Generalized Lyapunov exponents indicators in Hamiltonian dynamics: An application to a double star system

The Lyapunov characteristic numbers (LCNs) which are defined as the mean value of the distribution of the local variations of the tangent vectors to the flow (=ln _k ⁱ ) (see Froeschlé, 1984) have been found to be sensitive indicators of stochasticity. So we computed the distribution of these local variations and determined the moments of higher order for the integrable and stochastic regions in a binary star system with =0.5.     

Influence of shallow infiltration on time-lapse ERT: Experience of advanced interpretation

Previous time-lapse Electrical Resistivity Tomography (ERT) studies have experienced difficulties in reconstructing reliable calculated resistivity changes in the subsurface. Increases or decreases of resistivity appear in the calculated ERT image where no changes were noted in the subsurface, leading to erroneous hydrological interpretations of the geophysical results. In this article, we investigate how a variation of actual resistivity with time and at shallow depth can influence time-lapse ERT results and produce resistivity artefacts at depth. We use 1 and 2-D numerical modelling to simulate infiltration scenarios. Using a standard time-lapse inversion, we demonstrate the resistivity artefact production according to the electrode spacing parameter. We used an advanced inversion methodology with a decoupling line at shallow depth to attenuate or remove resistivity artefacts. We also applied this methodology to a field data set obtained in a semi-arid environment in Burkina Faso, West Africa. Here, time-lapse ERT shows several resistivity artefacts of calculated resistivity if a standard inversion is used. We demonstrate the importance of a dense sampling of shallow resistivity variations at shallow depth. Advanced interpretation allows us to significantly attenuate or remove the resistivity artefact production at intermediate depth and produce reliable interpretation of hydrological processes.     

Origin of magmatic sulfides in a Proterozoic island arc—an example from the Portneuf–Mauricie Domain,Grenville Province,Canada

The Portneuf–Mauricie Domain (PMD), located in the south-central part of the Grenville province, contains Mesoproterozoic Ni–Cu ± platinum-group element (PGE) prospects hosted in a variety of plutonic intrusions (layered, with simple structures, or zoned) and emplaced in a mature island arc setting. A two-stage model is envisaged to explain the formation of magmatic sulfides. An early loss of a small amount of sulfides in the conduits of primitive, hydrous mantle-derived melts under high fO₂, resulted in depletion of the magmas in chalcophile and precious metals (Cu/Pd ratios vary from initial mantle values up to 1.6 × 10⁶). Then, nearer the mineralized zones, the magmas interacted with sulfide-bearing country rocks, resulting in felsification of the magmas, assimilation of crustal sulfur (δ ³⁴S values up to +5.5‰), and the formation of an immiscible sulfide liquid. Liquid-sulfide formation was followed by variable interactions between the silicate and sulfide magmas, which were responsible for the enrichment of sulfides in Ni, Cu, and, locally, PGE. Indeed, low R factors are found for prospects hosted in intrusions with a simple internal structure and in layered intrusions whereas high R factors are found for prospects hosted in zoned intrusions. Finally, sulfide melt may have been partly incorporated into later pulses of magma and injected into shallow magma chambers to form the PMD prospects. The PMD prospects share common characteristics with other well-known deposits (Aguablanca, Vammala, Stormyrplunen, and deposits in Alaskan/Ural-type intrusions), attesting to the Ni, Cu, and PGE potential of deposits associated with subduction-zone settings.     

Confirmation of beach accretion by grain-size trend analysis: Camposoto beach, Cádiz, SW Spain

An application of the grain size trend analysis (GSTA) is used in an exploratory approach to characterize sediment transport on Camposoto beach (Cádiz, SW Spain). In May 2009 the mesotidal beach showed a well-developed swash bar on the upper foreshore, which was associated with fair-weather conditions prevailing just before and during the field survey. The results were tested by means of an autocorrelation statistical test (index I of Moran). Two sedimentological trends were recognized, i.e. development towards finer, better sorted and more negatively skewed sediment (FB–), and towards finer, better sorted and less negatively or more positively skewed sediment (FB+). Both vector fields were compared with results obtained from more classical approaches (sand tracers, microtopography and current measurements). This revealed that both trends can be considered as realistic, the FB+ trend being identified for the first time in a beach environment. The data demonstrate that, on the well-developed swash bar, sediment transported onshore becomes both finer and better sorted towards the coast. On the lower foreshore, which exhibits a steeper slope produced by breaking waves, the higher-energy processes winnow out finer particles and thereby produce negatively skewed grain-size distributions. The upper foreshore, which has a flatter and smoother slope, is controlled by lower-energy swash-backwash and overwash processes. As a result, the skewness of the grain-size distributions evolves towards less negative or more positive values. The skewness parameter appears to be distributed as a function of the beach slope and, thus, reflects variations in hydrodynamic energy. This has novel implications for coastal management.

Stability of interplay motions

A family of rectilinear periodic solutions of the three-body problem, in which the central body collides alternately with each of the two other bodies, is investigated numerically for all values of the three masses. It is found that for every mass combination there exists just one solution of this kind. The linear stability of the orbits with respect to arbitrary three-dimensional perturbations is also investigated. Domains of stability and instability are displayed in a triangular mass diagram. Their boundaries form one-parameter families of critical orbits, which are tabulated. Limiting cases where one or two masses vanish are studied in detail. The domains of stability cover nearly one half of the total area in the mass diagram: this reinforces the conclusion that real triple stars might have motions of a kind entirely different from the usual hierarchical arrangement.     

A plea for better astrophysical and astrometric data in case of double stars of peculiar interest

Summary TheIAU Symposium No. 61 (Perth, 1973, “New Problems in Astrometry’) makes clear that radiosources will play an important role for astrometry in view of the linkage of reference systems. The purposes developed later were to link the various systems from the earth and the solar system to the most inertial possible one. Extragalactic radiosources are the most reliable objects but they are faint. So, intermediate objects are needed. Among them the radiostars, optical objects having radioemission at a certain level and for given frequencies have a fundamental and key position. Most of such radiostars are double or multiple ‘binaries’ as it can be seen from the list of reference stars issued by the Working Group of Commission 24, Working Group created in 1978. The last issue of the core list of radiostars was presented by Ch. de Vegt (Chairman of the WG) on the occasion of the last General Assembly of the IAU (November 1985). A recent study of the system α Scorpii (Antares) has shown that the data concerning the magnitude and the spectral type are not accurate enough, according to the accuracy obtained for the astrometric position (±0 _. ^s 003 for an astrolabe campaign in right ascension). There is also a need for better knowledge about the orbits. In the case of the astrolabe observations, if the distance between the components in <3″ the astrometric position concerns the photocenter and accurate physical properties are needed for comparison with the radio position. Better astrophysical properties are strongly needed for all radiostars to be used as references, during the time the astrometrists have to improve the accuracy of their measurements both in optical and radio fields. Presented by S. Débarbat.     

Recent variations in the general circulation as related to glacier retreat in northern Scandinavia

Summary A review is given of the investigations on variations in the general circulation in middle latitudes made byWillett andPetterssen. According toWillett a «high-index» type of circulation pattern with a strong zonal flow has probably caused the recent climatic improvement in the northern latitudes while the «low-index» type with meridional flow would create a cooling off in the same areas. According toPetterssen an other type of «low-index» pattern with a weak zonal flow and strong meridional exchange of air has been the essential cause of the warming up of the northern latitudes in Europe. This implies that the definition of the «low-index» type is not clear and gives rise to misunderstanding. Making use of our experience on glacier retreat in northern Scandinavia it is concluded that thePetterssen type of circulation more probably than the «high-index» type has caused the warming-up in the North Atlantic area from which the retreat of the glaciers has followed.     

Secular resonances: New results

We integrated numerically, in the frame of the four body problem Sun-Jupiter-Saturn-asteroid the orbit of the asteroid 1974 MA, an Earth-crosser, which is located in a region where three resonances overlap: the two secular resonances ₅ and ₁₆ and the mean motion resonance 5/1. The numerical integration yields a qualitative orbital evolution of this particular region.     

Simple formulas for the dynamic stiffness of pile groups

Simple formulas are derived for the dynamic stiffness of pile group foundations subjected to horizontal and rocking dynamic loads. The formulations are based on the construction of a general model of impedance matrices as the condensation of matrices of mass, damping, and stiffness, and on the identification of the values of these matrices on an extensive database of numerical experiments computed using coupled finite element–boundary element models. The formulations obtained can be readily used for the design of both floating piles on homogeneous half‐space and end‐bearing piles and are applicable for a wide range of mechanical and geometrical parameters of the soil and piles, in particular for large pile groups. For the seismic design of a building, the use of the simple formulas rather than a full computational model is shown to induce little error on the evaluation of the response spectra and time histories. Copyright © 2009 John Wiley & Sons, Ltd.     

Funding low-carbon investments in the absence of a carbon tax

Introducing a carbon tax is difficult, partly because it suggests that current generations have to make sacrifices for the benefit of future generations. However, the climate change externality could be corrected without such a sacrifice. It is possible to set a carbon value, and use it to create ‘carbon certificates’ that can be accepted as part of commercial banks’ legal reserves. These certificates can be distributed to low-carbon projects, and be exchanged by investors against concessional loans, reducing capital costs for low-carbon projects. As the issuance of carbon certificates would increase the quantity of money, it will either lead to accelerated inflation or induce the Central Bank to raise interest rates. Low-carbon projects will thus have access to cheaper loans at the expense of either ‘regular’ investors (in case of higher interest rates) or of lenders and depositors (in case of accelerated inflation). Within this scheme, mitigation expenditures are compensated by a reduction in regular investments, so that immediate consumption is maintained. It uses future generation wealth to pay for a hedge against climate change. This framework is not as efficient as a carbon tax but is politically easier to implement and represents an interesting step in the trajectory towards a low-carbon economy.