from a given set of precession parameters. With the aim of recovering these parameters, we applied the cross-entropy method to our precession model, varying exhaustively the quantities associated with the method. Our results have shown that even in the most challenging tests, the cross-entropy method was able to find the correct parameters within a 1 per cent level. Even for a non-precessing jet, our optimization method could point out successfully the lack of precession.

Solid state NMR as a new approach for the structural characterization of rare-earth doped lead lanthanum zirconate titanate laser ceramics

To facilitate the design of laser host materials with optimized emission properties, detailed structural information at the atomic level is essential, regarding the local bonding environment of the active ions (distribution over distinct lattice sites) and their extent of local clustering as well as their population distribution over separate micro- or nanophases. The present study explores the potential of solid state NMR spectroscopy to provide such understanding for rare-earth doped lead lanthanum zirconate titanate (PLZT) ceramics. As the NMR signals of the paramagnetic dopant species cannot be observed directly, two complementary approaches are utilized: (1) direct observation of diamagnetic mimics using Sc-45 NMR and (2) study of the paramagnetic interaction of the constituent host lattice nuclei with the rare-earth dopant, using Pb-207 NMR lineshape analysis. Sc-45 MAS NMR spectra of scandium-doped PLZT samples unambiguously reveal scandium to be six-coordinated, suggesting that this rare-earth ion substitutes in the B site. Static Pb-207 spin echo NMR spectra of a series of Tm-doped PLZT samples reveal a clear influence of paramagnetic rare-earth dopant concentration on the NMR lineshape. In the latter case high-fidelity spectra can be obtained by spin echo mapping under systematic incrementation of the excitation frequency, benefiting from the signal-to-noise enhancement afforded by spin echo train Fourier transforms. Consistent with XRD data, the Pb-207 NMR lineshape analysis suggests that statistical incorporation into the PLZT lattice occurs at dopant levels of up to 1 wt.% Tm3+, while at higher levels the solubility limit is reached. (C) 2008 Elsevier Masson SAS. All rights reserved.