The point‐estimate method with large numbers of variables

Rosenbleuth's point‐estimate method has become widely used in geotechnical practice for reliability calculations. Although the point‐estimate method is a powerful and simple method for evaluating the moments of functions of random variables, it is limited by the need to make 2ⁿ evaluations when there are n random variables. Modifications of the method reduce this to 2n evaluations by using points on the diameters of a hypersphere instead of at the corners of the inscribed hypercube. However, these techniques force the co‐ordinates of the evaluation points farther from the means of the variables; for a bounded variable, the points may easily fall outside the domain of definition of the variable. The problem can be avoided by using other techniques for some special cases or by reducing the number of random variables that must be considered. Copyright © 2002 John Wiley & Sons, Ltd.     

Australasian microtektites and associated impact ejecta in the South China Sea and the Middle Pleistocene supereruption of Toba

Abstract— Australasian microtektites were discovered in Ocean Drilling Program (ODP) Hole 1143A in the central part of the South China Sea. Unmelted ejecta were found associated with the microtektites at this site and with Australasian microtektites in Core SO95–17957–2 and ODP Hole 1144A from the central and northern part of the South China Sea, respectively. A few opaque, irregular, rounded, partly melted particles containing highly fractured mineral inclusions (generally quartz and some K feldspar) and some partially melted mineral grains, in a glassy matrix were also found in the microtektite layer. The unmelted ejecta at all three sites include abundant white, opaque grains consisting of mixtures of quartz, coesite, and stishovite, and abundant rock fragments which also contain coesite and, rarely, stishovite. This is the first time that shock‐metamorphosed rock fragments have been found in the Australasian microtektite layer. The rock fragments have major and trace element contents similar to the Australasian microtektites and tektites, except for higher volatile element contents. Assuming that the Australasian tektites and microtektites were formed from the same target material as the rock fragments, the parent material for the Australasian tektites and microtektites appears to have been a fine‐grained sedimentary deposit. Hole 1144A has the highest abundance of microtektites (number/cm²) of any known Australasian microtektite‐bearing site and may be closer to the source crater than any previously identified Australasian microtektite‐bearing site. A source crater in the vicinity of 22° N and 104° E seems to explain geographic variations in abundance of both the microtektites and the unmelted ejecta the best; however, a region extending NW into southern China and SE into the Gulf of Tonkin explains the geographic variation in abundance of microtektites and unmelted ejecta almost as well. The size of the source crater is estimated to be 43 ± 9 km based on estimated thickness of the ejecta layer at each site and distance from the proposed source. A volcanic ash layer occurs just above the Australasian microtektite layer, which some authors suggest is from a supereruption of the Toba caldera complex. We estimate that deposition of the ash occurred ?800 ka ago and that it is spread over an area of at least 3.7 times 10⁷ km².     

Triple close approach in the three-body problem: A limit for the bounded orbits

Using the results of Sundman and Birkhoff as also the studies on the generalized Hill's curves, we develop a new method for computing a lower bound of the moment of inertia for the bounded orbits in the general three-body problem.Thus we obtain much higher values than in the classical results. We show for instance, that when the integral of the energy goes to zero, this lower bound goes to the minimum moment of inertia of the corresponding parabolic Euler motion of the same angular momentum: it is then the greatest lower bound.

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Résumé En utilisant les résultats de Sundman et de Birkhoff ainsi que les études sur les courbes de Hill généralisées, on développe une nouvelle méthode pour calculer un minorant du moment d'inertie pour les orbites bornées dans le problème des trois corps.On obtient ainsi des valeurs beaucoup plus élevées que dans les résultats classiques. On montre en particulier que lorsque I'intégrale de I'énergie tend vers zéro ce minorant tend vers le minimum du moment d'inertie du mouvement parabolique d'Euler correspondant de même moment cinétique: c'est alors la limite inférieure.

     

The Demeter microsatellite and ground segment

The Demeter program is the first application of the Myriade microsatellite program conducted by the Cnes (French Space Agency) since 1997. The Myriade objective was to benefit from the miniaturization of the technologies to develop a product with a reduced size, weight and cost able to implement either scientific missions, demonstrators or operational applications in different areas: earth observation, astronomy, fundamental physics or telecommunications, within limited financial budget.The Demeter satellite was launched in end of June 2004, from Baikonour, aboard a Dnepr launcher, on a sun synchronous orbit at 710 km altitude. Its main scientific objectives are the detection and characterization of ionosphere electrical and magnetic disturbances in connection with a seismic activity.The scientific payload has been built by French scientific institutes (LPCE, CESR, CETP) involved in external and internal geophysics and by SSD/ESTEC (ESA). It is composed of several electrical and magnetic sensors, an ion spectrometer, an energetic particle analyzer and a Langmuir probe.The Demeter platform is designed in order to offer a high level of performances in terms of power, attitude and orbit control, data storage and transmission, flexibility. For example the large amount of scientific data is transmitted to the ground station with a high data rate telemetry link in X band.This paper describes the Demeter satellite and ground segment. It focuses on the specific design adaptations of the Myriade product for Demeter and it presents the preliminary in orbit platform performances.     

Discovery of an asteroid and quasi‐satellite in an Earth‐like horseshoe orbit

Abstract— The newly discovered asteroid 2002 AA₂₉ moves in a very Earth‐like orbit that relative to Earth has a unique horseshoe shape and allows transitions to a quasi‐satellite state. This is the first body known to be in a simple heliocentric horseshoe orbit, moving along its parent planet's orbit. It is similarly also the first true co‐orbital object of Earth, since other asteroids in 1:1 resonance with Earth have orbits very dissimilar from that of our planet. When a quasi‐satellite, it remains within 0.2 AU of the Earth for several decades. 2002 AA₂₉ is the first asteroid known to exhibit this behavior. 2002 AA₂₉ introduces an important new class of objects offering potential targets for space missions and clues to asteroid orbit transfer evolution.