A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

A complex network-based approach for boundary shape analysis

This paper introduces a novel methodology to shape boundary characterization, where a shape is modeled into a small-world complex network. It uses degree and joint degree measurements in a dynamic evolution network to compose a set of shape descriptors. The proposed shape characterization method has all efficient power of shape characterization, it is robust, noise tolerant, scale invariant and rotation invariant. A leaf plant classification experiment is presented on three image databases in order to evaluate the method and compare it with other descriptors in the literature (Fourier descriptors, Curvature, Zernike moments and multiscale fractal dimension). (C) 2008 Elsevier Ltd. All rights reserved.

Anomalous content of chromium in a Cretaceous sandstone aquifer of the Bauru Basin, state of Sao Paulo, Brazil

Anomalous and natural concentrations of Cr(6+), occasionally exceeding the permitted limit for human consumption (0.05 mg/L), have been detected in groundwater in the northwestern region of the state of Sao Paulo. As part of a water-rock interaction investigation, this article describes the chemical and mineralogical characterization of rock samples taken from boreholes in the municipality of Urania, with the objective of identifying Cr-bearing minerals and determining how chromium is associated with these minerals. Rock sample analysis were performed using X-ray Fluorescence, X-ray Diffraction, Scanning Electron Microscopy, electron microprobe and sequential extraction techniques. Chemical analyses indicated that the quartzose sandstones show a geochemical anomaly of chromium, with an average content of 221 ppm, which is higher than the reported chromium content of generic sandstones (35 ppm). Diopside was identified as the primary Cr-bearing mineral potentially subject to weathering processes, with a chromium content of up to 1.2% as Cr(2)O(3). Many of the diopside grains showed dissolution features, confirming the occurrence of weathering. Sequential extraction experiments indicated that 99.3% of the chromium in samples is tightly bonded to minerals, whereas 0.24% is weakly bonded via adsorption. Assuming hypothetically that all adsorbed chromium is released via desorption, the theoretical Cr concentration in water would be one order of magnitude higher than the concentrations of Cr(6+) detected in groundwater. (C) 2010 Elsevier Ltd. All rights reserved.

A putative gnetalean gymnosperm Cariria orbiculiconiformis gen. nov et spec. nov from the Early Cretaceous of northern Gondwana

Cariria orbiculiconiformis gen. nov. et spec. nov., a gymnosperm with gnetoid characters is described from the upper Aptian Crato Formation of the Araripe Basin in northeastern Brazil. Gross-morphology and anatomical details have been studied and characters have been discussed in respect to various seed plants. Several of these characters fit best with those of Gnetales and their putative fossil allies. However, the fossil plant cannot be assigned to any known extinct or extant group of seed plants in their current circumscription. Stem gross-morphology, xylotomical characters and epidermal features indicate a gnetophytic relationship, whereas characters of the reproductive organs are rather distinct from those found in extant taxa. The reproductive unit of the new taxon represents a triple organ consisting of two dichasial ovulate structures and one median pollen-producing structure containing smooth, monosulcate, boat-shaped pollen in-situ. Each ovulate structure consists of two distinct pairs of bracts, a sterile one at the base and a fertile one forming a terminal orbicular capsule. Stiff processes found in the apex of the ovulate structure may represent micropylar tubes of seeds, as seen in the Bennettitales-Erdtmanithecales-Gnetales group. C orbiculiconiformis gen. nov. et spec. nov. was ans herbaceous or semi-shrub-like plant that may have been adapted to the r-strategy in a stressful environment. (C) 2011 Elsevier B.V. All rights reserved.

Cearania heterophylla gen. nov et sp nov., a fossil gymnosperm with affinities to the Gnetales from the Early Cretaceous of northern Gondwana

Vegetative and fertile shoots of a shrub-like seed plant from the late Aptian Crato Formation of Brazil are described as Cearania heterophylla Kunzmann, Mohr and Bernardes-de-Oliveira, gen. nov. et sp. nov. Anatomical details of the axes, epidermal features and separate ovulate and pollen producing organs indicate the gymnospermous nature of this plant. The vascular tissue of the axes includes tracheids with bordered pits and fiber tracheids. Vegetative shoots comprising at least three branching orders bear opposite-decussately arranged ovate to lanceolate, dorsiventrally flattened, parallelodromous, rather thick leaves that vary tremendously in size. The amphistomatic leaves bear (brachy-)paracytic stomatal complexes arranged in simple longitudinal files. The ovulate structure is interpreted as a terminally attached single globular ovule/seed surrounded by at least five to six lanceolate bracts. A terminally attached pollen-cone like structure grows on a lateral leafy shoot. The unusual character combination may indicate that the fossils belong to a hitherto unknown group with affinities to ephedroid Gnetales. Sterile shoots formerly often described as Podozamites, Nageiopsis or Lilites that are at least partly congeneric with C. heterophylla Kunzmann, Mohr and Bernardes-de-Oliveira, gen. nov. et sp. nov. had a wide geographic distribution during the Early Cretaceous. (C) 2009 Elsevier B.V. All rights reserved.

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.

To achieve safe and respectful maternity care in tertiary level hospitals in Nepal, relatives are a valued addition to the provision of maternity care

Introduction: The White Ribbon Alliance for safe motherhood believes respectful maternity care is the universal right of every childbearing woman. Methods: NHRC in 2012 approved an inquiry of respectful care at facility-based childbirth. Individual-, focus group interviews and content analysis was used for gathering and analysis of data. Findings: The participating women and the SBAs shared similar views, and this was that together the SBAs and relatives ensured the women remained within the comfort and safety zone when giving birth in a tertiary level maternity unit. Conclusion: The SBAs strategy of having relatives provides basic care alongside the provision of medical care by the SBAs is a strategy that Nepal could use to improve the quality of its maternity care without any additional costs. Clinical implication: Prenatal classes might contribute to preparing relatives. Further Research: Further research could evaluate such a strategy in order to determine its effectiveness in reduction of morbidity and mortality.