A hyperbolic model of chemotaxis on a network: a numerical study

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation

A numerical comparison between degenerate parabolic and quasilinear hyperbolic models of cell movements under chemotaxis

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the other one on a degenerate parabolic equation. The two models have the same stationary solutions, which may contain some regions with vacuum. We first explain in details how to discretize the quasilinear hyperbolic system through an upwinding technique, which uses an adapted reconstruction, which is able to deal with the transitions to vacuum. Then we concentrate on the analysis of asymptotic preserving properties of the scheme towards a discretization of the parabolic equation, obtained in the large time and large damping limit, in order to present a numerical comparison between the asymptotic behavior of these two models. Finally we perform an accurate numerical comparison of the two models in the time asymptotic regime, which shows that the respective solutions have a quite different behavior for large times.Comment: One sentence modified at the end of Section 4, p. 1

Rosario Villari, Un sogno di libertà. Napoli nel declino di un impero, 1585-1648, Mondadori, Milán, 2012, 716 pp.

La aparición en el mercado de un nuevo libro de Rosario Villari es siempre una magnífica noticia para la historiografía, pues se trata de uno de los grandes historiadores de nuestro tiempo. Modernista formado en los presupuestos metodológicos del marxismo y la historia económico-social, se ha caracterizado siempre por una amplitud de perspectivas que le ha llevado a ocuparse también, en ocasiones, de la época Contemporánea, abarcando un variado abanico de temas, entre los que destaca su preocupación por la historia del Mezzogiorno italiano y la llamada cuestión meridiona

La coopération intermunicipale : les modèles québécois et français

Au Québec comme en France, les contraintes économiques modernes remettent en question les découpages municipaux existants. Les gouvernements se heurtent aux réticences des acteurs locaux pour mettre en place des institutions intermunicipales de coopération permettant aux municipalités dont le territoire est trop exigu, ou dont les moyens économiques sont trop faibles, de satisfaire les besoins publics de leur population et de favoriser le développement local. L'étude des modalités de création et de fonctionne ment de ces institutions révèle, au-delà des correspondances conjoncturelles, d'importantes différences. Alors qu'en France l'intercommunalité se fonde toujours sur des préoccupations de recomposition territoriale, le Québec a développé une conception beaucoup plus fonctionnelle laissant une large place à laconsultation de la population. À partir de ces différences, les institutions de coopération intermunicipales québécoises et françaises s'efforcent d'acquérir une certaine autonomie à l'égard de leurs membres et de définir des stratégies économiques ou politiques spécifiques.In Quebec as in France, modem economic constraints put into question existing municipal divisions. Governments run into the reluctance of local citizens when setting up intermunicipal institutions for cooperaion thereby allowing municipalities with limited territory or economic means to satisfy the public needs of their population and favour local development. The study of the means for creating and operating such institutions demonstrates important differences that transcend current conditions. While in France intercommunality is always based on questions of territorial recomposition, Quebec has developed a far more operational conception that leaves much to popular consultation. On the basis of these differences, Quebec and French inter municipal institutions for cooperation attempt to acquire a certain indépendance with regard to their members and to define economic strategies or specific policies