Variational description of Gibbs-non-Gibbs dynamical transitions for spin-flip systems with a Kac-type interaction

We continue our study of Gibbs-non-Gibbs dynamical transitions. In the present paper we consider a system of Ising spins on a large discrete torus with a Kac-type interaction subject to an independent spin-flip dynamics (infinite-temperature Glauber dynamics). We show that, in accordance with the program outlined in \cite{vEFedHoRe10}, in the thermodynamic limit Gibbs-non-Gibbs dynamical transitions are \emph{equivalent} to bifurcations in the set of global minima of the large-deviation rate function for the trajectories of the empirical density \emph{conditional} on their endpoint. More precisely, the time-evolved measure is non-Gibbs if and only if this set is not a singleton for \emph{some} value of the endpoint. A partial description of the possible scenarios of bifurcation is given, leading to a characterization of passages from Gibbs to non-Gibbs and vice versa, with sharp transition times. Our analysis provides a conceptual step-up from our earlier work on Gibbs-non-Gibbs dynamical transitions for the Curie-Weiss model, where the mean-field interaction allowed us to focus on trajectories of the empirical magnetization rather than the empirical density.Comment: Key words and phrases: Curie-Weiss model, Kac model, spin-flip dynamics, Gibbs versus non-Gibbs, dynamical transition, large deviation principles, action integral, bifurcation of rate functio

Transmisión de empresas y regímenes complementarios por pensiones en el derecho comunitario: problemas de derecho colectivos

El fenómeno de la transmisión de empresas (en sus diferentes modalidades) se ha confirmado como una estrategia frecuentemente utilizada por los titulares del capital con la intención de mejorar su posición competitiva dentro de unos mercados cada vez más globalizados y, en los últimos tiempos, como último mecanismo para garantizar el futuro y viabilidad de la unidad productiva ante la actual coyuntura económica.Junto a él, la importancia de los compromisos por pensiones ha aumentado sustancialmente en las últimas dos décadas.El objetivo fundamental del presente artículo pasa, por tanto, por analizar cuál es el régimen jurídico y el tratamiento a nivel comunitario que han de recibir los sistemas complementarios implantados en una empresa en caso de que se transfieran sus instalaciones a otro titular, en particular por cuanto hace a las relaciones colectivas de trabajo. A tal fin, se analizará la Directiva 2001/23/CE, de 12 de marzo, así como los principales pronunciamientos del Tribunal de Justicia Comunitario derivados de su interpretación, pudiendo adelantar cómo la respuesta ofrecida por dicho texto en esta materia no resulta plenamente satisfactoria a la hora de garantizar los intereses de los beneficiarios.The companies� transmission phenomenon (in its different categories) is a strategy frequently used by the capital possessors with the intention of improving their competitive position in global markets and, recently, like the last alternative to guarantee the future and viability of the productive unit in the face of the current economic situation. With it, the importance of the pension commitments has showed a substantial increase during the last decades.Consequently, the main objective of this article is to analyse what are the legal regime and the treatment as far as EU regulations that have to receive the complementary systems introduced in a company when its installations are transferred to another owner, particularly, as regards labour collective relationships. With this aim in mind, the 2001/23/CE Directive and the principal European Court�s judicial judgements about it will be analysed. It is possible to bring the conclusion forward: the reply given by this text it is not fully satisfactory to guarantee the beneficiaries interests

Thin film instability with thermal noise

We study the effects of stochastic thermal fluctuations on the instability of the free surface of a flat liquid film upon a solid substrate. These fluctuations are represented as a standard Brownian motion that can be added to the deterministic equation for the film thickness within the lubrication approximation. Here, we consider that while the noise term is white in time, it is coloured in space. This allows for the introduction of a finite correlation length in the description of the randomized intermolecular interaction. Together with the expected spatial periodicity of the flow, we find a dimensionless parameter, $\beta$, that accounts for the relative importance of the spatial correlation. We perform here the linear stability analysis (LSA) of the film under the influence of both terms, and find the corresponding power spectra for the amplitudes of the normal modes of the instability. We compare this theoretical result with the numerical simulations of the complete non-linear problem, and find a good agreement for early times. For late times, we find that the stochastic LSA predictions on the dominant wavelength remains basically valid. We also use the theoretical spectra to fit experimental data from a nanometric melted copper film, and find the corresponding times of the evolution as well as the values of the parameter, $\beta$