Splitting hairs with transcendental entire functions

For polynomials of degree at least two, local connectivity of their Julia set is an important property, since it leads to a complete description of their topological dynamics in terms of a simpler model. There is no such connection between the topology of the Julia set of a transcendental entire function $f$ and its dynamics. Nonetheless, it has been shown that one can still describe the dynamics of $f$ in terms of a simpler model, assuming that its \textit{postsingular set} is bounded and $f$ satisfies certain additional hyperbolicity assumptions. Our goal in this paper is, for the first time, to give analogous results in cases when the postsingular set is unbounded. More specifically, we show that if $f$ is of finite order, has \textit{bounded criticality} on its Julia set, and its singular set consists of finitely many critical values that escape to infinity and satisfy a certain separation condition, then its Julia set $J(f)$ is a collection of \textit{dynamic rays} or \emph{hairs}, that \emph{split} at (preimages of) critical points, together with their corresponding landing points. In fact, our result holds for a much larger class of functions; in particular, the assumption of finite order is relaxed to the existence of a map in their parameter space whose Julia set is a \textit{Cantor bouquet}. The existence and landing of rays is a consequence of a more general result; we provide a \textit{topological model} for the action of $f$ on $J(f)$. Finally, we present new results concerning \textit{disjoint type} functions in the case that the Julia set is a Cantor bouquet.Comment: 69 pages, 8 figure

Study of the active flow control of an airfoil

The student will use a CFD code for simulating the turbulent flow around an airfoil with and without active flow control. The student should have to get familiar with the code and run several cases in order to analyse the influence of different parameters. Outcomes of the project is to analyse the changes in the boundary layer due to the active flow control

Integrating periurban agrarian ecosystem services into spatial planning to cope with urban pressure

According to Corine Land Cover databases, in Europe between 1990 and 2000,77% of new artificial surfaces were built on previous agrarian areas. Urban sprawl ¡s far from being under control, between 2000 and 2006 new artificial land has grown in larger proportion than the decade before. In Spain, like in most countries, the impact of urban sprawl during the last decades has been especially significant in periurban agrarian spaces: between 2000 and 2006, 73% of new artificial surfaces were built on previous agrarian areas. The indirect impact of this trend has been even more relevant, as the expectations of appreciation in the value of land after new urban developments reinforce the ongoing trend of abandonment of agricultural land. In Madrid between 1980 and 2000 the loss of agricultural land due to abandonment of exploitation was 2-fold that due to transformation into urban areas. By comparing four case studies: Valladolild, Montpellier.Florence and Den Haag, this paper explores if urban and territorial planning may contribute to reduce urban pressure on the hinterland. In spite of their diversity, these regions have in common a relative prosperity arising from their territorial endowments, though their landscapes are still under pressure. The three last ones have been working for years on mainstream concepts like multifunctional agriculture. The systematic comparison and the analysis of successful approaches provide some clues on how to reconsider urban planning in order to preserve agricultural land. The final remarks highlight the context in which public commitment, legal protection instruments and financial strategies may contribute to the goals of urban, peri-urban or regional planning about fostering agrarian ecosystem service

Joaquim Hugas i Wenceslao Marín, oftalmòlegs catalans (i la ginecòloga Montserrat Bobé)

Dades biogràfiques sobre Joaquim Hugas, el primer veritable metge oculista de Girona i pare de la primera dona òptica de la ciutat. També es dóna notícia de l’oftalmòleg Wenceslao Marín, que es va casar amb la manresana Montserrat Bobé, una de les poques dones que van estudiar Medicina a Barcelona a cavall de finals del segle XIX i principis del XX.Se aportan datos biográficos sobre que fue el primer médico oculista que ejerció en Gerona, y padre de la primera mujer óptica en la ciudad. También se da noticia del oftalmólogo Wenceslao Marín, que ejerció en Barcelona,  casado con Montserrat Bobé, de Manresa, una de las primeras mujeres que se licenció en Barcelona, cursando estudios en los años de cambio de siglo XIX al XX