Evolution of a rift basin dominated by subaerial deposits: The Guaritas Rift, Early Cambrian, Southern Brazil

Most existing models for the evolution of rift basins predict the development of deep-water depositional systems during the stage of greatest tectonic subsidence, when accommodation generation potentially outpaces sedimentation. Despite this, some rift basins do not present deep-water systems, instead being dominated by subaerial deposits. This paper focuses on one of these particular rift basins, the Cambrian Guaritas Rift, Southern Brazil, characterized by more than 1500 m of alluvial and aeolian strata deposited in a 50-km-wide basin. The deposits of the Guaritas Rift can be ascribed to four depositional systems: basin-border alluvial fans, bedload-dominated ephemeral rivers, mixed-load ephemeral rivers and aeolian dune fields. These four systems are in part coeval and in part succeed each other, forming three stages of basin evolution: (i) Rift Initiation to Early Rift Climax stage, (ii) Mid to Late Rift Climax stage, and (iii) Early Post-Rift stage. The first stage comprises most of the Guaritas Group and is characterized by homogeneous bed-load-dominated river deposits, which do not clearly record the evolution of subsidence rates. The onset of sedimentation of finer-grained deposits occurred as a consequence of a reactivation event that changed the outline of the basin and the distribution of the nearby highlands. This strongly suggests that the capture of the main river system to another depression decreased the sediment supply to the basin. The study of the Guaritas Rift indicates that rift basins in which the sediment supply exceeds the accommodation generation occur as a consequence of moderate subsidence combined with the capture of a major river system to the basin during the initial stages of basin evolution. In these basins, changes in the average discharge of the river system or tectonic modification of the drainage network may be the major control on the stratigraphic architecture. (c) 2009 Published by Elsevier B.V.

Structural analysis of the Itapucumi Group in the Vallemi region, northern Paraguay: Evidence of a new Brasiliano/Pan-African mobile belt

The Neoproterozoic (Ediacaran) Itapucumi Group in northern Paraguay is composed of carbonate and siliciclastic rocks, including ooid grainstones, marls, shales and sandstones, containing Cloudina fossils in the eastern region. It is almost undeformed over the Rio Apa Cratonic Block but shows a strong deformational pattern at its western edge. A detailed structural analysis of the Itapucumi Group was conducted in the Vallemi Mine, along with a regional survey in other outcrops downstream in the Paraguay River and in the San Alfredo, Cerro Paiva and Sargent Jose E. Lopez regions. In the main Vallemi quarry, the structural style is characterized by an axial-plane slaty cleavage in open to isoclinal folds, sometimes overturned, associated with N-S trending thrust faults and shear zones of E-vergence and with a low-grade chlorite zone metamorphism. The structural data presented here are compatible with the hypothesis of a newly recognized mobile belt on the western side of the Rio Apa Cratonic Block, with opposite vergence to that of the Paraguay Mobile Belt in Brazil. Both belts are related to the Late Brasiliano/Pan-African tectonic cycle with a Lower Cambrian deformation and metamorphism age. The deformation could be due to the late collision of the Amazonian Craton with the remainder of Western Gondwana or to the western active plate boundary related to the Pampean Belt. The structural and lithologic differences between the western Itapucumi Group in the Vallemi and Paraguay River region and the eastern region, near San Alfredo and Cerro Paiva, suggest that this group could be divided into two lithostratigraphic units, but more stratigraphic and geochronological analyses are required to confirm this possibility. (C) 2010 Elsevier Ltd. All rights reserved.

Precambrian geotectonic units of the Rio de La Plata craton

The main Precambrian tectonic units of Uruguay include the Piedra Alta tectonostratigraphic terrane (PATT) and Nico Perez tectonostratigraphic terrane (NPTT), separated by the Sarandi del Yi high-strain zone. Both terranes are well exposed in the Rio de La Plata craton (RPC). Although these tectonic units are geographically small, they record a wide span of geologic time. Therefore improved geological knowledge of this area provides a fuller understanding of the evolution of the core of South America. The PATT is constituted by low-to medium-grade metamorphic belts (ca. 2.1 Ga); its petrotectonic associations such as metavolcanic units, conglomerates, banded iron formations, and turbiditic deposits suggest a back-arc or a trench-basin setting. Also in the PATT, a late to post-orogenic, arc-related layered mafic complex (2.3-1.9 Ga), followed by A-type granites (2.08 Ga), and finally a taphrogenic mafic dike swarm (1.78 Ga) occur. The less thoroughly studied NPTT consists of Palaeoproterozoic high-grade metamorphic sequences (ca. 2.2 Ga), mylonites and postorogenic and rapakivi granites (1.75 Ga). The Brasiliano-Pan African orogeny affected this terrane. Neoproterozoic cover occurs in both tectonostratigraphic terranes, but is more developed in the NPTT. Over the past 15 years, new isotopic studies have improved our recognition of different tectonic events and associated processes, such as reactivation of shear zones and fluids circulation. Transamazonian and Statherian tectonic events were recognized in the RPC. Based on magmatism, deformation, basin development and metamorphism, we propose a scheme for the Precambrian tectonic evolution of Uruguay, which is summarized in the first Palaeoproterozoic tectonic map of the Rio de La Plata craton.

Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u equivalent to 1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain. (C) 2009 Elsevier Inc. All rights reserved.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

Boundary and internal conditions for adjoint fluid-flow problems

The ever-increasing robustness and reliability of flow-simulation methods have consolidated CFD as a major tool in virtually all branches of fluid mechanics. Traditionally, those methods have played a crucial role in the analysis of flow physics. In more recent years, though, the subject has broadened considerably, with the development of optimization and inverse design applications. Since then, the search for efficient ways to evaluate flow-sensitivity gradients has received the attention of numerous researchers. In this scenario, the adjoint method has emerged as, quite possibly, the most powerful tool for the job, which heightens the need for a clear understanding of its conceptual basis. Yet, some of its underlying aspects are still subject to debate in the literature, despite all the research that has been carried out on the method. Such is the case with the adjoint boundary and internal conditions, in particular. The present work aims to shed more light on that topic, with emphasis on the need for an internal shock condition. By following the path of previous authors, the quasi-1D Euler problem is used as a vehicle to explore those concepts. The results clearly indicate that the behavior of the adjoint solution through a shock wave ultimately depends upon the nature of the objective functional.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambo et al. (2005) [8]) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) [1]) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. (C) 2010 Elsevier Ltd. All rights reserved.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

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.

GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.