Two scenarios on a potential smoothness breakdown for the three-dimensional Navier-Stokes equations

In this paper we construct two families of initial data being arbitrarily large under any scaling-invariant norm for which their corresponding weak solution to the three-dimensional Navier-Stokes equations become smooth on either $[0,T_1]$ or $[T_2,\infty)$, respectively, where $T_1$ and $T_2$ are two times prescribed previously. In particular, $T_1$ can be arbitrarily large and $T_2$ can be arbitrarily small. Therefore, possible formation of singularities would occur after a very long or short evolution time, respectively. We further prove that if a large part of the kinetic energy is consumed prior to the first (possible) blow-up time, then the global-in-time smoothness of the solutions follows for the two families of initial data.Comment: 16 pages, no figures. Some typos have been correcte

Non-radial pulsations in the Be/X binaries 4U0115+63 and SAXJ2103.5+4545

The discovery of non-radial pulsations (NRP) in the Be/X binaries of the Magellanic Clouds (MC, eg. Fabrycky 2005, Coe et al. 2005, Schmidtke & Cowley 2005) provided a new approach to understand these complex systems, and, at the same time, favoured the synergy between two different fields: stellar pulsations and X-ray binaries. This breakthrough was possible thanks to the MACHO and OGLE surveys. However, in our Galaxy, only two Be/X have been reported to show NRP: GROJ2058+42 (Kiziloglu et al. 2007) and LSI+61 235 (Sarty et al. 2009). Our objective is to study the short-term variability of Galactic Be/X binaries, compare them to the Be/X of the MC and to the isolated Galactic Be observed with CoRoT and Kepler. We present preliminary results of two Be/X stars, namely 4U0115+63 and SAXJ2103.5+4545 showing multiperiodicity and periodicity respectively, most probably produced by non-radial pulsations.Comment: 2 pages, 2 figures, IAUS 272 "Active OB stars: structure, evolution, mass loss and critical limits" conference, Paris, July 2010, submitte

The Politics of Abstract Art. Forma 1 and the Italian Communist Party

Este artículo examina el papel del grupo de artistas abstractos Forma 1 en relación con la política cultural del Partido Comunista Italiano durante la posguerra, como ejemplo de los intentos de superar la dicotomía establecida en Italia entre arte abstracto y realismo socialista y producir una alternativa a la confrontación entre ambos discursos estéticos. Mientras los artistas realistas socialistas subrayaban la necesidad de expresar contenidos políticos explícitos con un estilo que asegurase su máxima legibilidad para una audiencia de masas, los artistas de Forma 1 argumentaban que la abstracción significaba una crítica de la representación pictórica que podía contribuir a la crítica de la ideología burguesa, armonizando de este modo el marxismo con los desarrollos artísticos más avanzados. El PCI, por su parte, basaba su política artística en amplias alianzas de artistas e intelectuales antifascistas, que cada vez eran más difíciles de mantener en el clima de creciente confrontación política y cultural que siguió a la II Guerra Mundial

Convergence to suitable weak solutions for a finite element approximation of the Navier-Stokes equations with numerical subgrid scale modeling

In this work we prove that weak solutions constructed by a variational multiscale method are suitable in the sense of Scheffer. In order to prove this result, we consider a subgrid model that enforces orthogonality between subgrid and finite element components. Further, the subgrid component must be tracked in time. Since this type of schemes introduce pressure stabilization, we have proved the result for equal-order velocity and pressure finite element spaces that do not satisfy a discrete inf-sup condition.Comment: 23 pages, no figure

Using quality models in software package selection

The growing importance of commercial off-the-shelf software packages requires adapting some software engineering practices, such as requirements elicitation and testing, to this emergent framework. Also, some specific new activities arise, among which selection of software packages plays a prominent role. All the methodologies that have been proposed recently for choosing software packages compare user requirements with the packages' capabilities. There are different types of requirements, such as managerial, political, and, of course, quality requirements. Quality requirements are often difficult to check. This is partly due to their nature, but there is another reason that can be mitigated, namely the lack of structured and widespread descriptions of package domains (that is, categories of software packages such as ERP systems, graphical or data structure libraries, and so on). This absence hampers the accurate description of software packages and the precise statement of quality requirements, and consequently overall package selection and confidence in the result of the process. Our methodology for building structured quality models helps solve this drawback.Peer ReviewedPostprint (published version

Participation of Married Women in the Labour Market and the 'Added Worker Effect' in Europe

In this paper, we estimate labour participation equations for married women for eleven European countries, using data from the European Community Household Panel corresponding to the years 1994, 1995 and 1996. The main objective of our study is to test whether the 'added worker effect' holds. From our results it can be concluded that the labour market participation of the married woman basically depends on her personal and family characteristics, her non-wage income and her potential earnings. In only a few countries does the participation of married women seem to be related to the work status of the husband. However, the consistently significant and negative effect of the woman's non-wage income (basically the husband's wage) prevents the 'added worker effect' from being completely rejected as a hypothesis. It seems, therefore, that female labour market participation continues to have a 'secondary' role in the family sphere in some European countries.Female participation ; added worker effect

On the approximation of turbulent fluid flows by the Navier-Stokes-α\alpha equations on bounded domains

The Navier-Stokes-$\alpha$ equations belong to the family of LES (Large Eddy Simulation) models whose fundamental idea is to capture the influence of the small scales on the large ones without computing all the whole range present in the flow. The constant $\alpha$ is a regime flow parameter that has the dimension of the smallest scale being resolvable by the model. Hence, when $\alpha=0$, one recovers the classical Navier-Stokes equations for a flow of viscous, incompressible, Newtonian fluids. Furthermore, the Navier-Stokes-$\alpha$ equations can also be interpreted as a regularization of the Navier-Stokes equations, where $\alpha$ stands for the regularization parameter. In this paper we first present the Navier-Stokes-$\alpha$ equations on bounded domains with no-slip boundary conditions by means of the Leray regularization using the Helmholtz operator. Then we study the problem of relating the behavior of the Galerkin approximations for the Navier-Stokes-$\alpha$ equations to that of the solutions of the Navier-Stokes equations on bounded domains with no-slip boundary conditions. The Galerkin method is undertaken by using the eigenfunctions associated with the Stokes operator. We will derive local- and global-in-time error estimates measured in terms of the regime parameter $\alpha$ and the eigenvalues. In particular, in order to obtain global-in-time error estimates, we will work with the concept of stability for solutions of the Navier-Stokes equations in terms of the $L^2$ norm