Regular and chaotic motion in softened gravitational systems

The stability of the dynamical trajectories of softened spherical gravitational systems is examined, both in the case of the full N -body problem and that of trajectories moving in the gravitational field of non-interacting background particles. In the latter case, for   N 10 000  , some trajectories, even if unstable, had exceedingly long diffusion times, which correlated with the characteristic e-folding time-scale of the instability. For trajectories of   N ≈100 000  systems this time-scale could be arbitrarily large – and thus appear to correspond to regular orbits. For centrally concentrated systems, low angular momentum trajectories were found to be systematically more unstable. This phenomenon is analogous to the well-known case of trajectories in generic centrally concentrated non-spherical smooth systems, where eccentric trajectories are found to be chaotic. The exponentiation times also correlate with the conservation of the angular momenta along the trajectories. For N up to a few hundred, the instability time-scales of N -body systems and their variation with particle number are similar to those of the most chaotic trajectories in inhomogeneous non-interacting systems. For larger N (up to a few thousand) the values of the these time-scales were found to saturate, increasing significantly more slowly with N . We attribute this to collective effects in the fully self-gravitating problem, which are apparent in the time variations of the time-dependent Liapunov exponents. The results presented here go some way towards resolving the long-standing apparent paradoxes concerning the local instability of trajectories. This now appears to be a manifestation of mechanisms driving evolution in gravitational systems and their interactions – and may thus be a useful diagnostic of such processes.     

Interaction of particles with ion cyclotron waves and magnetosonic waves. Observations from GEOS 1 and GEOS 2

Coordinated observations involving ion composition, thermal plasma, energetic particle, and ULF magnetic field data from GEOS 1 and 2 often reveal the presence of electromagnetic ion cyclotron and magnetosonic waves, which are distinguished by their respective polarization characteristics and frequency spectra. The ion cyclotron waves are identified by a magnetic field perturbation that lies in a plane perpendicular to the Earth's magnetic field B₀ and propagate along B₀. They are associated with the abundance of cold He⁺ in the presence of anisotropic pitch angle distributions of ions having energies E > 20 keV, and were observed at frequencies near the He⁺ gyrofrequency. The magnetosonic waves are characterized by a magnetic field perturbation parallel to B₀ and thus seem to be propagating perpendicular to the Earth's magnetic field. They often occur at harmonics (not always including the fundamental) at the proton gyrofrequency and are associated with phase-space-density distributions that peak at energies E ～ 5–30 keV and at a pitch angle of 90°. Such a ring-like distribution is shown to excite instability in the magnetosonic mode near harmonics of the proton gyrofrequency. Magnetosonic waves are associated in other cases with sharp spatial gradients in energetic ion intensity. Such gradients are encountered in the early afternoon sector (as a consequence of the drift shell distortion caused by the convection electric field) and could likewise constitute a source of free energy for plasma instabilities.     

Bizarre geochemistry of komatiites from the Crixás greenstone belt,Brazil

Komatiite lava flows in the Crixás greenstone belt, Goiás, Brazil, have textures and volcanic structures typical of Archean komatiites, but are geochemically most unusual. The flows are porphyritic and massive, or layered with spinifex upper parts and olivine cumulate lower parts. MgO contents range from 18 to 40%. In such lavas, only olivine (and minor chromite) can have crystallized, but neither major nor trace elements fall on olivine control lines. In MgO variation diagrams, CaO and Sr fall on lines with slopes steeper than olivine control lines; SiO₂, FeO, Na₂O, K₂O and Y show little systematic variation; Zr shows a large variation that does not correlate with MgO; and Al₂O₃ decreases markedly with decreasing MgO. The aberrant behaviour is highlighted by the REE (rare earth elements) in spinifex and olivine cumulate layers from three flows: in the spinifex layers, chondrite-normalized REE patterns are hump-shaped with maxima at Nd or Sm ((La/Sm)_N=0.6, (Gd/Yb)_N=1.6–2.3), whereas cumulate zones in the same flows have steadily sloping patterns, with LREE enriched relative to HREE ((La/Sm)_N=1.3, (Gd/Yb)_N=1.4). Neither normal magmatic processes acting during emplacement of the komatiites, nor thermal erosion and wall-rock assimilation can explain these effects, and we speculate that elements commonly thought of as “immobile” (e.g. Al, Zr, REE) migrated during hydrothermal alteration or metamorphism. A Pb-Pb whole rock isochron gave an age of 2,728±140 Ma and selected Sm-Nd analyses an apparent isochron age of 2,825±98 Ma (ɛ_Nd≈0). The Pb-Pb age is believed to be the approximate time of emplacement. Interpretation of the Sm-Nd data is complicated by the evidence of mobility of REE.     

The radio counterpart of the likely TeV binary HESS J0632+057

The few known γ-ray binary systems are all associated with variable radio and X-ray emission. The TeV source HESS J0632+057, apparently associated with the Be star MWC 148, is plausibly a new member of this class. Following the identification of a variable X-ray counterpart to the TeV source we conducted Giant Metrewave Radio Telescope (GMRT) and Very Large Array (VLA) observations in 2008 June–September to search for the radio counterpart of this object. A point-like radio source at the position of the star is detected in both 1280-MHz GMRT and 5-GHz VLA observations, with an average spectral index, α, of ∼0.6. In the VLA data there is significant flux variability on ∼month time-scales around the mean flux density of ≈0.3 mJy. These radio properties (and the overall spectral energy distribution) are consistent with an interpretation of HESS J0632+057 as a lower power analogue of the established γ-ray binary systems.     

Empirical ground-motion models for point- and extended-source crustal earthquake scenarios in Europe and the Middle East

This article presents the latest generation of ground-motion models for the prediction of elastic response (pseudo-) spectral accelerations, as well as peak ground acceleration and velocity, derived using pan-European databases. The models present a number of novelties with respect to previous generations of models (Ambraseys et al. in Earthq Eng Struct Dyn 25:371–400, 1996, Bull Earthq Eng 3:1–53, 2005; Bommer et al. in Bull Earthq Eng 1:171–203, 2003; Akkar and Bommer in Seismol Res Lett 81:195–206, 2010), namely: inclusion of a nonlinear site amplification function that is a function of $\text{ V }_\mathrm{S30}$ and reference peak ground acceleration on rock; extension of the magnitude range of applicability of the model down to $\text{ M }_\mathrm{w}$ 4; extension of the distance range of applicability out to 200 km; extension to shorter and longer periods (down to 0.01 s and up to 4 s); and consistent models for both point-source (epicentral, $\text{ R }_\mathrm{epi}$ , and hypocentral distance, $\text{ R }_\mathrm{hyp}$ ) and finite-fault (distance to the surface projection of the rupture, $\text{ R }_\mathrm{JB}$ ) distance metrics. In addition, data from more than 1.5 times as many earthquakes, compared to previous pan-European models, have been used, leading to regressions based on approximately twice as many records in total. The metadata of these records have been carefully compiled and reappraised in recent European projects. These improvements lead to more robust ground-motion prediction equations than have previously been published for shallow (focal depths less than 30 km) crustal earthquakes in Europe and the Middle East. We conclude with suggestions for the application of the equations to seismic hazard assessments in Europe and the Middle East within a logic-tree framework to capture epistemic uncertainty.     

Applying essentially non‐oscillatory interpolation to controlled‐source electromagnetic modelling*

Modelling and inversion of controlled‐source electromagnetic (CSEM) fields requires accurate interpolation of modelled results near strong resistivity contrasts. There, simple linear interpolation may produce large errors, whereas higher‐order interpolation may lead to oscillatory behaviour in the interpolated result. We propose to use the essentially non‐oscillatory, piecewise polynomial interpolation scheme designed for piecewise smooth functions that contains discontinuities in the function itself or in its first or higher derivatives. The scheme uses a non‐linear adaptive algorithm to select a set of interpolation points that represent the smoothest part of the function among the sets of neighbouring points. We present numerical examples to demonstrate the usefulness of the scheme. The first example shows that the essentially non‐oscillatory interpolation (ENO) scheme better captures an isolated discontinuity. In the second example, we consider the case of sampling the electric field computed by a finite‐volume CSEM code at a receiver location. In this example, the ENO interpolation performs quite well. However, the overall error is dominated by the discretization error. The other examples consider the comparison between sampling with essentially non‐oscillatory interpolation and existing interpolation schemes. In these examples, essentially non‐oscillatory interpolation provides more accurate results than standard interpolation, especially near discontinuities.     

Evidence for244Pu fission tracks in hibonites from Murchison carbonaceous chondrite

We have developed a technique for revealing nuclear tracks in the mineral hibonite (CaAl₁₂O₁₉), found in the refractory inclusions from carbonaceous chondrites. The tracks in hibonitesfrom Murchison carbonaous chondrite are dominated by fission tracks from²⁴⁴Pu (constituting more than 90% of the total). The measured uranium contents in these crystals range from 1.2 to 62 ppb. We deduce that the average value for the²⁴⁴Pu/²³⁸U ratio in most of the Murchison hibonites at the time of track retention is0.022 ± 0.011.     

Evolution of central stars of planetary nebulae towards the crystallizing white dwarf stage

The evolution of the central stars of planetary nebulae, interpreted as hot white dwarfs with liquefying cores, towards the cold white dwarf stage is discussed and theoretical (non-computational) evolutionary tracks are built for such central stars as they cool towards the crystallizing region. The conclusions seem to hint a picture in which crystalline white dwarfs can be looked at as final stages of the central stars of planetary nebulae.