Numerical experiments on the efficiency of second-order mixed-variable symplectic integrators for N-body problems

We discuss the efficiency of the so-called mixed-variable symplectic integrators for N-body problems. By performing numerical experiments, we first show that the evolution of the mean error in action-like variables is strongly dependent on the initial configuration of the system. Then we study the effect of changing the stepsize when dealing with problems including close encounters between a particle and a planet. Considering a previous study of the slow encounter between comet P/Oterma and Jupiter, we show that the overall orbital patterns can be reproduced, but this depends on the chosen value of the maximum integration stepsize. Moreover the Jacobi constant in a restricted three-body problem is not conserved anymore when the stepsize is changed frequently: over a 10⁵ year time span, to keep a relative error in this integral of motion of the same order as that given by a Bulirsch-Stoer integrator requires a very small integration stepsize and much more computing time. However, an integration of a sample including 10⁴ particles close to Neptune shows that the distributions of the variation of the elements over one orbital period of the particles obtained by the Bulirsch-Stoer integrator and the symplectic integrator up to a certain integration stepsize are rather similar. Therefore, mixed-variable symplectic integrators are efficient either for N-body problems which do not include close encounters or for statistical investigations on a big sample of particles.     

Planetary close encounters: Importance of nearly tangent orbits

It is shown that close encounters between Jupiter and minor bodies are generally more efficient if the initial orbit of the small body is nearly tangent to that of the planet. Starting from the analysis of the results of previous numerical simulations, some indications on the mobility of the small bodies in the semiaxis-eccentricity diagram are given.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratory di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

A comparison of approximate techniques for non-linear seismic soil response

Some equivalent linearization techniques, applicable to problems dealing with non-linear seismic amplification of layered soils, are systematically treated and critically compared in this paper. The discussion concerns, in particular, the theoretical consistency, the operative modalities, the computational complexity and the numerical reliability of these methods. A comparison is made between the results furnished by some techniques among those examined and the results obtained through a step-by-step integration of the non-linear equations of motion, assuming as a test-problem the one-dimensional amplification of a horizontally stratified soil deposit characterized by the Ramberg-Osgood constitutive model.     

Electrical conductivity structure in the lower crust

The subject is reviewed, notwithstanding the existence of a number of disagreeing and/or controversial results found in the literature. First, a brief critical reexamination of the methodology is presented. Second, it is attempted to put the results, or partial conclusions by different authors, using different methods and referring to different geographical regions, into a working scheme. This is done by investigating, as far as possible, the relationships between the electrical conductivity information and other types of geophysical and geological information for each geographical area investigated. It appears almost impossible to draw general conclusions that hold for the entire Earth. Conclusions are given for those areas with some very well-defined geomorphological characters. Unfortunately, the available investigations still appear to give a poor coverage of several types of geographic areas with specific tectonic characteristics, and certainly the scientific coverage by electromagnetic methods of investigation cannot be compared with those available today from seismological methods. Investigating the electrical conductivity structure of the lower crust certainly opens relevant heuristic possibilities, but there appears to be a great need both for a refinement in the basic methodology, and for a better coverage of the investigated areas.     

A first insight into the constitution of the upper mantle under the hoggar area (Southern Algeria): The lherzolite xenoliths in the alkali-basalts

Quaternary alkali olivine basalts and nephelinites from the Hoggar area (Southern Algeria) contain numerous lherzolite inclusions. The investigated nodules have been classified into three textural categories: coarse, porphyroclastic and granuloblastic. Microprobe analyses have been carried out on the coexisting phases (olivine, clinopyroxene, orthopyroxene, spinel, pargasite, Al rich glass) from 10 selected samples, with a special attention to pyroxene porphyroclasts which are zoned in Al and Cr. Most of the porphyroclastic xenoliths contain secondary pargasite (or its breakdown products) which is thought to reflect a metasomatic event in mantle conditions. Equilibrium temperatures and pressures have been calculated for the three groups, using the single-pyroxene method: the coarse samples have been equilibrated at higher pressures (20–25 kb) and temperatures (1,000° C–1,100° C) than the granuloblastic samples (about 10 kb and 900° C); with regards to the porphyroclastic xenoliths, the estimated T and P have been related to two stages of crystallization (corresponding to porphyroclasts and neoblasts). Relationships between phase compositions, rock-textures and metasomatism are briefly discussed.     

Image analysis and circular statistics for shape-fabric analysis: applications to lithified ignimbrites

 Computer-assisted image analysis can be successfully used to derive quantitative textural data on pyroclastic rock samples. This method provides a large number of different measurements such as grain size, particle shape and 2D orientation of particle main axes (directional- or shape-fabric) automatically and in a relatively short time. Orientation data reduction requires specific statistical tests, mainly devoted to defining the kind of particle distribution pattern, the possible occurrence of preferred particle orientation, the confidence interval of the mean direction and the degree of randomness with respect to pre-assigned theoretical frequency distributions. Data obtained from image analysis of seven lithified ignimbrite samples from the Vulsini Volcanic District (Central Italy) are used to test different statistics and to provide insight about directional fabrics. First, the possible occurrence of a significant deviation from a theoretical circular uniform distribution was evaluated by using the Rayleigh and Tukey χ ² tests. Then, the Kuiper test was performed to evaluate whether or not the observation fits with a unimodal, Von Mises-like theoretical frequency distribution. Finally, the confidence interval of mean direction was calculated. With the exception of one sample (FPD10), which showed a well-developed bimodality, all the analysed samples display significant anisotropic and unimodal distributions. The minimum number of measurements necessary to obtain reasonable variabilities of the calculated statistics and mean directions was evaluated by repeating random collections of the measured particles at increments of 100 particles for each sample. Although the observed variabilities depend largely on the pattern of distribution and an absolute minimum number cannot be stated, approximately 1500–2000 measurements are required in order to get meaningful mean directions for the analysed samples. Received: 9 April 1996 / Accepted: 26 December 1996     

Deformation of “Villafranchian” lacustrine sediments in the Chisone Valley (Western Alps, Italy)

The Chisone Valley is located in the internal NW Alps, in the Pinerolese District, an area characterized by present low to medium seismicity. Fine-grained sediments (sand, silt and clay with interbedded gravel) crop out in the lower Chisone Valley: they were first interpreted as glaciolacustrine deposits, and then as a lacustrine infilling of the valley floor probably due to differential uplifting of the valley mouth. Review of this data, together with new field and palynological observations, lead us to refer the lacustrine deposits to approximately the Lower Pleistocene (Villafranchian). In many outcrops, the lacustrine deposits show strong soft-sediment deformation such as convolute laminations, water-escape structures and disrupted beds, some of them associated with folds and faults (cm to dm in size); only two sites show metric to decametric folds and faults trending E-W and N-S. Detailed structural analysis conducted along a recently exposed section (Rio Gran Dubbione site) shows several soft-sediment deformation features on the limbs of mesoscale folds. Because of their intimate structural association, the origin of these minor structures seems to be connected to synsedimentary activity on reverse and normal faults (m to dm in size) affecting the lacustrine deposits in the same locality. Soft-sediment deformation features can be interpreted as possible paleoseismites. If so, the present seismicity of the Pinerolese District, which is the major area of such activity in NW Italy, cannot be considered an isolated episode in the geological evolution of the region; even if there is no supporting evidence for continuous seismicity, the deformations in the lacustrine sediments of the Chisone Valley testify to Early Pleistocene seismic activity, probably related to the recent tectonic evolution of the internal side of the NW Alps.     

Silicate-silicate liquid immiscibility and graphite ribbons in Libyan desert glass

Transmission electron microscopic (TEM) investigation of the dark (brown or bluish) streaks occurring in Libyan Desert Glass reveals the common presence of small glass spherules. The spherules, mostly 100 nm in size, are homogeneously dispersed within the silica-glass matrix. The complete absence of electron diffraction effects confirms their amorphous nature. The spherules are Al-, Fe- and Mg-enriched with respect to the surrounding silica matrix and their (Mg + Al + Fe) : Si ratio is close to 1.The silica-glass matrix and amorphous spherules form an emulsion texture (i.e., globules of one glass in a matrix of another glass), which originates from silicate-silicate liquid immiscibility. This texture has also been observed in other impact-derived glasses.The silica glass also contains carbonaceous inclusions consisting of 5-50 nm thick, polygonalized graphite ribbons that form closed structures up to 200 nm in diameter.These observations are in agreement with an impact origin for Libyan Desert Glass.     

Plankton-Derived Resting Stages in Marine Coastal Sediments along the Salento Peninsula (Apulia, South-Eastern Italy)

Abstract. An oceanographic survey was carried out along the Salento Peninsula in March 2000. Resting stages of plankton were searched for in coastal sediments to study the microplankton composition in addition to the classical analysis of active stages in the water column. A total of 215 taxa were recognised, 149 as active stages in the water column and 74 as resting stages in the sediments. Cysts were widely distributed and at Brindisi and Alimini their abundance was higher than elsewhere. A general trend was observed with resting stage abundance, species richness and diversity in the sediments: all three decreased with distance from the coast. The integrated water/sediments approach used in this study allowed us to collect 37 species (mainly as resting stages) new for the studied area.     

Approach to the geostrategy of the oceans: The case of the mediterranean

It is known that by the general ‘geostrategy’ for the oceans we mean the behaviour of countries of the world in defending their own vital economic interests as projected on different oceans. The means for protecting national interests can be economic, political, diplomatic or military. This paper dwells in particular on these last aspects, offering in the first part some useful reflections on the analysis of regional seas. The second part gives elements for the understanding of the complex Mediterranean situation where the East-West confrontation is accentuated by widespread economic, political, ideological and ethnic contrasts between coastal states. For these reasons this sea can be defined as one of the most unstable and belligerent regions in the world.