Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Dynamics of integrable birational maps preserving genus 0 foliations

Pòster presentat al congrés NPDDS2014

Desenvolupament de codis numèrics per a la resolució de fluxos turbulents en ordinadors paral·lels emprant discretitzacions tipus symmetry-preserving

Projecte de recerca elaborat a partir d’una estada a la University of Groningen, Holanda, entre 2007 i 2009. La simulació directa de la turbulència (DNS) és una eina clau dins de la mecànica de fluids computacional. Per una banda permet conèixer millor la física de la turbulència i per l'altra els resultats obtinguts són claus per el desenvolupament dels models de turbulència. No obstant, el DNS no és una tècnica vàlida per a la gran majoria d'aplicacions industrials degut al elevats costos computacionals. Per tant, és necessari cert grau de modelització de la turbulència. En aquest context, s'han introduïts importants millores basades en la modelització del terme convectiu (no lineal) emprant symmetry-preserving regularizations. En tracta de modificar adequadament el terme convectiu a fi de reduir la producció d'escales més i més petites (vortex-stretching) tot mantenint tots els invariants de les equacions originals. Fins ara, aquest models s'han emprat amb èxit per nombres de Rayleigh (Ra) relativament elevats. En aquest punt, disposar de resultats DNS per a configuracions més complexes i nombres de Ra més elevats és clau. En aquest contexte, s'han dut a terme simulacions DNS en el supercomputador MareNostrum d'una Differentially Heated Cavity amb Ra=1e11 i Pr=0.71 durant el primer any dels dos que consta el projecte. A més a més, s'ha adaptat el codi a fi de poder simular el fluxe al voltant d'un cub sobre una pared amb Re=10000. Aquestes simulacions DNS són les més grans fetes fins ara per aquestes configuracions i la seva correcta modelització és un gran repte degut la complexitat dels fluxes. Aquestes noves simulacions DNS estan aportant nous coneixements a la física de la turbulència i aportant resultats indispensables per al progrés de les modelitzacións tipus symmetry-preserving regularization.

On the preservation of combinatorial types for maps on trees

We study the preservation of the periodic orbits of an A-monotone tree map f:T→T in the class of all tree maps g:S→S having a cycle with the same pattern as A. We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of ƒ into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees T and S (which need not be homeomorphic) are essentially preserved

Linear and nonlinear terrain deformation maps from a reduced set of interferometric SAR images

In this paper, an advanced technique for the generation of deformation maps using synthetic aperture radar (SAR) data is presented. The algorithm estimates the linear and nonlinear components of the displacement, the error of the digital elevation model (DEM) used to cancel the topographic terms, and the atmospheric artifacts from a reduced set of low spatial resolution interferograms. The pixel candidates are selected from those presenting a good coherence level in the whole set of interferograms and the resulting nonuniform mesh tessellated with the Delauney triangulation to establish connections among them. The linear component of movement and DEM error are estimated adjusting a linear model to the data only on the connections. Later on, this information, once unwrapped to retrieve the absolute values, is used to calculate the nonlinear component of movement and atmospheric artifacts with alternate filtering techniques in both the temporal and spatial domains. The method presents high flexibility with respect to the required number of images and the baselines length. However, better results are obtained with large datasets of short baseline interferograms. The technique has been tested with European Remote Sensing SAR data from an area of Catalonia (Spain) and validated with on-field precise leveling measurements.

Research work in Tokyo Institute of Technology

Research carried out in Tokyo Institute of Technology. The objective is to determine the influence of Interfacial Transition Zone (ITZ) around Lightweight aggregate in concrete on Chloride ion diffusivity. The ITZ of conventional concretes is the weakest point of concrete. The accumulating water on ITZ zone forms the most permeable area inside the concrete. Hence ITZ paves the way for chloride ion diffusion. The quality of ITZ depends on type and quality of aggregates used, water-cement ratio and also the method used for the production of concrete. It has been used two types of lightweight aggregates will be used, Chinese and Japanese, with different absorption capacities. The idea is to produce concrete with same effective water - cement ratio, using the same aggregates in two different conditions, dry and saturated, and compare the chloride ion diffusivity in these concretes (by diffusion test). A comparison of ITZ thickness of these concretes by SEM and EDAX-maps is also proposed. The chloride ion diffusion of concretes produced with the same effective water – cement ratio and same aggregates (dry and ssd) will depend, mainly, on ITZ.

Catalan Policies and Experiences on Cooperative Repositories

The Centre de Supercomputació de Catalunya (CESCA) together with the Consorci de Biblioteques Universitàries de Catalunya (CBUC) started in 1999 a cooperative repository, named TDR, to file in digital format the full-text of the read thesis at the universities of our country to spread them worldwide in open access preserving the intellectual copyright of the authors. This became operational in 2001 and today it is a service fully consolidated not only among the Catalan universities, but also used by other Spanish universities. Since then, there are four additional cooperative repositories which have been created: RECERCAT, for research papers; RACO, for scientific, cultural and erudite Catalan magazines; PADICAT, for archiving Catalan web sites; and MDC, for Catalan digital collections of pictures, maps, posters, old magazines... These five repositories have some common characteristics: they are open access, that is, they are accessible on the internet for free; they mostly comply with the Open Archive Initiative interoperability protocol for facilitating the efficient dissemination of content; and they have been built in a cooperative manner so that it is easy to adopt common procedures and to share the repository developing and managing costs, it permits more visibility of the indexed documents throughout the search engines, and a better provision for long-term preservation can be made. In this paper we present the common policy established for the Catalan cooperative repositories, we describe the five of them briefly, and we comment on the results obtained of our 6-year experience since the first one became operational.

Milk, from medicine to food Mediterranean Europe: Catalonia, 19th-20th centuries

The spread of milk consumption was a significant change in the diet of Europeans, however it is one that has not been greatly studied with regard to the populations of Mediterranean Europe. In this article we shall analyse the ain circumstances that conditioned that process in Catalonia between the middle of the 19th century and 1936. In our study we shall argue that the consumption of milk in this area was only relevant in the 19th century in situations of illness or old age, and that it subsequently increased and acquired a new significance as a result of various factors. In particular, we shall emphasise: (a) the scientific advances in microbiology and nutrition, (b) the activities carried out by doctors and various public institutions to promote the consumption of fresh milk, and (c) the technological innovations in the milk producing sector. In Appendix 1 we show two maps representing the main territorial references that we shall mention.

Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

The EU as a security provider in its neighbourhood: the case of non-proliferation of WMD in the Mediterranean area

As a consequence of the terrorist attacks of 9/11 and the US-led war against Iraq, WMD and their proliferation have become a central element of the EU security agenda. In December 2003, the European Council adopted even a EU Strategy against Proliferation of WMD. The approach adopted in this Strategy can be largely described as a ‘cooperative security provider’ approach and is based on effective multilateralism, the promotion of a stable international and regional environment and the cooperation with key partners. The principal objective of this paper is to examine in how far the EU has actually implemented the ‘cooperative security provider’ approach in the area which the Non-proliferation Strategy identifies as one of its priorities – the Mediterranean. Focusing on the concept of security interdependence, the paper analyses first the various WMD dangers with which the EU is confronted in the Mediterranean area. Afterwards, it examines how the EU has responded to these hazards in the framework of the Barcelona process and, in particular, the new European Neighbourhood Policy. It is argued that despite its relatively powerful rhetoric, the EU has largely failed, for a wide range of reasons, to apply effectively its non-proliferation approach in the Mediterranean area and, thus, to become a successful security provider.

Iniciativas para el desarrollo sostenible del Área de Conservación Arenal- Huetar Norte, Costa Rica

El presente proyecto tiene como zona de estudio el Área de Conservación Arenal- Huetar Norte (ACA-HN), concretamente los cantones de Upala, Los Chiles y Guatuso. El propósito del proyecto es promover el desarrollo sostenible de la zona mediante los pilares de la educación y la economía. Para ello se elabora un manual de educación ambiental de la cuenca de río Frío y así poder solventar algunas de las carencias en educación que tienen los docentes de las escuelas de la cuenca hidrográfica. Por otro lado, se diagnostica la cadena de valor sobre usos alternativos de la biodiversidad, específicamente zoocriaderos de mariposas diurnas, en los cantones de Upala y Los Chiles. Por último, se trata la información de la zona de estudio con Sistemas de Información Geográfica (SIG) para elaborar mapas que ilustren los proyectos anteriores y el proyecto sobre el diagnóstico de la industria de turismo local.

Patrimoni Digital de Catalunya, a year and a half experience

E-repositories are part of the e-science, and they are based on the e-infrastructure. The Centre de Supercomputació de Catalunya (CESCA) together with the Consorci de Biblioteques Universitàries de Catalunya (CBUC) started in 1999 a cooperative repository, named TDR, to file, in digital format, the full-text of the read thesis at the universities of our country in order to spread them worldwide in open access, while at the same time, preserving the intellectual copyright of the authors. Since then, four additional cooperative repositories have been created: RECERCAT for research papers; RACO for scientific, cultural and erudite Catalan magazines; MDC for Catalan digital collections of pictures, maps, posters and old magazines; and PADICAT for archiving Catalan digital web content; The main objective of the latter is to archive Catalan web sites. That is, PADICAT collects, processes and provides permanent access to the entire cultural, scientific and general output of Catalonia in digital format. The repository manager is the Biblioteca de Catalunya, as the institution responsible for compiling, processing and distributing the bibliographic heritage of Catalonia, while CESCA is the technology partner. On September 11th, 2006 the repository went into operation for the general public, with some thirty websites archived. After one year and a half, it has 2.720 captures of more than 1.000 websites. This includes 34 million files (HTML, images...) and two terabytes of data. The objective of this paper is to present PADICAT and our experience developing and managing it.We describe the repository briefly, we explain the technology used to implement it and we comment our experiences during its first year and a half.

The spatial inequality of wage income in Barcelona Metropolitan Area

ABSTRACT The measure and estimation of income levels in Barcelona Metropolitan Area (BMA) goes back a long way. Using different approaches and focusing on different municipalities, there is a lot of work in the field. The majority of the literature has focused on the estimation of income levels using variables related to consumption. The empirical evidence on wage differentials has shown an important growth during 80’s and 90’s especially in United Kingdom and USA. Less is known on spatial distribution of inequality. This paper presents a new data set for analyzing spatial distribution of wage income. This data is obtained by matching Wage Structure Survey (WSS) with data from Census disaggregated by census tracts. In this way we have a unique data set with wage incomes for every census track for 36 municipalities belonging to BMA. We develop a descriptive analysis of spatial distribution, testing for spatial autocorrelation and use the family of Generalised Entropy Indices to measure inequality. Properties of the index allow us to decompose inequality into inter and intra-municipality measures. Since we have two cross-sectional data for WSS (1995-2002) we can also analyze the evolution of the inequality in this period of economic growth. Key words: spatial distribution of wages, spatial autocorrelation, inequality indices.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Quasiconformal maps, analytic capacity, and non linear potentials

"Vegeu el resum a l'inici del document del fitxer adjunt."