On the Structure of Symplectic Mappings. The Fast Lyapunov Indicator: a Very Sensitive Tool

It is already known (Froeschlé, Lega and Gonczi, 1997) that the Fast Lyapunov Indicator (FLI), that is the computation on a relatively short time of the largest Lyapunov indicator, allows to discriminate between ordered and weak chaotic motion. We have found that, under certain conditions, the FLI also discriminates between resonant and non-resonant orbits, not only for two-dimensional symplectic mappings but also for higher dimensional ones. Using this indicator, we present an example of the Arnold web detection for four and six-dimensional symplectic maps. We show that this method allows to detect the global transition of the system from an exponentially stable Nekhoroshevs like regime to the diffusive Chirikovs one.     

Spatio-temporal changes in the abundance of the populations of the gastrotrich community in a shallow lake of tropical Africa

Studies on the biodiversity and population dynamics of freshwater planktonic Gastrotricha have been carried out in conjunction with a physical–chemical analysis of the water in the Yaounde Municipal Lake (Cameroon, Central Africa) over a 14 months period (November 1996–December 1997). The results obtained allow to consider the Yaounde Municipal Lake as an eutrophic lake. It harbours eight species of Gastrotricha belonging to four genera (Chaetonotus, Dasydytes, Neogossea and Polymerurus) of the order Chaetonotida. This community was characterized by high abundances of populations, and was dominated by the genus Neogossea and Chaetonotusreaching up to 2000 ind. L⁻¹. Polymerurus was mostly abundant at the almost anoxic bottom layers. The highest abundances were found mostly during the rainy season, when there is an important sedimentation process of organic matter, and were influenced by several different environmental factors such as dissolved oxygen, temperature and pH of the water.

Finally this community which may play an important role in the water bodies, is a potential water quality indicator.     

What explains agricultural performance: climate normals or climate variance?

This paper measures the influence of climate normals (average long-term surface wetness and temperature) and interannual climate variance on farms in the United States and Brazil using satellite data. The paper finds that just climate normals or just climate variance variables can explain both net revenues and how much land is used for cropland. However, because they are correlated with each other, it is important to include both normals and variance in the same statistical model to get accurate measures of their individual contribution to farm outcomes. In general, higher climate variance increases the probability that land is used for cropland in both countries and higher temperatures reduce both cropland and land values. Other annual effects were not consistent across the two countries.     

Comparison of convergence towards invariant distributions for rotation angles, twist angles and local Lyapunov characteristic numbers

Using the standard map as a model problem and in the spirit of cluster analysis we have studied the invariance of the distributions of different indicators introduced to detect and measure weak chaos. We show that the problem is less straightforward than expected and that, except for very strong chaotic dynamical systems, all the complexities (islands, sticking phenomena, cantori) of mixed Hamiltonian systems are reflected into the indicators of convergence towards invariant distributions.     

Structure,diversity and stability of two oligochaete communities according to sedimentary inputs in Lake Geneva (Switzerland)

Two oligochaete communities were sampled monthly during one year in two 35 m deep locations of Lake Geneva (Switzerland). Organic sedimentation was lower and less variable in station 1 than in station 2 (157 versus 214 g C m⁻²yr⁻¹). The oligochaete community in station 1 was more diverse and more stable (persistent over time) than in station 2, as long as the organic sedimentation was low. Diversity and stability decreased in station 1 when the organic sedimentation increased, and during anOscillatoria bloom. The less diverse community in station 2 was more resistent to these changes. Diversity was associated with environmental stability, but resistance to perturbation was greater in the simpler community which is adapted to changing environmental conditions. The value of oligochaete communities as an indicator of the level of eutrophication was reassessed according to our present data. Changes in the structure of oligochaete communities were related to changes in sedimentation processes.     

Pyroxene geothermometry and geobarometry: experimental and thermodynamic evaluation of some subsolidus phase relations involving pyroxenes in the system CaO-MgO-Al2O3-SiO2

One petrogenetic grid for plagioclase-, spinel- and garnet-lherzolite analogues in the system CaO-MgO-Al₂O₃-SiO₂ is presented from 1 bar to 30 kbar and 400 to 1500°C. Another grid for olivine-gabbro, spinel-gabbro and garnet-pyroxenite analogues in the same system is presented from 1 bar to 25 kbar and 500 to 1500°C. Both grids show the distribution of the mineral assemblages and the variations in the composition of clinopyroxene with temperature and pressure. They were developed by applying simple thermodynamic mixing models of clinopyroxene to experimentally determined clino-pyroxene compositions.Calcium tschermak's pyroxene (CaAl₂SiO₆) in complex CaMgSi₂O₆-CaAl₂SiO₆-Mg₂Si₂O₆ clinopyroxenes is best represented by a local charge balance mixing model where Enthalpy and entropy changes of subsolidus reactions involving variations in the CaAl₂SiO₆ and Mg₂Si₂O₆ content of clinopyroxene are interdependent due to nonideal mixing of these two end-members. CaAl₂SiO₆ can strongly reduce the mutual solubility of clinopyroxene and orthopyroxene at moderate pressures and high temperatures. Failure to take this into account can result in temperature underestimates (up to 150°C) of spinel-lherzolites, garnet-pyroxenites, low pressure garnet-lherzolites, spinel-gabbros, and high pressure plagioclase-lherzolites and olivine-gabbros. However, at temperatures and pressures where the Al₂O₃ content of clinopyroxene is low (e.g. garnet-lherzolite nodules in kimberlite), the mutual solubility is adequantely represented by experimental results in the system CaO-MgO-SiO₂.     

87Rb-86Sr age of rocks from the Apollo 15 landing site and significance of internal isochrons

Internal isochrons for two Apollo 15 rocks give an age of(3.34 ± 0.09)and(3.46 ± 0.04) × 10⁹ years with an identical⁸⁷Sr/⁸⁶Sr initial ratio of 0.69928. Considering the possibility for the line obtained in a⁸⁷Sr/⁸⁶Sr,⁸⁷Rb/⁸⁶Sr diagram to be a mixing line, the significance of these results are discussed.     

The NdSr isotopic correlation in mantle materials and geodynamic consequences

The neodymium-strontium isotopic correlation observed in most of the Earth mantle materials is evaluated by means of direct modelling. Several geochemical models are quantitatively developed to explain the observations. The main results of this modelling are that such a correlation is not geochemically trivial and that it corresponds to specific conditions in chemical fractionation. These specific conditions seem to be satisfied by solid-liquid partitioning in magmatic conditions. The discussion of the experimental data supports a continuous convecting-magmatic fractionation model for a large proportion of the mantle.