Chemistry of Biotites and Whole Rocks from the Rapakivi Itu Complex (Late Precambrian), State of São Paulo, SE Brazil

Chemical analyses for biotites and their host rocks from the Cabreúva (three facies) and Salto (five facies) intrusions from the multiple-centered rapakivi Itu Complex, State of São Paulo, Brazil, are presented and compared. The Cabreúva intrusion comprises different kinds of mainly even-grained biotite and hornblende-bearing syenogranites, monzogranites and quartz syenites and the Salto intrusion several types of mainly porphyritic biotite syenogranites, some of them hornblende-bearing. The biotites from the Salto intrusion (S-micas) show a more restricted composition than those from the Cabreúva intrusion (C-micas). This reflects the chemical variability of the two bodies which is smaller in the Salto intrusion and larger in the Cabreúva pluton. In the AlIV x Fet/(Fet+Mg) diagram the S- and C-micas show similar AlIV contents, around 2.2-2.3, but C-micas have higher Fet/(Fet+Mg) ratios (0.7-0.9) compared to those of S-micas (0.5-0.6). In the Mg:(Al+Fe+3+Ti):(Fe+2+Mn) diagram the S-micas are defined as Fe+2-biotites and the C-micas occupy the area between the Fe+2-biotites and the siderophyllite/lepidomelane fields, slightly overlapping the latter. In the Al2O3 × FeOt, MgO × FeOt, Al2O3 x MgO and Alt x Mg diagrams, the S-micas always lie on the calc-alkaline/alkaline boundary (or in the subalkaline field) whereas the C-micas systematically plot in the alkaline field, reflecting the higher alkalis content of the Cabreúva intrusion. In the Fet/(Fet+Mg) x SiO2 diagram, the S-micas lie on a smooth line whereas the C-micas from the different facies are separated by distinct chemical gaps reflecting the major or minor chemical overlapping of the facies from the Salto and Cabreúva intrusions.

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.

Testing the Cambrian explosion hypothesis by using a molecular dating technique

Molecular studies have the potential to shed light on the origin of the animal phyla by providing independent estimates of the divergence times, but have been criticized for failing to account adequately for variation in rate of evolution. A method of dating divergence times from molecular data addresses the criticisms of earlier studies and provides more realistic, but wider, confidence intervals. The data are not compatible with the Cambrian explosion hypothesis as an explanation for the origin of metazoan phyla, and provide additional support for an extended period of Precambrian metazoan diversification.

Solution to Darwin's dilemma: Discovery of the missing Precambrian record of life

In 1859, in On the Origin of Species, Darwin broached what he regarded to be the most vexing problem facing his theory of evolution—the lack of a rich fossil record predating the rise of shelly invertebrates that marks the beginning of the Cambrian Period of geologic time (≈550 million years ago), an “inexplicable” absence that could be “truly urged as a valid argument” against his all embracing synthesis. For more than 100 years, the “missing Precambrian history of life” stood out as one of the greatest unsolved mysteries in natural science. But in recent decades, understanding of life's history has changed markedly as the documented fossil record has been extended seven-fold to some 3,500 million years ago, an age more than three-quarters that of the planet itself. This long-sought solution to Darwin's dilemma was set in motion by a small vanguard of workers who blazed the trail in the 1950s and 1960s, just as their course was charted by a few pioneering pathfinders of the previous century, a history of bold pronouncements, dashed dreams, search, and final discovery.

An Eulerian Immersed Boundary Method for flow simulations over stationary and moving rigid bodies

The fluid flow over bodies with complex geometry has been the subject of research of many scientists and widely explored experimentally and numerically. The present study proposes an Eulerian Immersed Boundary Method for flows simulations over stationary or moving rigid bodies. The proposed method allows the use of Cartesians Meshes. Here, two-dimensional simulations of fluid flow over stationary and oscillating circular cylinders were used for verification and validation. Four different cases were explored: the flow over a stationary cylinder, the flow over a cylinder oscillating in the flow direction, the flow over a cylinder oscillating in the normal flow direction, and a cylinder with angular oscillation. The time integration was carried out by a classical 4th order Runge-Kutta scheme, with a time step of the same order of distance between two consecutive points in x direction. High-order compact finite difference schemes were used to calculate spatial derivatives. The drag and lift coefficients, the lock-in phenomenon and vorticity contour plots were used for the verification and validation of the proposed method. The extension of the current method allowing the study of a body with different geometry and three-dimensional simulations is straightforward. The results obtained show a good agreement with both numerical and experimental results, encouraging the use of the proposed method.

Alluvial-eolian interaction in a Cambrian rift margin: the Pedra das Torrinhas and Pedra Pintada formations (Guaritas Group, RS)

This work presents a study of selected outcrops from the Pedra das Torrinhas Formation of the Guaritas Group (Cambrian, Camaquã Basin), near the basin bordering Encantadas Fault Zone. The studied succession includes alluvial fan deposits that pass laterally into eolian deposits. Sedimentary facies and architectural element analysis were performed, followed by sedimentary petrography and microscopic porosity analysis, aiming to characterize the porosity of the deposits and its spatial distribution. The main objective was to contribute to a better understanding of the porosity spatial distribution in depositional systems characterized by the interaction between alluvial and eolian processes, with special reference to deposits formed prior to the development of terrestrial plants. Porosity values are related to depositional processes, with higher porosities associated to eolian dune deposits (mean of 8.4%), and lower porosity related to interdunes (mean of 3.4%) and alluvial fans (mean of 4.3%). Architectural elements analysis revealed the spatial relationships of these deposits, a response to the interplay of the eolian and alluvial processes. The integration of porosity data reveals that the interaction of alluvial and eolian processes results in heterogeneous distribution of porosity at the facies association scale. Eolian reworking of alluvial facies increases porosity whereas sheet-flood and other alluvial processes in the interdune areas reduce porosity.

Quantum statistical correlations in thermal field theories: Boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field phi(c), and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrodinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field phi(c), a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.

Pressure of massless hot scalar theory in the boundary effective theory framework

We use the boundary effective theory approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is essentially nonperturbative. To lowest order, the main ingredient is the solution of the free Euler-Lagrange equation with nontrivial (time) boundary conditions. We derive a resummed pressure, which is in good agreement with recent calculations found in the literature, following a very direct and compact procedure.

Energy gain induced by boundary crisis

We consider a nonlinear system and show the unexpected and surprising result that, even for high dissipation, the mean energy of a particle can attain higher values than when there is no dissipation in the system. We reconsider the time-dependent annular billiard in the presence of inelastic collisions with the boundaries. For some magnitudes of dissipation, we observe the phenomenon of boundary crisis, which drives the particles to an asymptotic attractive fixed point located at a value of energy that is higher than the mean energy of the nondissipative case and so much higher than the mean energy just before the crisis. We should emphasize that the unexpected results presented here reveal the importance of a nonlinear dynamics analysis to explain the paradoxical strategy of introducing dissipation in the system in order to gain energy.

Dynamical Casimir effect for a massless scalar field between two concentric spherical shells with mixed boundary conditions

In this work we analyze the dynamical Casimir effect for a massless scalar field confined between two concentric spherical shells considering mixed boundary conditions. We thus generalize a previous result in literature [Phys. Rev. A 78, 032521 (2008)], where the same problem is approached for the field constrained to the Dirichlet-Dirichlet boundary conditions. A general expression for the average number of particle creation is deduced considering an arbitrary law of radial motion of the spherical shells. This expression is then applied to harmonic oscillations of the shells, and the number of particle production is analyzed and compared with the results previously obtained under Dirichlet-Dirichlet boundary conditions.

Homogenization in a thin domain with an oscillatory boundary

In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type R(epsilon) = {(x(1), x(2)) is an element of R(2) vertical bar x(1) is an element of (0, 1), 0 < x(2) < epsilon G(x(1), x(1)/epsilon)} where the function G(x, y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter epsilon. (C) 2011 Elsevier Masson SAS. All rights reserved.

Non-linear boundary element formulation applied to contact analysis using tangent operator

This work presents a non-linear boundary element formulation applied to analysis of contact problems. The boundary element method (BEM) is known as a robust and accurate numerical technique to handle this type of problem, because the contact among the solids occurs along their boundaries. The proposed non-linear formulation is based on the use of singular or hyper-singular integral equations by BEM, for multi-region contact. When the contact occurs between crack surfaces, the formulation adopted is the dual version of BEM, in which singular and hyper-singular integral equations are defined along the opposite sides of the contact boundaries. The structural non-linear behaviour on the contact is considered using Coulomb`s friction law. The non-linear formulation is based on the tangent operator in which one uses the derivate of the set of algebraic equations to construct the corrections for the non-linear process. This implicit formulation has shown accurate as the classical approach, however, it is faster to compute the solution. Examples of simple and multi-region contact problems are shown to illustrate the applicability of the proposed scheme. (C) 2011 Elsevier Ltd. All rights reserved.

Dual boundary element formulation applied to analysis of multi-fractured domains

This paper deals with analysis of multiple random crack propagation in two-dimensional domains using the boundary element method (BEM). BEM is known to be a robust and accurate numerical technique for analysing this type of problem. The formulation adopted in this work is based on the dual BEM, for which singular and hyper-singular integral equations are used. We propose an iterative scheme to predict the crack growth path and the crack length increment at each time step. The proposed scheme able us to simulate localisation and coalescence phenomena, which is the main contribution of this paper. Considering the fracture mechanics analysis, the displacement correlation technique is applied to evaluate the stress intensity factors. The propagation angle and the equivalent stress intensity factor are calculated using the theory of maximum circumferential stress. Examples of simple and multi-fractured domains, loaded up to the rupture, are considered to illustrate the applicability of the proposed scheme. (C) 2010 Elsevier Ltd. All rights reserved.