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.     

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.     

A molal-based model for strong acid chemistry at low temperatures (<200 to 298 K)

Geochemical processes occurring in cold environments on Earth, Mars, and Europa have elicited considerable interest in the application of geochemical models to subzero temperatures. Few existing geochemical models explicitly include acid chemistry and those that do are largely restricted to temperatures ≥0°C or rely on the mole-fraction scale rather than the more common molal scale. This paper describes (1) use of the Clegg mole-fraction acid models to develop a molal-based model for hydrochloric, nitric, and sulfuric acids at low temperatures; (2) incorporation of acid chemistry and nitrate minerals into the FREZCHEM model; (3) validation and limitations of the derived acid model; and (4) simulation of hypothetical acidic brines for Europa.The Clegg mole-fraction acid models were used to estimate activities of water and mean ionic activity coefficients that serve as the database for estimating molal Pitzer-equation parameters for HCl (188 to 298 K), HNO₃ (228 to 298 K), and H₂SO₄ (208 to 298 K). Model eutectics for HNO₃ and H₂SO₄ agree with experimental measurements to within ± 0.2°C. In agreement with previous work, the experimental freezing point depression (fpd) data for pure HCl at subzero temperatures were judged to be flawed and unreliable. Three alternatives are discussed for handling HCl chemistry at subzero temperatures. In addition to defining the solubility of solid-phase acids, this work also adds three new nitrate minerals and six new acid salts to the FREZCHEM model and refines equilibria among water ice, liquid water, and water vapor over the temperature range from 180 to 298 K. The final system is parameterized for Na-K-Mg-Ca-H-Cl-SO₄-NO₃-OH-HCO₃-CO₃-CO₂-H₂O.Simulations of hypothetical MgSO₄-H₂SO₄-H₂O and Na₂SO₄-MgSO₄-H₂SO₄-H₂O brines for Europa demonstrate how freezing can convert a predominantly salt solution into a predominantly acid solution at subzero temperatures. This result has consequences for the effects of salinity, acidity, and temperature as limiting factors for potential life on Europa. Strong acidity would limit life-forms to highly acidophilic organisms.     

The BEAM-project: prediction and assessment of mixture toxicities in the aquatic environment

Freshwater and marine ecosystems are exposed to various multi-component mixtures of pollutants. Nevertheless, most ecotoxicological research and chemicals regulation focus on hazard and exposure assessment of individual substances only, the problem of chemical mixtures in the environment is ignored to a large extent. In contrast, the assessment of combination effects has a long tradition in pharmacology, where mixtures of chemicals are specifically designed to develop new products, e.g. human and veterinary drugs or agricultural and non-agricultural pesticides. In this area, two concepts are frequently used and are thought to describe fundamental relationships between single substance and mixture effects: Independent Action (Response Addition) and Concentration Addition. The question, to what extent these concepts may also be applied in an ecotoxicological and regulatory context may be considered a research topic of major importance, as the concepts would allow to make use of already existing single substance toxicity data for the predictive assessment of mixture toxicities. Two critical knowledge gaps are identified: (a) There is a lack of environmental realism, as a huge part of our current knowledge about the applicability of the concepts is restricted to artificial situations with respect to mixture composition or biological effect assessment. (b) The knowledge on what exactly is needed for using the concepts as tools for the predictive mixture toxicity assessment is insufficient. Both gaps seriously hamper the necessary, scientifically sound consideration of mixture toxicities in a regulatory context.In this paper, the two concepts will be briefly introduced, the necessity of considering the toxicities of chemical mixtures in the environment will be demonstrated and the applicability of Independent Action and Concentration Addition as tools for the prediction and assessment of mixture toxicities will be discussed. An overview of the specific aims and approaches of the BEAM project to fill in the identified knowledge gaps is given and first results are outlined.     

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.     

Effects of pressure on aqueous chemical equilibria at subzero temperatures with applications to Europa

Pressure plays a critical role in controlling aqueous geochemical processes in deep oceans and deep ice. The putative ocean of Europa could have pressures of 1200 bars or higher on the seafloor, a pressure not dissimilar to the deepest ocean basin on Earth (the Mariana Trench at 1100 bars of pressure). At such high pressures, chemical thermodynamic relations need to explicitly consider pressure. A number of papers have addressed the role of pressure on equilibrium constants, activity coefficients, and the activity of water. None of these models deal, however, with processes at subzero temperatures, which may be important in cold environments on Earth and other planetary bodies. The objectives of this work were to (1) incorporate a pressure dependence into an existing geochemical model parameterized for subzero temperatures (FREZCHEM), (2) validate the model, and (3) simulate pressure-dependent processes on Europa. As part of objective 1, we examined two models for quantifying the volumetric properties of liquid water at subzero temperatures: one model is based on the measured properties of supercooled water, and the other model is based on the properties of liquid water in equilibrium with ice.The relative effect of pressure on solution properties falls in the order: equilibrium constants(K) > activity coefficients (γ) > activity of water (a_w). The errors (%) in our model associated with these properties, however, fall in the order: γ > K > a_w. The transposition between K and γ is due to a more accurate model for estimating K than for estimating γ. Only activity coefficients are likely to be significantly in error. However, even in this case, the errors are likely to be only in the range of 2 to 5% up to 1000 bars of pressure. Evidence based on the pressure/temperature melting of ice and salt solution densities argue in favor of the equilibrium water model, which depends on extrapolations, for characterizing the properties of liquid water in electrolyte solutions at subzero temperatures, rather than the supercooled water model. Model-derived estimates of mixed salt solution densities and chemical equilibria as a function of pressure are in reasonably good agreement with experimental measurements.To demonstrate the usefulness of this low-temperature, high-pressure model, we examined two hypothetical cases for Europa. Case 1 dealt with the ice cover of Europa, where we asked the question: How far above the putative ocean in the ice layer could we expect to find thermodynamically stable brine pockets that could serve as habitats for life? For a hypothetical nonconvecting 20 km icy shell, this potential life zone only extends 2.8 km into the icy shell before the eutectic is reached. For the case of a nonconvecting icy shell, the cold surface of Europa precludes stable aqueous phases (habitats for life) anywhere near the surface. Case 2 compared chemical equilibria at 1 bar (based on previous work) with a more realistic 1460 bars of pressure at the base of a 100 km Europan ocean. A pressure of 1460 bars, compared to 1 bar, caused a 12 K decrease in the temperature at which ice first formed and a 11 K increase in the temperature at which MgSO₄·12H₂O first formed. Remarkably, there was only a 1.2 K decrease in the eutectic temperatures between 1 and 1460 bars of pressure. Chemical systems and their response to pressure depend, ultimately, on the volumetric properties of individual constituents, which makes every system response highly individualistic.