On the log-Sobolev constant of log-concave measures

It is well known that a log-Sobolev inequality implies sub-gaussian decay of the tails. In the spirit of the KLS conjecture, we investigate whether this implication can be reversed under a log-concavity assumption. In the general setting, we improve on a result of Bobkov, establishing the best dimension dependent bound on the log-Sobolev constant of subgaussian log-concave measures, and we investigate some special cases

Fatigue crack growth in thin notched woven glass composites under tensile loading. Part I: experimental

Helicopter blades are made of composite materials mainly loaded in fatigue and have normally relatively thin skins. A through-the-thickness crack could appear in these skins. The aim of this study is to characterize the through-the-thickness crack propagation due to fatigue in thin woven glass fabric laminates. A technological test specimen is developed to get closer to the real loading conditions acting on these structures. An experimental campaign is undertaken which allows evaluating crack growth rates in several laminates. The crack path is linked through microscopic investigations to specify damage in woven plies. Crack initiation duration influence on experimental results is also underlined

Influence of woven ply degradation on fatigue crack growth in thin notched composites under tensile loading

This paper deals with the fatigue of the through the-thickness crack propagation in thin notched composite laminates made of two glass woven plies. It highlights the different crack growths between warp and weft directions of the woven ply. Experimental results show a decrease of the crack growth rate per cycle with the increase of the crack initiation time. Moreover, it has been shown that it is necessary to take into account the fatigue damage of the woven plies in term of loss of rigidity in the initiation phase. The fatigue crack growth rates are then quantified using Paris law type equations and linear elastic fracture mechanics (LEFM)

Fatigue crack growth in thin notched woven glass composites under tensile loading. Part II: modelling

Fatigue propagation of a through-the-thickness crack in thin woven glass laminates is difficult to model when using homogeneous material assumption. Crack growth depends on both the fatigue behaviour of the fibres and of the matrix, these two phenomena occurring at different time and space scales. The developed finite element model is based on the architecture of the fabric and on the fatigue behaviours of the matrix and the fibre, even if the pure resin and fibre behaviours are not used. That thus limits the physical meaning of this model. Basically, the objective of this simulation is to illustrate and to confirm proposed crack growth mechanism. The fatigue damage matrix is introduced with user spring elements that link the two fibre directions of the fabric. Fibre fatigue behaviour is based on the S-N curves. Numerical results are compared to experimental crack growth rates and observed damage in the crack tip. Relatively good agreement between predictions and experiments was found

Positive solutions for large random linear systems

Consider a large linear system where $A_n$ is a $n\times n$ matrix with independent real standard Gaussian entries, $\boldsymbol{1}_n$ is a $n\times 1$ vector of ones and with unknown the $n\times 1$ vector $\boldsymbol{x}_n$ satisfying$$\boldsymbol{x}_n = \boldsymbol{1}_n +\frac 1{\alpha_n\sqrt{n}} A_n \boldsymbol{x}_n\, .$$We investigate the (componentwise) positivity of the solution $\boldsymbol{x}_n$ depending on the scaling factor $\alpha_n$ as the dimension $n$ goes to $\infty$. We prove that there is a sharp phase transition at the threshold $\alpha^*_n =\sqrt{2\log n}$: below the threshold ($\alpha_n\ll \sqrt{2\log n}$), $\boldsymbol{x}_n$ has negative components with probability tending to 1 while above ($\alpha_n\gg \sqrt{2\log n}$), all the vector's components are eventually positive with probability tending to 1. At the critical scaling $\alpha^*_n$, we provide a heuristics to evaluate the probability that $\boldsymbol{x}_n$ is positive.Such linear systems arise as solutions at equilibrium of large Lotka-Volterra systems of differential equations, widely used to describe large biological communities with interactions such as foodwebs for instance. In the domaine of positivity of the solution $\boldsymbol{x}_n$, that is when $\alpha_n\gg \sqrt{2\log n}$, we establish that the Lotka-Volterra system of differential equations whose solution at equilibrium is precisely \x_n is stable in the sense that its jacobian$${\mathcal J}(\boldsymbol{x}_n) = \mathrm{diag}(\boldsymbol{x}_n)\left(-I_n + \frac {A_n}{\alpha_n\sqrt{n}}\right)$$has all its eigenvalues with negative real part with probability tending to one.Our results shed a new light and complement the understanding of feasibility and stability issues for large biological communities with interaction

Le retour du mythe en modernité

In seinem US-amerikanischen Exil musste Cassirer zugeben, dass der Mythos in der Moderne nicht verschwunden war, wie er dies geglaubt und gehofft hatte. Der Mythos hatte im Gegenteil in Europa die Vernunft besiegt. Diese Feststellung brachte ihn dazu, The Myth of the State zu schreiben. In diesem posthum erschienenen Buch kritisiert Cassirer die modernen politischen Mythen, die wie Kriegswaffen eingesetzt werden. In einem wenig bekannten Text, den er auch während der Exilzeit verfasst hatte, musste er sich allerdings eingestehen, dass der Mensch nicht nur ein „rationales Lebewesen“ ist, wie Aristoteles es betonte, sondern auch ein „mythisches Lebewesen“, und dass er dies auch bleibt.Dans son exil américain, Cassirer dut admettre que le mythe n’avait pas disparu en modernité, comme il l’avait cru et souhaité, mais qu’il avait fini, au contraire, par triompher de la raison en Europe. Ce constat l’amena à rédiger The Myth of the State. Cassirer dénonce dans cet ouvrage paru de manière posthume les mythes politiques modernes qui sont utilisés comme des armes de guerre. Dans un texte moins connu également rédigé en exil, il doit toutefois admettre que l’homme n’est pas uniquement un « animal rationnel », comme l’affirmait Aristote, mais également un « animal mythique », et qu’il le demeure.During his American exile, Cassirer had to admit that myth in modernity had not disappeared, as he had believed and hoped, but that it had, on the contrary, ended up triumphing over reason in Europe. This observation led him to write The Myth of the State. In this posthumous book, Cassirer criticizes the modern political myths, which are used as weapons of war. In a less well-known text, which he also wrote during the exile period, he must concede the fact, however, that a human being is and still remains not only a “rational animal”, as Aristotle believed, but also a “mythical animal”

Study of the fatigue crack growth in thin composite skins made of woven plies

Helicopter blades are made of composite sandwich materials mainly loaded in fatigue. Normally, they have relatively thin skins. A through-the-thickness crack could appear in these coatings. The aim of this study is to characterize the through-the-thickness crack propagation in fatigue in thin woven glass fabric laminates. A specific fatigue test is developed so that these structures parts can undergo real stress conditions. A wide experimental campaign is undertaken which allows stating crack growth rates in several laminates. The propagation path is linked through microscopic investigations to specific damages of woven plies. Crack initiation duration influence on experimental results is also underlined. The finite element modelling is based on the architecture of the fabric and on the fatigue behaviours of the matrix and the fibre. The fatigue damage matrix is introduced with user spring elements that link the two fibres directions of the fabric. The glass fibre fatigue behaviour is based on S-N curves. Numerical results are compared to measured crack growth rates levels and observed damages in the crack tip

Migration et républicanisme en Allemagne

L’Allemagne, devenue après-guerre un pays d’immigration de main-d’œuvre, a engagé dans les années 1980 un débat sur l’élaboration d’un nouveau modèle d’intégration. Soumis au poids d’un passé culturaliste, à l’héritage d’un Code de la nationalité restrictif et aux peurs d’une “culture de référence” imaginaire menacée par le multiculturalisme, le modèle républicain des politiques et des juges hésite. Mais le républicanisme des intellectuels, ouvert à la diversité sur le modèle anglo-saxon de la société civile, s’impose peu à peu. Aujourd’hui, la culture nationale s’affirme comme un ensemble de valeurs plurielles et malléables permettant l’intégration des étrangers