Families of double symmetric “Schubart-like” periodic orbits

We consider a class of Hamiltonian systems with two degrees of freedom with singularities. This class includes several symmetric subproblems of the $n$ -body problem where the singularities are due to collisions involving two or more bodies. “Schubart-like” periodic orbits having two collisions in one period, are present in most of these subproblems. The purpose of this paper is to study the existence of families of such a periodic orbits in a general setting. The blow up techniques of total collision and infinity are applied to our class of Hamiltonian system. This allows us to derive sufficient conditions to ensure the existence of families of double symmetric “Schubart-like” periodic orbits having many singularities. The orbits in the family can be parametrized by the number of singularities in one period. The results are applied to some subproblems of the gravitational $n$ -body problem.     

GGR Biennial Review: Reference Materials in Geoanalytical and Environmental Research – Review for 2008 and 2009

This review gives an overview of the literature on reference materials of geochemical and environmental interest for the two-year period 2008–2009. Reference materials play an increasingly important role in all fields of geoanalytical research. This is demonstrated by the large number of publications containing data on reference materials. Although many reference materials exist, there is still a great need for certified samples, so-called delta zero materials for stable isotopic work and homogeneous microanalytical reference materials. This review focuses on six topics: developments of certification processes of reference materials mainly postulated in ISO guidelines and the IAG protocol, new developments of the GeoReM database, investigations of powdered rock reference materials, Chinese reference materials published in Chinese journals, microanalytical reference materials and isotopic reference materials.     

Vertical deformation partitioning across a collapsing large and hot orogen

Featuring 3 000-km-long large and hot orogen, the Mantiqueira Province provides a rare opportunity to study the process of gravitational collapse at mid to deep crustal levels. Distinct but contemporary (~500 Ma) post-collisional intrusions show structures and anisotropy of magnetic susceptibility (AMS) fabrics related to their emplacements, recording different flow patterns. In southern deep-seated intrusions, ellipsoidal-shaped roots with gabbroic-to-hybrid cores surrounded by granitic rocks show concentric patterns of AMS fabrics that cut across the NE-trending regional foliation. In contrast, northern intrusions, exposed as the upper sections of batholith-size bodies of coarse-grained granite emplaced at the shallow to mid-crust, show general NS-trending magnetic fabrics roughly parallel to strike of the orogen and the regional foliation of host rocks. These contrasting magnetic patterns from shallow to deeper crust suggest vertical magma migration from the overthickened orogenic core to be emplaced across its thinner stretched flanks during the gravitational collapse of the orogenic edifice.