Bonds, lone pairs, and shells probed by means of on-top dynamical correlations

The Electron Localization Function (ELF) by Becke and Edgecombe [J. Chem. Phys. {\bf 92}, 5397 (1990)] is routinely adopted as a descriptor of atomic shells and covalent bonds. Since the ELF and its related quantities find useful exploitation also in the construction of modern density functionals, the interest in complementing the ELF is linked to both the quests of improving electronic structure descriptors and density functional approximations. The ELF uses information which is available by considering parallel-spin electron pairs in single-reference many-body states. In this work, we complement this construction with information obtained by considering antiparallel-spin pairs whose short-range correlations are modeled by a density functional approximation. As a result, the approach requires only a contained computational effort. Applications to a variety of systems show that, in this way, we gain a spatial description of the bond in H$_2$ (which is not available with the ELF) together with some trends not optimally captured by the ELF in other prototypical situations

ÉQUILIBRE ET POSSIBILITÉ DE CRISES DANS LE MODÈLE DE REPRODUCTION ÉLARGIE DE MARX

In the numerical examples used by Marx to study the reproduction of social capital, the economy reaches a steady growth path in only two periods. This surprising outcome has been interpreted by Marx‟s readers as a property of a model which excludes any sort of economic crisis. This paper shows that this is not the case. Depending on the proportion between sectors and on the accumulation rate in the sector producing the means of production, two kinds of crises can occur. Following a suggestion of Marx, we emphasize the analysis of the physical conditions of reproduction and, on such a basis, we determine the critical proportions beyond which a crisis occurs. If, as in Marx, commodities are exchanged at their labor value, the critical proportions will be changedDans les exemples numériques que Marx utilise pour étudier la reproduction du capital social, l‟économie atteint, dès la seconde période, un régime de croissance régulière. Ce résultat a surpris les lecteurs de Marx qui l‟ont interprété comme la propriété d‟un modèle qui exclut toute crise. On montre ici qu‟il n‟en est rien. Nous avons identifié deux formes de crise dont l‟occurrence dépend de la proportion entre les secteurs et du taux d‟accumulation du secteur qui produit les moyens de production. Suivant une suggestion de Marx, nous accordons une attention particulière à l‟analyse des conditions physiques de la reproduction, même si son schéma ne connaît que des quantités monétaires. Sur cette base, nous déterminons les proportions critiques au-delà desquelles une crise se produira. On montre que si, comme Marx l‟admet, les marchandises s‟échangent à leur valeur, les proportions critiques seront modifiées

ÉQUILIBRE ET POSSIBILITÉ DE CRISES DANS LE MODÈLE DE REPRODUCTION ÉLARGIE DE MARX

Dans les exemples numériques que Marx utilise pour étudier la reproduction du capital social, l‟économie atteint, dès la seconde période, un régime de croissance régulière. Ce résultat a surpris les lecteurs de Marx qui l‟ont interprété comme la propriété d‟un modèle qui exclut toute crise. On montre ici qu‟il n‟en est rien. Nous avons identifié deux formes de crise dont l‟occurrence dépend de la proportion entre les secteurs et du taux d‟accumulation du secteur qui produit les moyens de production. Suivant une suggestion de Marx, nous accordons une attention particulière à l‟analyse des conditions physiques de la reproduction, même si son schéma ne connaît que des quantités monétaires. Sur cette base, nous déterminons les proportions critiques au-delà desquelles une crise se produira. On montre que si, comme Marx l‟admet, les marchandises s‟échangent à leur valeur, les proportions critiques seront modifiées.Marx, reproduction, crises

High spectral resolution imaging of the dynamical atmosphere of the red supergiant Antares in the CO first overtone lines with VLTI/AMBER

We present high spectral resolution aperture-synthesis imaging of the red supergiant Antares (alpha Sco) in individual CO first overtone lines with VLTI/AMBER. The reconstructed images reveal that the star appears differently in the blue wing, line center, and red wing and shows an asymmetrically extended component. The appearance of the star within the CO lines changes drastically within one year, implying a significant change in the velocity field in the atmosphere. Our modeling suggests an outer atmosphere (MOLsphere) extending to 1.2--1.4 stellar radii with CO column densities of (0.5--1)x10^{20} cm^{-2} and a temperature of ~2000 K. While the velocity field in 2009 is characterized by strong upwelling motions at 20--30 km/s, it changed to strong downdrafts in 2010. On the other hand, the AMBER data in the continuum show only a slight deviation from limb-darkened disks and only marginal time variations. We derive a limb-darkened disk diameter of 37.38+/-0.06 mas and a power-law-type limb-darkening parameter of (8.7+/-1.6)x10^{-2} (2009) and 37.31+/-0.09 mas and (1.5+/-0.2)x10^{-1} (2010). We also obtain Teff = 3660+/-120 K and log L/Lsun = 4.88+/-0.23, which suggests a mass of 15+/-5 Msun with an age of 11-15 Myr. This age is consistent with the recently estimated age for the Upper Scorpius OB association. The properties of the outer atmosphere of Antares are similar to those of another well-studied red supergiant, Betelgeuse. The density of the extended outer atmosphere of Antares and Betelgeuse is higher than predicted by the current 3-D convection simulations by at least six orders of magnitude, implying that convection alone cannot explain the formation of the extended outer atmosphere.Comment: 18 pages, 16 figures, accepted for publication in Astronomy and Astrophysics, short discussion on the age of Antares and the Upper Scorpius OB association added, movies of the reconstructed images available at http://www.mpifr-bonn.mpg.de/staff/kohnaka

Relative Best Response Dynamics in Finite and Convex Network Games

Motivated by theoretical and experimental economics, we propose novel evolutionary dynamics for games on networks, called the h-Relative Best Response (h–RBR) dynamics, that mixes the relative performance considerations of imitation dynamics with the rationality of best responses. Under such a class of dynamics, the players optimize their payoffs over the set of strategies employed by a time–varying subset of their neighbors. As such, the h-RBR dynamics share the defining non–innovative characteristic of imitation based dynamics and can lead to equilibria that differ from classic Nash equilibria. We study the asymptotic behavior of the h–RBR dynamics for both finite and convex games in which the strategy spaces are discrete and compact, respectively, and provide preliminary sufficient conditions for finite–time convergence to a generalized Nash equilibrium

A quasi-Monte Carlo integration method applied to the computation of the Pollaczek integral

Nos remerciements à IEEE pour l'autorisation de mise à disposition du papier complet. © IEEE Copyright Notice : Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.International audienceThis paper presents an effective numeric method to compute Pollaczek integral. This integral is widely used in transmission-line theory when computing the mutual impedance between an overhead conductor and another overhead or underground conductor and the earth-return impedance of an underground cable. At first, we present mutual expressions proposed by Pollaczek and underline the numerical complexities that often lead to the adoption of alternative simplified methods. Then a brief review of the so called "quasi-Monte Carlo" integration method along with its advantages is given. Such an approach is then applied to compute numerically Pollaczek expressions. Comparison between our numerical procedure and an algorithm that has already been published proves both the procedure accuracy, one of its main advantages along with its ease of implementation, and its relatively low time consumption, independent of the input parameters. Finally, as an application example, quasi-Monte Carlo method is used to assess the adequacy, for several study cases, of the simplified formula by Lucca, which is a widely used approximate expression of interest

Monetary objectivity and physical objectivity in Marx's reproduction model

Marx étudie la reproduction élargie du capital social à l'aide d'exemples numériques. Ses schémas décrivent la reproduction de flux monétaires. Seuls sont connus les produits des quantités par les valeurs unitaires : valeurs du produit brut, de la masse salariale et du capital constant dans les deux secteurs. On montre que, si Marx part exclusivement de données de la circulation monétaire qui ne permettent de calculer ni les quantités relatives de biens produits et utilisés par les secteurs, ni leur valeur relative, son schéma fournit tous les éléments d'une étude des conditions physiques de la reproduction.Marx, reproduction, accumulation, crise