Fold, transcritical and pitchfork singularities for time-reversible systems

This paper deals with a class of singularly perturbed reversible planar vector fields around the origin where the normal hyperbolicity assumption is not assumed. We exhibit conditions for the existence of infinitely many periodic orbits and hetero-clinic cycles converging to singular orbits with respect to the Hausdorf distance. In addition, generic normal forms of such singularities are presented.

The thrust and the relation factor kr in linear induction machines

This paper shows a new manner to establish the thrust of a linear induction machine. A new factor is established, named ''Relation Factor, which provides conditions to establish the thrust and other important variables of the linear and sector induction machines.

The Serido Group of NE Brazil, a late Neoproterozoic pre- to syn-collisional basin in West Gondwana: insights from SHRIMP U-Pb detrital zircon ages and Sm-Nd crustal residence (T-DM) ages

The Serido Group is a deformed and metamorphosed metasedimentary sequence that overlies early Paleoproterozoic to Archean basement of the Rio Grande do Norte domain in the Borborema Province of NE Brazil. The age of the Serido Group has been disputed over the past two decades, with preferred sedimentation ages being either Paleoproterozoic or Neoproterozoic. Most samples of the Serido Formation, the upper part of the Serido Group, have Sm-Nd T-DM ages between 1200 and 1600 Ma. Most samples of the Jucurutu Formation, the lower part of the Serido Group, have T-DM ages ranging from 1500 to 1600 Ma; some basal units have T-DM ages as old as 2600 Ma, reflecting proximal basement. Thus, based on Sm-Nd data, most, if not all, of the Serido Group was deposited after 1600 Ma and upper parts must be younger than 1200 Ma.Cathodoluminescence photos of detrital zircons show very small to no overgrowths produced during ca. 600 Ma Brasiliano deformation and metamorphism, so that SHRIMP and isotope dilution U-Pb ages must represent crystallization ages of the detrital zircons. Zircons from meta-arkose near the base of the Jucurutu Formation yield two groups of ages: ca. 2200 Ma and ca. 1800 Ma. In contrast, zircons from a metasedimentary gneiss higher in the Jucurutu Formation yield much younger ages, with clusters at ca. 1000 Ma and ca. 650 Ma. Zircons from metasedimentary and metatuffaceous units in the Serido Formation also yield ages primarily between 1000 and 650 Ma, with clusters at 950-1000, 800, 750, and 650 Ma. Thus, most, if not all, of the Serido Group must be younger than 650 Ma. Because these units were deformed and metamorphosed in the ca. 600 Ma Brasiliano fold belt during assembly of West Gondwana, deposition probably occurred ca. 610-650 Ma, soon after crystallization of the youngest population of zircons and before or during the onset of Brasiliano deformation.The Serido Group was deposited upon Paleoproterozoic basement in a basin receiving detritus from a variety of sources. The Jucurutu Formation includes some basal volcanic rocks and initially received detritus from proximal 2.2-2.0 Ga (Transamazonian) to late Paleoproterozoic (1.8-1.7 Ga) basement. Provenance for the upper Jucurutu Formation and all of the Serido Formation was dominated by more distal and younger sources ranging in age from 1000 to 650 Ma. We suggest that the Serido basin may have developed as the result of late Neoproterozoic extension of a pre-existing continental basement, with formation of small marine basins that were largely floored by cratonic basement (subjacent oceanic crust has not yet been found). Immature sediment was initially derived from surrounding land; as the basin evolved much of the detritus probably came from highlands to the south (present coordinates). Alternatively, if the Patos shear zone is a major terrane boundary, the basin may have formed as an early collisional foredeep associated with south-dipping subduction. In any case, within 30 million years the region was compressed, deformed, and metamorphosed during final assembly of West Gondwana and formation of the Brasiliano-Pan African fold belts. (C) 2003 Elsevier B.V. All rights reserved.

Vertical displacement during late-collisional escape tectonics (Brasiliano Orogeny) in the Ribeira Belt, São Paulo State, Brazil

During the Brasiliano-Pan-African Orogeny, West Gondwana formed by collisional processes around the Sao Francisco-Congo Craton. The Ribeira belt, in southeastern Brazil, resulted from northwestward collision (650-600 Ma), followed by large-scale northeast-southwest dextral strike-slip shear movements related to late-collisional escape tectonics (ca 600 Ma).In São Paulo State, three groups, also interpreted as terranes, are recognised in the Ribeira Belt, the Embu, Itapira and Sao Rogue Groups. The Embu and Itapira Groups are formed of sillimanite-gneisses, schists and migmatites intruded by Neoproterozoic calc-alkaline granitoids, all thrusted northwestward. The Sao Rogue Group is composed of metasediments and metavolcanics in greenschist-facies. Its deformation indicates a transpressional regime associated with tectonic escape. Sub-alkaline granites were emplaced in shallow levels during this regime. Microstructural studies along the Itu, Moreiras and Taxaquara Shear Zones demonstrate the coexistence of horizontal and Vertical displacement components during the transpressional regime. The vertical component is regarded as responsible for the lateral juxtaposition of different crustal levels. (C) 1999 Elsevier B.V. Limited. All rights reserved.

The Aster Project: Flight to a Near-Earth Asteroid

The information on the project being developed in Brazil for a flight to binary or triple near-Earth asteroid is presented. The project plans to launch a spacecraft into an orbit around the asteroid and to study the asteroid and its satellite within six months. Main attention is concentrated on the analysis of trajectories of flight to asteroids with both impulsive and low thrust in the period 2013-2020. For comparison, the characteristics of flights to the (45) Eugenia triple asteroid of the Main Belt are also given.

Controlling the Eccentricity of Polar Lunar Orbits with Low-Thrust Propulsion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Atlantic granulite belt, Brazil.

The low- to medium-P Atlantic granulite belt was largely formed at 2700 m.y., but 3100 m.y. ages have been obtained from the granulite belt and adjacent craton. -J.A.H.

U Pb and Sm Nd geochronologic studies of the eastern Borborema Province, Northeastern Brazil: initial conclusions

The Borborema Province of NE Brasil comprises the central part of a wide Pan-African-Brasiliano orogenetic belt that formed as a consequence of late Neoproterozoic convergence and collision of the São Luis-West Africa craton and the São Francisco-Congo-Kasai cratons. New Sm Nd and U Pb results from the eastern part of this province help to define the basic internal architecture and pre-collisional history of this province, with particular emphasis on delineating older cratonic terranes, their fragmentation during the Mesoproterozoic, and their assembly into West Gondwana during the Pan African-Brasiliano orogeny at ca. 600 Ma. The region can be divided into three major geotectonic domains: a) Rio Piranhas-Caldas Brandão massif, with overlying Paleoproterozoic to Neoproterozoic supracrustal rocks, north of the Patos Lineament; b) the Archean to Paleoproterozoic São Francisco craton (SFC) to the south; and c) a complex domain of Paleoproterozoic to Archean basement blocks with several intervening Mesoproterozoic to Neoproterozoic fold belts in the center (south of Patos Lineament and north of SFC). The northern and central domains comprise the Borborema Province. Archean basement gneiss and Transamazonian granulite of northern SFC are exposed in the southern part of the central domain, underlying southern parts of the Sergipano fold belt. Basement in the Rio Piranhas massif appears to consist mostly of Transamazonian (2.1 to 2.2 Ga) gneissic rocks; Nd model ages (TDM) of ca. 2.6 Ga for 2.15 Ga gneisses indicate a substantial Archean component in the protoliths to these gneisses. The Caldas Brandão massif to the east yields both Transamazonian and Archean U Pb zircon and Nd (TDM) ages, indicating a complex architecture. Metasedimentary rocks of the Jucurutu Formation yield detrital zircons with original crystallization ages as young as 1.8 Ga, indicating that these rocks may be late Paleoproterozoic and correlate with other ca. 1.8 Ga cratonic supracrustal rocks in Brazil such as the Roraima Group and Espinhaço Group. Most metavolcanic and pre-Brasiliano granitic units of the Sergipano (SDS), Pajeú-Paraíba (SPP), Riacho Pontal (SRP), and Piancó-Alto Brígida (SPAB) fold belts in the central domain formed ~ 1.0 ± 0.1 Ga, based on U Pb ages of zircons. Nd model ages (TDM) for these same rocks, as well as Brasiliano granites intruded into them and large parts of the Pernambuco-Alagoas massif, are commonly 1.3-1.7 Ga, indicating that rocks of the fold belts were not wholly derived from either older (> 2.1 Ga) or juvenile (ca. 1.0 Ga) crust, but include mixtures of both components. A simple interpretation of Brasiliano granite genesis and the Nd data implies that there is no Transamazonian or Archean basement underlying large parts of these fold belts or of the Pernambuco-Alagoas massif. An exception is a belt of syenitic Brasiliano plutons (Syenitoid Line) and host gneisses between SPAB and SPP that clearly has a Transamazonian (or older) source. In addition, there are several smaller blocks of Archean to Transamazonian gneiss that can be defined within and among these fold belts. These blocks do not appear to constitute a continuous basement complex, but appear to be isolated older crustal fragments. Our data support a model in which ca. 1.0 Ga rifting was an important tectonic and crust-forming event along the northern edge of the São Francisco craton. Our data also show that significant parts of the Borborema Province are not remobilized Transamazonian to Archean crust, but that Mesoproterozoic crust is a major feature of the Province. There are several small remnants of older crust within the area dominated by Mesoproterozoic crust, suggesting that the rifting event created several small continental fragments that were later incorporated into the Brasiliano collisional orogen. We cannot at present determine if the Rio Piranhas-Caldas Brandão massifs and the older crustal blocks of the central domain were originally part of the São Francisco craton or whether some (or all) of them came from more exotic parts of the Proterozoic Earth. Finally, our data have not yet revealed any juvenile terranes of either Transamazonian or Brasiliano age. © 1995.

Tectonic setting and U/Pb zircon dating of the plutonic Socorro Complex in the Transpressive Rio Paraíba do Sul Shear Belt, SE Brazil

The Precambrian Rio Paraíba do Sul Shear Belt comprises a 200-km-wide anastomosing network of NE-SW trending ductile shear zones extending over 1000 km of the southeastern coast of Brazil. Granulitic, gneissic-migmatitic, and granitoid terrains as well as low- to medium-grade metavolcanosedimentary sequences are included within it. These rocks were affected by strong contractional, tangential tectonics, due to west-northwestward oblique convergence of continental blocks. Subsequent transpressional tectonics accomodated large dextral, orogen-parallel movements and shortening. The plutonic Socorro Complex is one of many deformed granites with a foliation subparallel to that of the shear belt and exposes crosscutting relationships between its tectonic, magmatic, and metamorphic structures. These relationships point to a continuous magmatic evolution related to regional thrusts and strike slip, ductile shear zones. The tectonic and magmatic structural features of the Serra do Lopo Granite provide a model of emplacement by sheeting along shear zones during coeval strike-slip and cross shortening of country rocks. Geochronological data indicate that the main igneous activity of Socorro Complex spanned at least 55 million years, from the late stage of the northwestward ductile thrusting (650 Ma), through right-lateral strike slip (595 Ma) deformation. The country rocks yield discordant age data, which reflect a strong imprint of the Transamazonian tectono-metamorphic event (1.9 to 2.0 Ma). We propose a model for the origin of calcalkaline granites of the Ribeira Belt by partial melting of the lower crust with small contributions of the lithospheric mantle during transpressional thickening of plate margins, which were bounded by deep shear zones. The transpressional regime also seems to have focused granite migration from deeper into higher crustal levels along these shear zones.

Northwestern overthrusting and related lateral escape during the Brasiliano orogeny north of the Patos lineament, Borborema province, northeast Brazil

The Borborema province (BP) of northeastern Brazil, located between the São Luís and São Francisco cratons, represents a branching system of Precambrian orogens of the South American platform. It is composed of segments of Archean and Proterozoic crust that were deformed by the convergence of the West African and São Francisco-Congo cratons during assembly of the Brasiliano collage (650 to 500 Ma), a period of intense orogenic activity considered to be the strongest and most pervasive tectonic event that affected the Precambrian of the South American platform. The tectonic and kinematic history of the Brasiliano/Panafrican orogeny is fundamental for reconstructing South American and African Precambrian geology. The correlation between Neoproterozoic tectonic processes occurring in both continents should use structural elements, of regional or local character, with identical kinematic and metamorphic conditions manifested in both basement and supracrustal units. North of the Patos shear zone, subhorizontal Brasiliano thrusts (0.65 to 0.58 Ga) affected the basement and the supracrustal Seridó belt with such related regional D1/D2 structures as foliation, lineation, isoclinal folds, and related metamorphism. Overprinting the previous structures, regional folding with a vertical S3 foliation and an associated strike-slip shear zone were developed (0.58 to 0.52 Ga). The metamorphism is similar for all deformation phases, ranging from upper-greenschist to amphibolite facies with mineral assemblages including biolite and garnet throughout the Seridó fold belt. We propose, on the basis of deformational and kinematic reconstructions, that the structural evolution of the Seridó fold belt was characterized by transition from a syn-collisional to a strike-slip regime. The transition between regimes occurred, progressively or instantaneously, by the switching of the maximum and intermediary strain axes of the strain ellipsoid. The entire tectonic history can be related to a frontal or oblique collision and lateral escape tectonics, with local, syn-collisional transpression and transtension. The Patos shear zone represents a final vertical shearing, juxtaposing different terranes of the northern and southern Borborema province.

Bayesian and multivariate methods applied to favorability quantification in recôncavo Basin and Ribeira Belt, Brazil

A methodology to define favorable areas in petroleum and mineral exploration is applied, which consists in weighting the exploratory variables, in order to characterize their importance as exploration guides. The exploration data are spatially integrated in the selected area to establish the association between variables and deposits, and the relationships among distribution, topology, and indicator pattern of all variables. Two methods of statistical analysis were compared. The first one is the Weights of Evidence Modeling, a conditional probability approach (Agterberg, 1989a), and the second one is the Principal Components Analysis (Pan, 1993). In the conditional method, the favorability estimation is based on the probability of deposit and variable joint occurrence, with the weights being defined as natural logarithms of likelihood ratios. In the multivariate analysis, the cells which contain deposits are selected as control cells and the weights are determined by eigendecomposition, being represented by the coefficients of the eigenvector related to the system's largest eigenvalue. The two techniques of weighting and complementary procedures were tested on two case studies: 1. Recôncavo Basin, Northeast Brazil (for Petroleum) and 2. Itaiacoca Formation of Ribeira Belt, Southeast Brazil (for Pb-Zn Mississippi Valley Type deposits). The applied methodology proved to be easy to use and of great assistance to predict the favorability in large areas, particularly in the initial phase of exploration programs. © 1998 International Association for Mathematical Geology.

Transpressional tectonics and strain partitioning during oblique collision between three plates in the Precambrian of southeast Brazil

This paper is part of the special publication Continental transpressional and transtensional tectonics (eds R.E. Holdsworth, R.A. Strachan and J.F. Dewey). Two orogenic belts have been recognized in south- east Brazil, which are interpreted to have been formed as a product of diachronous collisions between three continental plates. Wide crustal-scale shear belts have developed both between and inboard of the collided and amalgamated plate borders. These shear belts record frontal, oblique or lateral displacements during oblique plate convergence and A-type subduction. The overall structural style of each belt depends on the angle subtended between the plate boundary and the convergence vector. The E-W branch between the Sao Paulo and Brasilia plates the Campo do Meio strike-slip shear belt, has undergone dominantly sinistral wrench dominated transpression along a set of folds and shear zones dipping southwards. The NE-SW branch between the Sao Paulo and Vitoria plates, the Paraiba do Sul strike-slip shear belt, has undergone a partitioned dextral transpression, whereas the north-south branch between the Brasilia and Vitoria plates is essentially a frontal thrust system with only a weak component of dextral strike-slip. These complex structural patterns, formed at deep to mid-crustal levels, reflect temporal and spatial partitioning at all scales between flattening and non- coaxial deformation, and down-dip and strike-slip shearing, in tangential as well as in transcurrent structural domains. Additionally, this area demonstrates that regional flower structures, lateral extrusion and other secondary deformations across the yz sections of transpressional belts are important in accommodating shortening in obliquely convergent orogens.

Isotopic characterization of the metabasites and amphibolites of the Acungui and Setuva Groups of the Ribeira Belt

Pb, Rb, Sr, Sm and Nd isotope analyses were carried out on amphibolitic rocks from Campo Largo (PR), Rio Branco do Sul (PR) and Adrianópolis (PR) and for the metabasite from Adrianópolis and Apiai (SP), all belonging to the Açungui and Setuva Groups, southern portion of the Ribeira Belt. These occurrences were chosen because each exhibits geochemical data indicative of a mantle source, having different signatures. Geochronologic determinations are available only for the Apiai metagabbro with Neoproterozoic ages of 617 ± 4 Ma (U/Pb in zircon) and 839 ± 85 Ma (Rb/Sr, whole rock). Age determinations by Sm/Nd mineral isochron using whole rock, plagioclase and pyroxene yield values of 885 ± 53 Ma for the Apiai metagabbro and 820 ± 84 Ma for the Adrianópolis metabasite. These results agree within error with the Rb/Sr isochron of 839 ± 85 Ma may possibly be interpreted as the time of extraction of the magma from the mantle, as suggested by positive εNd(850) values (+2,76) from an Adrianópolis sample. An εNd values versus 87Sr/86Sr diagram shows that each studied occurrence plots in a different position, following approximately the mantle array trend, the most primitive being the metabasite of Adrian-acopolis, near the MORB field, and the most enriched being the amphibolite from the same region, near the enriched mantle and or crustal contamination field. The distinct difference in isotopic signatures between the amphibolite and metabasite suggests derivation from different mantle sources, as supported by available geochemical data. Nevertheless, some of the samples show isotopic evidence of the action of metamorphism, crustal contamination and weathering.