Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

U-Pb zircon in situ dating with LA-MC-ICP-MS using a mixed detector configuration

The LA-MC-ICP-MS method applied to U-Pb in situ dating is still rapidly evolving due to improvements in both lasers and ICP-MS. To test the validity and reproducibility of the method, 5 different zircon samples, including the standard Temora-2, ranging in age between 2.2 Ga and 246 Ma, were dated using both LA-MC-ICP-MS and SHRIMP. The selected zircons were dated by SHRIMP and, after gentle polishing, the laser spot was driven to the same site or on the same zircon phase with a 213 nm laser microprobe coupled to a multi-collector mixed system. The data were collected with a routine spot size of 25 μm and, in some cases, of 15 and 40 μm. A careful cross-calibration using a diluted U-Th-Pb solution to calculate the Faraday reading to counting rate conversion factors and the highly suitable GJ-1 standard zircon for external calibrations were of paramount importance for obtaining reliable results. All age results were concordant within the experimental errors. The assigned age errors using the LA-MC-ICP-MS technique were, in most cases, higher than those obtained by SHRIMP, but if we are not faced with a high resolution stratigraphy, the laser technique has certain advantages.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Pullback exponential attractors for evolution processes in Banach spaces: properties and applications

This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.

Structural stability of flexible lines in catenary configuration under torsion

Catenary risers can present during installation a very low tension close to seabed, which combined with torsion moment can lead to a structural instability, resulting in a loop. This is undesirable once it is possible that the loop turns into a kink, creating damage. This work presents a numerical methodology to analyze the conditions of loop formation in catenary risers. Stability criteria were applied to finite element models, including geometric nonlinearities and contact constraint due to riser-seabed interaction. The classical Greenhill's formula was used to predict the phenomenon and parametric analysis shows a “universal plot” able to predict instability in catenaries using a simple equation that can be applied for typical risers installation conditions and, generically, for catenary lines under torsion.

Gold ion implantation into alumina using an “inverted ion source” configuration.

We describe an approach to ion implantation in which the plasma and its electronics are held at ground potential and the ion beam is injected into a space held at high negative potential, allowing considerable savings both economically and technologically. We used an “inverted ion implanter” of this kind to carry out implantation of gold into alumina, with Au ion energy 40 keV and dose (3–9) × 1016 cm−2. Resistivity was measured in situ as a function of dose and compared with predictions of a model based on percolation theory, in which electron transport in the composite is explained by conduction through a random resistor network formed by Au nanoparticles. Excellent agreement is found between the experimental results and the theory.

Polyphase drive systems configuration aiming EMI mitigation

Topologies of motor drive systems are studied, aiming the reduction of common-mode (CM) currents. Initially, the aspects concerning the CM currents circulation are analysed. The reason of common-mode voltages generation, the circulating paths for the resulting CM currents and their effects are discussed. Then, a non-conventional drive system configuration is proposed in order to reduce the CM currents and their effects. This configuration comprehends a non-conventional inverter module wired to a motor with an unusual connection. The cables arrangement differs from the standard solution, too. The proposed topology is compared with other ones, like the active circuit for common-mode voltages compensation. The contribution of the configuration to the reduction of CM voltages and currents and their related interferences are evaluated, based on numerical simulations. Some results are presented and discussed regarding the suitability of the proposed configuration as a potential solution to reduce the CM currents effects, when the state of art and implementation cost of drives are taken into account.

Intersections on moduli spaces of curves

We present a new approach to perform calculations with the certain standard classes in cohomology of the moduli spaces of curves. It is based on an important lemma of Ionel relating the intersection theoriy of the moduli space of curves and that of the space of admissible coverings. As particular results, we obtain expressions of Hurwitz numbers in terms of the intersections in the tautological ring, expressions of the simplest intersection numbers in terms of Hurwitz numbers, an algorithm of calculation of certain correlators which are the subject of the Witten conjecture, an improved algorithm for intersections related to the Boussinesq hierarchy, expressions for the Hodge integrals over two-pointed ramification cycles, cut-and-join type equations for a large class of intersection numbers, etc.

A fixed point theorem for Meir-Keeler contractions in ordered metric spaces

[EN] The purpose of this paper is to present some fixed point theorems for Meir-Keeler contractions in a complete metric space endowed with a partial order. MSC: 47H10.

Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations

[EN] The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equations.

Paisajes epigráficos en la Provincia Hispana Citerior en época de Augusto

[ES] Se estudia la diversidad de contextos de exhibición de las inscripciones romanas en la provincia Hispania citerior en época augustea, atendiendo a la importancia que adquirieron las ciudades en el proceso de romanización del territorio, así como a la configuración de nuevos espacios de exposición de las inscripciones, en algunos casos dentro de las estrategias de promoción y autorrepresentación de las elites locales.

Il contributo dell’Unione europea all’affermazione dello stato di diritto nella comunità internazionale

This thesis is aimed at analysing EU external relations from the perspective of the promotion of the rule of law in order to evaluate the effectiveness and consistency of its action within the international community. The research starts with an examination of the notion of the rule of law from a theoretical point of view. The first chapter initially describes the historical-political evolution of the establishment of the notion of the rule of law. Some of the most significant national experiences (France, the UK, Germany and Austria) are discussed. Then, the focus is put on the need to propose interpretations which explain the grounds of the rule of law, by highlighting the different formal and substantive interpretations. This philosophical-historical analysis is complemented by a reconstruction of how the notion of the rule of law was developed by the international community, with a view to searching a common notion at the international level by comparing theory and practice within the main international organisations such as the UN, OECD and the Council of Europe. Specific mention is made of the EU experience, whose configuration as a Community based on the rule of law is often debated, starting from the case law of the European Court of Justice. The second chapter deals with the conditionality policy and focuses on the development and scope of democratic conditionality according to the dominant approach of the doctrine. First, the birth of conditionality is analysed from an economic point of view, especially within international financial organisations and the different types of conditionality recreated in the scientific sector. Then an analysis is provided about the birth of democratic conditionality in the EC – in relation to its external relations – firstly as a mere political exercise to be then turned into a standardised system of clauses. Specific reference is made to the main scope of conditionality, that is to say enlargement policy and the development of the Copenhagen criteria. The third chapter provides further details about the legal questions connected to the use of democratic clauses: on the one hand, the power of the EC to include human rights clauses in international agreements, on the other, the variety and overlapping in the use of the legal basis. The chapter ends with an analysis of the measures of suspension of agreements with third countries in those rare but significant cases in which the suspension clause, included in the Lomè Convention first and in the Cotonou Agreement then, is applied. The last chapter is devoted to the analysis of democratic clauses in unilateral acts adopted by the European Union which affect third countries. The examination of this practice and the comparison with the approach analysed in the previous chapter entails a major theoretical question. It is the clear-cut distinction between conditionality and international sanction. This distinction is to be taken into account when considering the premises and consequences, in terms of legal relations, which are generated when democratic clauses are not complied with. The chapter ends with a brief analysis of what, according to the reconstruction suggested, can be rightly labelled as real democratic conditionality, that is to say the system of incentives, positive measures developed within the community GSP. The dissertation ends with a few general considerations about the difficulties experienced by the EU in promoting the rule of law. The contradictory aspects of the EU external actions are manifold, as well as its difficulties in choosing the most appropriate measures to be taken which, however, reflect all the repercussions and tension resulting from the balance of power within the international community. The thesis argues that it is difficult to grant full credibility to an entity like the EU which, although it proclaims itself as the guardian and promoter of the rule of law, in practice, is too often biased in managing its relations with third countries. However, she adds, we must acknowledge that the EU is committed and constantly strives towards identifying new spaces and strategies of action.

Fixed point theorems in partially ordered spaces and aplications

[ES]Recientemente, en la Teoría del punto fijo, han aparecido muchos resultados que obtienen condiciones suficientes para la existencia de un punto fijo si trabajamos con aplicaciones en un conjunto dotado de un orden parcial. Generalmente, estos resultados combinan dos teoremas del punto fijo fundamentales: el Teorema de la contracción de Banach y el Teorema de Knaster-Tarski.

Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..