The Rondonian-San Ignacio Province in the SW Amazonian Craton: An overview

The Rondonian-San Ignacio Province (1.56-1.30 Ga) is a composite orogen created through successive accretion of arcs, ocean basin closure and final oblique microcontinent-continent collision. The effects of the collision are well preserved mostly in the Paragua Terrane (Bolivia and Mato Grosso regions) and in the Alto Guapore Belt and the Rio Negro-Juruena Province (Rondonia region), considering that the province was affected by later collision-related deformation and metamorphism during the Sunsas Orogeny (1.25-1.00 Ga). The Rondonian-San Ignacio Province comprises: (1) the Jauru Terrane (1.78-1.42 Ga) that hosts Paleoproterozoic basement (1.78-1.72 Ga), and the Cachoeirinha (1.56-1.52 Ga) and the Santa Helena (1.48-1.42 Ga) accretionary orogens, both developed in an Andean-type magmatic arc; (2) the Paragua Terrane (1.74-1.32 Ga) that hosts pre-San Ignacio units (>1640 Ma: Chiquitania Gneiss Complex, San Ignacio Schist Group and Lomas Manechis Granulitic Complex) and the Pensamiento Granitoid Complex (1.37-1.34 Ga) developed in an Andean-type magmatic arc; (3) the Rio Alegre Terrane (1.51-1.38 Ga) that includes units generated in a mid-ocean ridge and an intra-oceanic magmatic arc environments; and (4) the Alto Guapore Belt (<1.42-1.34 Ga) that hosts units developed in passive marginal basin and intra-oceanic arc settings. The collisional stage (1.34-1.32 Ga) is characterized by deformation, high-grade metamorphism, and partial melting during the metamorphic peak, which affected primarily the Chiquitania Gneiss Complex and Lomas Manechis Granulitic Complex in the Paragua Terrane, and the Colorado Complex and the Nova Mamore Metamorphic Suite in the Alto Guapore Belt. The Paragua Block is here considered as a crustal fragment probably displaced from its Rio Negro-Juruena crustal counterpart between 1.50 and 1.40 Ga. This period is characterized by extensive A-type and intra-plate granite magmatism represented by the Rio Crespo Intrusive Suite (ca. 1.50 Ga), Santo Antonio Intrusive Suite (1.40-1.36 Ga), and the Teotonio Intrusive Suite (1.38 Ga). Magmatism of these types also occur at the end of the Rondonian-San Ignacio Orogeny, and are represented by the Alto Candeias Intrusive Suite (1.34-1.36 Ga), and the Sao Lourenco-Caripunas Intrusive Suite (1.31-1.30 Ga). The cratonization of the province occurred between 1.30 and 1.25 Ga. (C) 2009 Elsevier Ltd. All rights reserved.

Relics of eclogite facies assemblages in the Ceara Central Domain, NW Borborema Province, NE Brazil: Implications for the assembly of West Gondwana

The Borborema Province, in the NE of Brazil, is a rather complex piece in the Brazil-Africa puzzle as it represents the junction of the Dahomeyide/Pharusian, Central African, Aracuai and Brasilia fold belts located between the West-African/Sao Luis, Congo/Sao Francisco and Amazonas craton. The correlation between the Dahomeyides from W-Africa (Ghana, Benin, Togo, and Mali) and the Borborema Province involves the Medio Coreau and Central Ceara domains. The inferred continuation of the main oceanic suture zone exposed in the Dahomeyides of W Africa is buried beneath the Phanerozoic Parnaiba Basin in Brazil (northwest of the Medio Coreau domain) where some high density gravity anomalies may represent hidden remnants of an oceanic suture. In addition to this major suture a narrow, nearly continuous strip composed of mainly mafic pods containing relics of eclogite-facies assemblages associated with partially migmatized granulite-facies metapelitic gneisses has been found further east in the NW Borborema Province. These high pressure mafic rocks, interpreted as retrograded eclogites, are located between the Transbrasiliano Lineament and the Santa Quiteria continental arc and comprise primitive to evolved arc-related rocks with either arc- or MORB-type imprints that can indicate either deep subduction of oceanic lithosphere or roots of continental and oceanic magmatic arcs. Average peak P-T conditions under eclogite-facies metamorphism (T=770 degrees C and P = 17.3 kbar) were estimated using garnet-clinopyroxene thermometry and Jd content in clinopyroxene. Transition to granulite-facies conditions, as well as later widespread re-equilibration under amphibolite facies, were registered both in the basic and the metapelitic rocks and suggest a clockwise P-T path characterized by an increase in temperature followed by strong decompression. A phenomenon possibly related to the exhumation of a highly thickened crust associated with the suturing of the Medio Coreau and Central Ceara domains, two distinct crustal blocks separated by the Transbrasiliano Lineament. (C) 2009 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

GEOCHEMISTRY AND U-PB ZIRCON AGE OF THE INTERNAL OSSA-MORENA ZONE OPHIOLITE SEQUENCES: A REMNANT OF RHEIC OCEAN IN SW IBERIA

The Early Paleozoic geodynamic evolution in SW Iberia is believed to have been dominated by the opening of the Rheic Ocean. The Rheic Ocean is generally accepted to have resulted from the drift of peri-Gondwanan terranes such as Avalonia from the northern margin of Gondwana during Late Cambrian-Early Ordovician times. The closure of the Rheic Ocean was the final result of a continent-continent collision between Gondwana and Laurussia that produced the Variscan orogen. The Ossa-Morena Zone is a peri-Gondwana terrane, which preserves spread fragments of ophiolites - the Internal Ossa-Morena Zones Ophiolite Sequences (IOMZOS). The final patchwork of the IOMZOS shows a complete oceanic lithospheric sequence with geochemical characteristics similar to the ocean-floor basalts, without any orogenic fingerprint and/or crustal contamination. The IOMZOS were obducted and imbricated with high pressure lithologies. Based on structural, petrological and whole-rock geochemical data, the authors argue that the IOMZOS represent fragments of the oceanic lithosphere from the Rheic Ocean. Zircon SHRIMP U-Pb geochronological data on metagabbros point to an age of ca. 480 Ma for IOMZOS, providing evidence of a well-developed ocean in SW Iberia during this period, reinforcing the interpretation of the Rheic Ocean as a wide ocean among the peri-Gondwanan terranes during Early Ordovician times.

Rhyacian (2.23-2.20 Ga) juvenile accretion in the southern Sao Francisco craton, Brazil: Geochemical and isotopic evidence from the Serrinha magmatic suite, Mineiro belt

The Serrinha magmatic suite (Mineiro belt) crops out in the southern edge of the Sao Francisco craton, comprising the Brito quartz-diorite, Brumado de Cima and Brumado de Baixo granodiorites, granophyres and felsic sub-volcanic and volcanic rocks, part of which intruded into the Nazareno greenstone belt. The suite rocks have petrographic features that are consistent with magma supercooling due to the low water content combined with volatile loss, leading to crystallization of quartz and alkaline feldspar at the rims of plagioclase phenocrysts (granophyric intergrowth). The investigated rocks are sub-alkaline, calc-alkaline and show low content in rare earth elements. The U-Pb zircon crystallization ages for the Brumado de Cima granodiorite [2227 +/- 22 (23) Ma] and a coeval granophyre [2211 +/- 22 (23) Ma], coupled with available single-zircon Pb evaporation ages for the Brito and Brumado de Baixo plutons, are significantly older than the ""Minas orogeny"" (ca. 2100-2050 Ga) of Quadrilatero Ferrifero area, eastward from the Serrinha suite. Our data establish an early Rhyacian event tectonically linked with the evolution of the Mineiro belt. The bulk Nd isotopic signature [low negative to positive epsilon(Nd(t)) values] of the Serrinha samples are consistent with the important role of Paleoproterozoic mantle components in the magma genesis. The integrated geologic, geochemical and isotopic information suggests that Paleoproterozoic evolution of the Mineiro belt initiated in a passive continental margin basin with deposition of the Minas Supergroup at ca. 2500 Ma. This stage was succeeded by outboard rupture of the oceanic lithosphere with development and coalescence of progressively younger magmatic arcs during Rhyacian time. One of the earliest arcs formed the Serrinha suite. The tectonic collage of the Serrinha and Ritapolis (2190-2120 Ma) arcs produced the NE-SW Lenheiro shear zone, resulting in mylonitization and recrystallization of both the granitoid intrusions and host rocks. As a matter of fact juxtaposition of distinct magmatic units in age and origin took place along the Lenheiros structure in this sector of the Mineiro belt. (C) 2009 Elsevier Ltd. All rights reserved.

New and improved results for packing identical unitary radius circles within triangles, rectangles and strips

The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of non-linear equations systems through the Newton-Raphson method, the herein presented algorithm succeeds in improving the accuracy of previous results attained by continuous optimization approaches up to numerical machine precision. The computer implementation and the data sets are available at http://www.ime.usp.br/similar to egbirgin/packing/. (C) 2009 Elsevier Ltd, All rights reserved.

Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C(1), ... , C(k)} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is Sigma(k)(i=1) vertical bar C(i)vertical bar. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width. (C) 2008 Elsevier B.V. All rights reserved.

Minimizing the object dimensions in circle and sphere packing problems

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Improving ultimate convergence of an augmented Lagrangian method

Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its `pure` counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://www.ime.usp.br/similar to egbirgin/tango/.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Tilt-critical algebras of tame type

Let A be a finite dimensional k-algebra over an algebraically closed field. Assume A=kQ/I where Q is a quiver without oriented cycles. We say that A is tilt-critical if it is not tilted but every proper convex subcategory of A is tilted. We describe the tilt-critical algebras which are strongly simply connected and tame.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.