Synchronization of perturbed non-linear Hamiltonians

We propose a new method based on Lie transformations for simplifying perturbed Hamiltonians in one degree of freedom. The method is most useful when the unperturbed part has solutions in non-elementary functions. A non-canonical Lie transformation is used to eliminate terms from the perturbation that are not of the same form as those in the main part. The system is thus transformed into a modified version of the principal part. In conjunction with a time transformation, the procedure synchronizes the motions of the perturbed system onto those of the unperturbed part.A specific algorithm is given for systems whose principal part consists of a kinetic energy plus an arbitrary potential which is polynomial in the coordinate; the perturbation applied to the principal part is a polynomial in the coordinate and possibly the momentum.We demonstrate the strategy by applying it in detail to a perturbed Duffing system. Our procedure allow us to avoid treating the system as a perturbed harmonic oscillator. In contrast to a canonical simplification, our method involves only polynomial manipulations in two variables. Only after the change of time do we start manipulating elliptic functions in an exhaustive discussion of the flows.     

Metallicity measurements using atomic lines in M and K dwarf stars

We report the first survey of chemical abundances in M and K dwarf stars using atomic absorption lines in high-resolution spectra. We have measured Fe and Ti abundances in 35 M and K dwarf stars using equivalent widths measured from  λ/Δλ≈ 33 000  spectra. Our analysis takes advantage of recent improvements in model atmospheres of low-temperature dwarf stars. The stars have temperatures between 3300 and 4700 K, with most cooler than 4100 K. They cover an iron abundance range of  −2.44 < [Fe/H] < +0.16  . Our measurements show [Ti/Fe] decreasing with increasing [Fe/H], a trend similar to that measured for warmer stars, where abundance analysis techniques have been tested more thoroughly. This study is a step towards the observational calibration of procedures to estimate the metallicity of low-mass dwarf stars using photometric and low-resolution spectral indices.     

Analysis of coupled Sr/Ca and Sr/Sr variations in enamel using laser-ablation tandem quadrupole-multicollector ICPMS

We present in this study results obtained with a laser-ablation coupled with both a quadrupole and a multi-collector ICPMS. The simultaneous in situ Sr/Ca and ⁸⁷Sr/⁸⁶Sr measurements along growth profiles in enamel allows the concomitant diet and migration patterns in mammals to be reconstructed. Aliquots of the powdered international standard NIST “SRM1400 Bone Ash” with certified Sr and Ca contents, was sintered at high pressure and temperature and was adopted as the reference material for external reproducibility and calibration of the results. A total of 145 coupled elemental and isotopic measurements of herbivores enamel from the Kruger National Park, South Africa, gives intra-tooth Sr/Ca and ⁸⁷Sr/⁸⁶Sr variations that are well larger than external reproducibility. Sr/Ca profiles systematically decrease from the dentine-enamel junction to the outer enamel whereas ⁸⁷Sr/⁸⁶Sr profiles exhibit variable patterns. Using a simple geometric model of hypsodont teeth growth, we demonstrate that a continuous recording of the ⁸⁷Sr/⁸⁶Sr variations can be reconstructed in the tooth length axis. This suggests that the mobility of a mammal can be reconstructed over a period of more than a year with a resolution of a ten of days, by sampling enamel along growth profiles. Our geometric model of hypsodont teeth growth predicts that an optimal distance between two successive profiles is equal to the enamel thickness. However, this model does not apply to the Sr/Ca signal which is likely to be altered during the enamel maturation stage due to differential maturation processes along enamel thickness. Here, the observed constant decreases of the Sr/Ca ratios in the ungulates of Kruger National Park suggests that they did not changed of diet, while some of them were migrating.     

Chlorine isotopic composition in seafloor serpentinites and high-pressure metaperidotites. Insights into oceanic serpentinization and subduction processes

Bulk-rock chlorine content and isotopic composition (δ³⁷Cl) were determined in oceanic serpentinites, high-pressure metaperidotites and metasediments in order to gain constraints on the global chlorine cycle associated with hydrothermal alteration and subduction of oceanic lithosphere. The distribution of insoluble chlorine in oceanic serpentinites was also investigated by electron microprobe. The hydrothermally-altered ultramafic samples were dredged along the South West Indian Ridge and the Mid-Atlantic Ridge. The high-pressure metamorphic samples were collected in the Western Alps: metaperidotites in the Erro-Tobbio unit and metasediments in the Schistes Lustrés nappe.Oceanic serpentinites show relatively large variations of bulk-rock Cl contents and δ³⁷Cl values with mean values of 1105 ± 596 ppm and −0.7 ± 0.4‰, respectively (n = 8; 1σ). Serpentines formed after olivine (meshes) show lower Cl content than those formed after orthopyroxene (bastites). In bastites of two different samples, Cl is positively correlated with Al₂O₃ and negatively correlated with SiO₂. These relationships are interpreted as reflecting preferential Cl-incorporation into the bastite structure distorted by Al (substituted for Si) rather than different alteration conditions between olivine and orthopyroxene minerals. High-pressure metaperidotites display relatively homogeneous Cl contents and δ³⁷Cl values with mean values of 467 ± 88 ppm and −1.4 ± 0.1‰, respectively (n = 7; 1σ). A macroscopic high-pressure olivine-bearing vein, formed from partial devolatilization of serpentinites at ∼2.5 GPa and 500-600 °C, shows a Cl content and a δ³⁷Cl value of 603 ppm and −1.6‰, respectively. Metasediments (n = 2) show low whole-rock Cl contents (<15 ppm Cl) that did not allow Cl isotope analyses to be obtained.The range of negative δ³⁷Cl values observed in oceanic serpentinites is likely to result from water-rock interaction with fluids that have negative δ³⁷Cl values. The homogeneity of δ³⁷Cl values from the high-pressure olivine-bearing vein and the metaperidotite samples implies that progressive loss of Cl inherited from oceanic alteration throughout subduction did not significantly fractionate Cl isotopes. Chlorine recycled in subduction zones via metaperidotites should thus show a range of δ³⁷Cl values similar to the range found in oceanic serpentinized peridotites.     

Mediterranean flash flood transfer through karstic area

Karstic aquifers influence flash floods propagation in Mediterranean countries. Near Montpellier, Southern France, discharge data are recorded on the Coulazou River upstream and downstream of the Aumelas Causse. Two gauging stations are used to describe the hydrodynamics of this binary karstic system. The first station characterizes the non-karstic catchment area. The second one is representative of the karstic part of the watershed. Records since April 2004 are used to understand how the river interacts with a karstic aquifer. Hydrograph analysis of three flash flood events is described. Corresponding discharge time series recorded at the two gauging stations are used to describe the modification of the hydrographs by auto- and crosscorrelations analyses. Finally, linear system analyses are used to provide the transfer functions of this binary karstic system according to the three flood events characteristics (initial conditions, volume, spatial distribution of rainfall, etc.). Theses functions summarize the hydrodynamic behaviour of the system: their shapes are indicative of the dynamics of the storage, the release and the contribution to surface waters.

Turbulence,billows and gravity waves in a high shear region of the upper atmosphere

Measurements on a downleg trail of lithium in morning twilight show definite turbulent features and also a wave structure at 107 km which could be generated by the intense wind shear.     

Emplacement of a Debris Avalanche during the 1883 eruption of Krakatau (Sunda Straits,Indonesia)

Conclusion The data collected during the Mentawai cruise help to clarify understanding of the 1883 eruption of Krakatau. We have previously discussed the weaknesses of the interpretation of Williams (1941) and others (Self and Rampino 1981) and emphasized that only a Mount St. Helens-type collapse during the course of the eruption could account for all the characteristics of the eruption and of the related deposits.The discovery on land of deposits attributable to a debris-avalanche, in the stratigraphic position where they were expected, is a strong argument for the validity of our scenario.Marine surveys confirm that the sea bottom around Krakatau is covered by a thick ignimbritic deposit. But the presence of this deposit does not invalidate the presence of a debris-avalanche deposit under the ignimbrites. The hummocky morphology favours this hypothesis.Flank-failure of volcanoes is generally considered as a very efficient mechanism for triggering tsunamis (Kienle et al. 1987; Siebert et al. 1987). However, the majority of the volcanoes where flank-failure has been described are tall and bulky and the collapse of a broad edifice like Krakatau may be surprising. However the geological evidence shows that such a mechanism can act at various scales; for example the flank collapse of Mayu Yama volcano (height 700 m, volume 0,3 km³), a parasitic cone of Unzen volcano (Japan), triggered a debris-avalanche into the sea that was 1 km long, with a characteristic hummocky surface; the resulting tsunami killed 9528 people (Katayama 1974). In the same way, a partial collapse of Iliwerung volcano, Indonesia (50 × 10⁶ m³) in July 1979, triggered a tsunami which killed several hundred people (McClelland et al. 1989). At Krakatau, the main summit was 822 m asl; the collapse took place along the edge of the prehistoric caldera and this structural unconformity probably facilitated the triggering of the process.     

Dating in the Craven Dales

The Craven Dales of North Yorkshire contain some of the finest examples of limestone geology and landscape in the UK. The extensive limestone pavements with their clints, grikes and other water‐worn features, are a key attraction for both scientists and recreational visitors. Likewise the cave systems attract attention with their remarkable sediment accumulations, some of which are in excess of 500 000 years old and others contain the bones of mammals that are either extinct or no longer present in the British Isles. The glacial erratic boulders at Norber and the loessic sediments that, in places, mask the limestone have also provided stimulus for investigation. Summarized below are the findings of several recent studies that focussed on establishing the age of various features. Whilst the reports answer some long‐standing questions, they also demonstrate that there is still much that can be learned about this seemingly familiar territory.