A Theoretical Framework for Lagrangian Descriptors

This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigourous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for LDs. The definition is stated for $n$-dimensional systems with general time dependence, however we rigorously prove that this method reveals the stable and unstable manifolds of hyperbolic points in four particular 2D cases: a hyperbolic saddle point for linear autonomous systems, a hyperbolic saddle point for nonlinear autonomous systems, a hyperbolic saddle point for linear nonautonomous systems and a hyperbolic saddle point for nonlinear nonautonomous systems. We also discuss further rigorous results which show the ability of LDs to highlight additional invariants sets, such as $n$-tori. These results are just a simple extension of the ergodic partition theory which we illustrate by applying this methodology to well-known examples, such as the planar field of the harmonic oscillator and the 3D ABC flow. Finally, we provide a thorough discussion on the requirement of the objectivity (frame-invariance) property for tools designed to reveal phase space structures and their implications for Lagrangian descriptors

Dust environment and dynamical history of a sample of short-period comets: II. 81P/Wild 2 and 103P/Hartley 2

Aims. This paper is a continuation of the first paper in this series, where we presented an extended study of the dust environment of a sample of short-period comets and their dynamical history. On this occasion, we focus on comets 81P/Wild 2 and 103P/Hartley 2, which are of special interest as targets of the spacecraft missions Stardust and EPOXI. Methods. As in the previous study, we used two sets of observational data: a set of images, acquired at Sierra Nevada and Lulin observatories, and the Afρ data as a function of the heliocentric distance provided by the amateur astronomical association Cometas-Obs. The dust environment of comets (dust loss rate, ejection velocities, and size distribution of the particles) was derived from our Monte Carlo dust tail code. To determine their dynamical history we used the numerical integrator Mercury 6.2 to ascertain the time spent by these objects in the Jupiter family Comet region. Results. From the dust analysis, we conclude that both 81P/Wild 2 and 103P/Hartley 2 are dusty comets, with an annual dust production rate of 2.8 × 109 kg yr-1 and (0.4-1.5) × 109 kg yr-1, respectively. From the dynamical analysis, we determined their time spent in the Jupiter family Comet region as ~40 yr in the case of 81P/Wild 2 and ~1000 yr for comet 103P/Hartley 2. These results imply that 81P/Wild 2 is the youngest and the most active comet of the eleven short-period comets studied so far, which tends to favor the correlation between the time spent in JFCs region and the comet activity previously discussed

Corrosion of Copper in Unpolluted Chloride-Rich Atmospheres

The atmospheric corrosion of copper in pure coastal atmospheres has not been extensively studied. This paper presents the results of research carried out in pure coastal atmospheres with annual chloride deposition rates of between 110–1640 mg/m2·d. Copper specimens (99.99 wt % Cu) were exposed for 3, 6, 9, and 12 months at six testing stations located at different distances from the seashore. Tests were performed to determine the copper corrosion rate, the surface area coated with corrosion products, and the evolution of both magnitudes with exposure time. Conventional and grazing X-ray diffraction techniques were used to analyze the corrosion products formed—cuprite and the polymorphs botallackite, atacamite, and clinoatacamite—and their presence through the patina thickness, while scanning electron microscopy/energy dispersive X-ray spectrometry was employed to study the morphology of the resulting corrosion layers. The most relevant findings are a notable increase in atacamite and clinoatacamite formation at higher atmospheric salinity levels and longer exposure times, and the flaking-off of the corrosion product layer formed in the marine atmospheres with the highest chloride deposition rates.To CSIC Agency (Spain) for support.Peer reviewe