Family <Emphasis Type="Italic">h</Emphasis> of periodic solutions of the restricted problem for small μ

The results of the calculation of the family h of symmetric periodic solutions of the planar restricted three-body problem for four values of μ = 0, 10^?3, 0.1, and 0.2 are presented. This family begins with retrograde circular orbits around the body of bigger mass. Associated with each value of μ are the table of critical orbits, the orbit pictures, graphs of the characteristics of the family in four coordinate systems, and graphs of the period and of traces (planar and vertical). Regularities on the family and its connection to the generating family are observed.     

Photoelectric observations of CH Cygni during the explosive phases of 1967–68

Observations made at Trieste in 1967 and 1968 of CH Cygni reveal a strong variability, particularly in U colour. From the observed colours, a suggestion is made about the existence of a hot companion which could be a subdwarf.Presented at the Trieste Colloquium on Mass Loss from Stars, September 12–16, 1968.     

Precision measurement of the Sun's gravitational field by means of the twin probe method

An accurate measurement of the gravitational field of the Sun, needed for the verification of the theories of gravitation, requires the use of a geodesic test body. To eliminate the effect of non-gravitational forces (mainly the solar radiation pressure) we propose to use two twin space probes, whose surface has identical geometrical and optical properties, but with different mass. Their differential motion leads to the determination of the motion of an ideal geodesic point. We discuss in detail the various conditions which are needed to ensure the required degree of identity and submit as a possible solution two cylindrical probes, whose sides are covered by cavities to make them absorbing, rotating at a fast rate around an axis orthogonal to the ecliptic plane. We discuss briefly also the accuracy in the determination of the parameters of the metric field of the Sun obtainable from range measurements.Work done at the European Space Research Institute, Frascati, Italy     

Sediments and pollution in the Northern Adriatic Sea: a statistical analysis

Data concerning grain-size distribution, mineralogy, geochemistry, and chlorinated hydrocarbon concentrations, obtained from 246 surface sediment samples collected in the Northern Adriatic sea (Italian area), provide the basis for a multivariate statistical analysis which evaluates the influence of riverine inputs, the differences among various depositional environments and the presence of polluted zones.Cluster analysis applied to grain size has identified nine groups of lithotypes associated with the morphology and the hydrology of the basin.In the Gulf of Venice, principal component analysis on clay minerals and carbonates has permitted recognition of two main areas located north and south of the Brenta river. More subareas correspond to other lithological types.Principal component analysis of nine metal (Hg, Cd, Cu, Pb, Cr, Zn, Fe, Ni, and Co) concentrations reveals that the studied sea area is more complex from the geochemical point of view. Three geochemical zones related to riverine inputs, different lithotypes and specific forms of contamination are identified. High pollution of both halocarbons and heavy metals is associated with fine grain size.     

Multiphase model for inclusion‐reinforced geostructures: Application to rock‐bolted tunnels and piled raft foundations

A multiphase model is proposed to describe the mechanical behaviour of geomaterials reinforced by linear inclusions. This macroscopic approach considers the reinforced soil or rock mass as the superposition of continuous media. Equations of motion and constitutive laws of the model are first derived. Its implementation in a finite element computer code is then detailed. A modified implicit algorithm for elastoplastic problems is proposed. The model and its implementation are fully validated for rock‐bolted tunnels (comparison with scale model experiments) and piled raft foundations (comparison with the classical ‘hybrid method’). The Messeturm case history is finally presented to assess the handiness of the approach for real structures. Copyright © 2001 John Wiley & Sons, Ltd.     

High-pressure,low-temperature metamorphism in Alpujarride Units of southeastern Betics (Spain)Métamorphisme de haute pression et basse température dans les unités Alpujarrides du Sud-Est de la cordillère Bétique (Espagne)

We present the first occurrences of high-pressure, low-temperature ferro-magnesiocarpholite-bearing mineral assemblages associated to quartz segregations in the Alpujarride units of southeastern Betics (Sierra de Almagro, Sierra de los Pinos and Sierra Cabrera). Thermobarometric results show that the carpholite-bearing rocks underwent the same P–T conditions in the three outcrops, i.e. 8–10 kbar, 350–400 °C. Metamorphic and structural data allow us to conclude that these rocks belong to the same Alpujarride unit. In the Sierra de Almagro, tectonic units with carpholite-bearing rocks overlie low-pressure, low-temperature Alpujarride units, then forming a stack with an inverted tectono-metamorphic sequence, as observed in the central and western part of the Alpujarride complex. The preservation of carpholite-bearing assemblages in these rocks implies that no significant temperature increase occurred during the exhumation history. To cite this article: G. Booth-Rea et al., C. R. Geoscience 334 (2002) 857–865.     

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     

Foldbelts with early salt withdrawal and diapirism: Physical model and examples from the northern Gulf of Mexico and the Flinders Ranges, Australia

A physical experiment shows that shortening applied to existing diapirs and minibasins produces anomalous structural styles that are unlike those of more typical foldbelts. Strong minibasins remain largely undeformed while weak diapirs localize contractional strain. Short diapirs form the cores to folds and thrusted folds, whereas tall diapirs are squeezed and often welded, commonly leading to the extrusion of allochthonous material. Key features of the model are observed in real examples. In the northern Gulf of Mexico passive margin, minibasins were originally separated by a polygonal pattern of deep salt ridges, with diapirs located at ridge intersections. Gravity spreading resulted in squeezed diapirs (and associated allochthonous salt) connected by variably oriented contractional, extensional, and strike-slip structures. In the Flinders Ranges convergent-margin foldbelt of South Australia, preexisting diapirs were squeezed, welded, and thrusted, with anticlines plunging away in multiple directions, so that minibasins are surrounded by highly variable structures. A different geometry is observed in La Popa Basin, Mexico, where squeezing of a linear salt wall produced a vertical weld with diapirs at the terminations, rather than the culmination. In all areas, foldbelt geometries are strongly influenced by the preestablished salt-minibasin architecture.     

The Limit Problems for the Equation of Oscillations of a Satellite

We consider the ordinary differential equation of the second order, which describes oscillations of a satellite with respect to its mass center moving along an elliptic orbit with eccentricity e. The equation has two parameters: e and μ. It is regular for 0 ≤ e < 1 and singular when e = 1. For 1 we obtain three limit problems. Their bounded solution to the first limit problem form a two-dimensional (2D) continuous invariant set with a periodic structure. Solutions to the second limit problem form 2D and 3D manifolds. The μ-depending families of odd bounded solutions are singled out. One of the families is twisted into a self-similar spiral. To obtain the limit families of the periodic solutions to the original problem match together the odd bounded solutions to the first and the second limit problem. The point of conjunction is described by the third (the basic) limit problem. The limit families are very close to prelimit ones computed in earlier studies. This revised version was published online in July 2006 with corrections to the Cover Date.