Experiences numeriques sur des billards C1 formes de quatre arcs de cercles

The paper deals with some properties of the dynamical system with two degrees of freedom defined by the motion of a particle in a certain type of billiard. These properties are studied by means of numerical experiments. Most results are represented in the now classical surface of section. One parameter families of billiards with a C¹ boundary constructed with four arcs of circles are defined; we use the property that the four meeting points of such billiards lie on the same circle. These billiards may be convex or non convex. They generalize the ‘oval’ billiard with two axes of symmetry studied by Benettin and Strelcyn. We call them generalized billiards. We find the following results:

1. The periodic orbit along the small diameter of a billiard is stable or unstable in the linear approximation according to the position of the center of each relevant are with respect to the opposite one. This orbit is always stable if the billiard is symmetric with respect to its large diameter.
2. When the center of an arc lies on the opposite arc two different transition patterns from order to chaos are observed for the same billiard. If the billiard is of the Benettin and Strelcyn type three distinct nested chaotic seas are seen two of which are separated by a pseudo-invariant curve generated by a so called cancellation orbit.
3. The total area of non chaotic regions is greater for symmetric billiards.
4. Peanut shaped billiards always look ergodic. It can happen also that strictly convex asymmetric billiards look ergodic. This is important since no strictly convex billiard is known for which ergodicity has been proven. The conjecture is proposed that a generalized billiard with neither 2-periodic nor 4-periodic stable orbit in the linear approximation is ergodic.
5. Transverse invariant curves such as the one found by Hénon and Wisdom seem common for billiards with two axes of symmetry but probably do not exist for asymmetric billiards.

There are therefore several properties which differentiate symmetric billiards from asymmetric ones. We conclude by emphasizing that C¹ generalized billiards are indeed inadequate models for smooth mappings in general.     

Th sorption and export models in the water column: A review

Over the past few decades, the radioisotope pair of ²³⁸U / ²³⁴Th has been widely and increasingly used to describe particle dynamics and particle export fluxes in a variety of aquatic systems. The present paper is one of five review articles dedicated to ²³⁴Th. It is focused on the models associated with ²³⁴Th whereas the companion papers (same issue) are focused on present and future methodologies and techniques (Rutgers van der Loeff et al.), C / ²³⁴Th ratios (Buesseler et al.), ²³⁴Th speciation (Santschi et al.) and present and future applications of ²³⁴Th [Waples, J.T., Benitez-Nelson, C.R., Savoye, N., Rutgers van der Loeff, M., Baskaran, M., Gustafsson, Ö., this issue. An Introduction to the application and future use of ²³⁴Th in aquatic systems. Marine Chemistry, FATE special issue]. In this paper, we review current ²³⁴Th scavenging models and discuss the relative importance of the non-steady state and physical terms associated with the most commonly used model to estimate ²³⁴Th flux. Based on this discussion we recommend that for future work the use of models should be accompanied by a discussion of the effect that model and data uncertainty have on the model results. We also suggest that future field work incorporate repeat occupations of sample sites on time scales of 1–4 weeks in order to evaluate steady state versus non-steady state estimates of ²³⁴Th export, especially during high flux events (> ca. 800 dpm m^− 2 d^− 1). Finally, knowledge of the physical oceanography of the study area is essential, particularly in ocean margins and in areas of established upwelling (e.g., Equatorial Pacific). These suggestions will greatly enhance the application of ²³⁴Th as a tracer of particle dynamics and flux in more complicated regimes.     

Structure and physics of solar faculae

Taking into account the effect of roughness (or local departures from sphericity) of the emitting layers in the chromosphere-corona transition zone (CCT) allows one to determine the optical depths of layers responsible for resolved structures in Cii, Ciii, Oiv, and Ovi lines. The result, at the top of the irregularities, is of the order of respectively ₁ 3.5,2.0, 1.6,0.5, and for the bottom of these irregularities, ₂ = 0.7, 0.4, 0.3, 0.25. The characteristic angle of these irregularities is, respectively, of the order of 35 °, 33 °, 35 °, and 41 °. For unresolved structures of Civ and Ovi (already analyzed in the spherical symmetry hypothesis in Paper III), one finds ₁ 0.6; 0.9 and ₂ 0.12; 0.2 in the case of quiet areas; in the case of active areas, the range is broader for Civ and Ovi, from 1.0 to 1.7 for ₁ and from 0.2 to 0.9 for ₂. The values obtained from Ovi are in reasonable agreement with each other for resolved and unresolved structures. And the obtained values of ₁ and ₂ correspond not too badly with the determinations made in Paper III, by methods not exceedingly influenced by the spherical symmetry hypothesis.     

Alkaline fluid circulation in ultramafic rocks and formation of nucleotide constituents: a hypothesis

Seawater is constantly circulating through oceanic basement as a low-temperature hydrothermal fluid (<150°C). In cases when ultramafic rocks are exposed to the fluids, for instance during the initial phase of subduction, ferromagnesian minerals are altered in contact with the water, leading to high pH and formation of secondary magnesium hydroxide, among other – brucite, that may scavenge borate and phosphate from seawater. The high pH may promote abiotic formation of pentoses, particularly ribose. Pentoses are stabilized by borate, since cyclic pentoses form a less reactive complex with borate. Analyses have shown that borate occupies the 2' and 3' positions of ribose, thus leaving the 5' position available for reactions like phosphorylation. The purine coding elements (adenine, in particular) of RNA may be formed in the same general hydrothermal environments of the seafloor.     

Fan beheading and drainage diversion as evidence of a 3200-2800 BP earthquake event in the Esmeraldas-Tumaco seismic zone: A case study for the effects of great subduction earthquakes

The San Lorenzo area belongs to the Esmeraldas–Tumaco seismic zone where some of the strongest earthquakes of South America occurred during the 20th century. This paper provides evidence for a succession of geomorphic changes characterized by the disruption of the Quaternary drainage network and the reshaping of the Cayapas–Santiago estuary. The rise of the La Boca uplift bordered by the La Boca and San Lorenzo faults is responsible for the southward diversion of the Palabi, Tululbi, Bogotá and Carolina rivers toward the Santiago and Cayapas rivers. The increase of the discharge directed to the Cayapas River generated the change of the channel pattern downstream from the confluence, and the avulsion of a new estuary through the coastal plain. According to the dating of beach ridges the avulsion occurred in the period 3200–2800 BP. This period corresponds also to a faster accretion of the beach ridge margin, interpreted as a response to a small uplift of the shore. The coherency of the three morphologic evidences—diversion of drainage network, avulsion and increase of coastal accretion—suggest a unique morphotectonic event, in relation with the activity of the Esmaraldas–Tumaco seismic zone. The opening of a direct communication through the mangrove margin may have brought favorable conditions for the development of the La Tolita archaeological site after 3000 BP.     

Re-Os Isotopic Measurements at the Femtomole Level in Natural Samples

Here we describe a new chemical separation method for Os and an improved mass spectrometric procedure for Re and Os. This technique is based on the selective extraction of OsO₄ from aqueous solution in liquid bromine. Among other advantages, this procedure avoids the cumbersome distillation procedure for Os and uses only commercial "off the shelf" PFA teflon labware. Blank levels for 0.5 g sample sizes are: 0.06 pg and 0.5 pg for Os and Re respectively. Samples containing as little as 1 pg g⁻¹ Os can be analysed reliably with this method. Adaptation to other dissolution methods is also discussed.     

Morphological and microtectonic analysis of Quaternary deformation from Puná and Santa Clara Islands, Gulf of Guayaquil, Ecuador (South America)

This paper presents the neotectonic study of Santa Clara and Puná Islands sited in the Gulf of Guayaquil eastern part. Both islands are located on the south-western segment of the fault zone bounding to the east the North Andean Block. Fault motion and morphostructural analysis were carried out from Pleistocene age terrain. A two step deformation characterises the South Puná tectonics. The first step involves the Zambapala Cordillera uplift that post-dates Pleistocene sediments and pre-dates a marine terrace correlated with the M.I.S. 11 or 13 (440–550 ka). The second step is the formation of a pull-apart that shows evidence of 2.9 km dextral offset since the M.I.S. 11 or 13, giving an offset mean rate of 5.3 to 6.6 mm/yr. This rate is higher than the one calculated on the Pallatanga Fault northeast of the study area, in the Western Andean Cordillera, suggesting that deformation is split in different fault segments from the Gulf of Guayaquil to the continent. The Zambapala Cordillera uplift and transpression deformation requires a compressive event that may have been induced by the subduction process during the early Pleistocene.     

Nouvelles données pour l’histoire des fluctuations holocènes du niveau du lac de Neuchatel (Suisse): la séquence sédimentaire de Marin-Les Piécettes

Resume. Les fouilles archéologiques réalisées de 1998 à 2002 sur le site néolithique de Marin-Les Piécettes sur la rive nord-ouest du lac de Neuchatel ont offert l’opportunité d’observer deux séquences sédimentaires intéressantes pour la reconstitution des variations holocènes du niveau du lac, en particulier au cours de la période correspondant au changement de cours de l’Aar en direction du nord-est, vers 5650–5500 cal BP. La géométrie des corps sédimentaires et les changements lithologiques permettent de reconna?tre plusieurs phases majeures de bas niveaux relatifs du plan d’eau vers 6870, 5660, 5060–3990, 3580, 2280, 1640 et 1170 cal BP. Le site néolithique de Marin-Les Piécettes s’est développé vers 5454–5433 cal BP à la faveur d’un court épisode de bas niveau du lac qui a interrompu une importante phase de haut niveau au début du Subboréal. Les événements paléohydrologiques identifiés à Marin-Les Piécettes apparaissent cohérents avec ceux reconstitués sur le site de Montilier au bord du lac de Morat, ainsi qu’avec les variations paléohydrologiques reconstituées à partir des lacs du Jura, du Plateau suisse et des Préalpes du Nord fran?aises. Ceci suggère qu’ils témoignent d’un signal climatique. La séquence sédimentaire de Marin-Les Piécettes met enfin en évidence la formation d’un cordon littoral sur la rive nord-ouest du lac juste après 5660 cal BP. Manuscrit re?u le 22 septembre 2004 Révision acceptée le 11 mars 2005     

Hydrogen isotopic composition of water from fossil micrometeorites in howardites

We have measured the hydrogen isotopic composition (D/H ratios) of the water from 13 carbonaceous chondritic microclasts (CCMs, size <1 mm) trapped in two howardites (Kapoeta and Yamato-793497) early in the evolution of Solar System. The division into tochilinite-rich; magnetite-rich, olivine-poor; magnetite-rich, olivine-rich CCM types is corroborated by the hydrogen isotopic compositions. Both mineralogy and hydrogen isotopic compositions demonstrate that tochilinite-rich CCMs represent CM2 chondritic matter. In contrast, there is no good match between the isotopic and mineralogical properties of the magnetite-rich CCMs and the known groups of carbonaceous chondrites, suggesting that magnetite-rich CCMs represent a new kind of chondritic matter, not yet sampled in meteorite collections. This demonstrates that the view of the asteroid belt revealed by the collection of meteorites is incomplete. The study of (micro)clasts offers a unique opportunity to better decipher the nature and relative abundance of asteroids.The average hydrogen isotopic composition of water belonging to CCMs, D/H = (152.0 ± 4.8) × 10⁻⁶ (1σ_m), is similar to that of Antarctic micrometeorites (AMMs), D/H = (161.2 ± 3.8) × 10⁻⁶ (1σ_m). The similarity, in terms of mineralogy and hydrogen isotopic composition, between CCMs and AMMs demonstrates that the composition of the micrometeorites has not been modified over the whole history of the Solar System. It indicates that the composition of the micrometeorite flux onto Earth has been, and is, dominated by a mixture of CM2-like; magnetite-rich, olivine-poor; magnetite-rich, olivine-rich carbonaceous chondritic matter exemplified by CCMs found in howardites. Because CCMs have not suffered atmospheric entry, they provide an abundant source of pristine micrometeorites.The average D/H ratio of the whole population of CCMs is identical within errors to that of the Earth (149 ± 3 × 10⁻⁶). The match between the CCMs D/H ratio and that of the Earth is especially remarkable because 1) three different populations of CCMs are needed to make the D/H ratio of the Earth; 2) there is no single carbonaceous chondrite group for which a similar match exists. This observation suggests that CCMs population might be representative of the late veneer agent(s) that delivered water to the Earth.