École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Finite element method. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Anisotropic damage law of evolution

Abstract: A formulation for anisotropic damage is established in the framework of the principle of strain equivalence The damage variable is still related to the surface density of microcracks and microvoids and, as its evolution is governed by the plastic strain, it is represented by a second order tensor and is orthotropic The coupling of damage with elasticity is written through a tensor on the deviatoric part of the energy and through a scalar taken as its trace on the hydrostatic part The kinetic law of damage evolution is an extension of the isotropic case Here, the principal components of the damage rate tensor are proportional to the absolute value of principal components of the plastic strain rate tensor and are a nonlinear function of the effective elastic strain energy The proposed damage evolution law does not introduce any other material parameter Several series of experiments on metals give a good validation of this theory The coupling of damage with plasticity and the quasi-unilateral conditions of partial closure of microcracks naturally derive from the concept of effective stress Finally, a study of strain localization makes it possible to determine the critical value of the damage at mesocrack initiation

A Weak Lensing Study of X-ray Groups in the Cosmos Survey: Form and Evolution of the Mass-Luminosity Relation

Abstract: Measurements of X-ray scaling laws are critical for improving cosmological constraints derived with the halo mass function and for understanding the physical processes that govern the heating and cooling of the intracluster medium. In this paper, we use a sample of 206 X-ray-selected galaxy groups to investigate the scaling relation between X-ray luminosity (L_X) and halo mass (M_(200)) where M_(200) is derived via stacked weak gravitational lensing. This work draws upon a broad array of multi-wavelength COSMOS observations including 1.64 degrees^2 of contiguous imaging with the Advanced Camera for Surveys to a limiting magnitude of I_(F814W) = 26.5 and deep XMM-Newton/Chandra imaging to a limiting flux of 1.0 × 10^(–15) erg cm6(–2) s^(–1) in the 0.5-2 keV band. The combined depth of these two data sets allows us to probe the lensing signals of X-ray-detected structures at both higher redshifts and lower masses than previously explored. Weak lensing profiles and halo masses are derived for nine sub-samples, narrowly binned in luminosity and redshift. The COSMOS data alone are well fit by a power law, M_(200) (L_X)^α, with a slope of α = 0.66 ± 0.14. These results significantly extend the dynamic range for which the halo masses of X-ray-selected structures have been measured with weak gravitational lensing. As a result, tight constraints are obtained for the slope of the M-L_X relation. The combination of our group data with previously published cluster data demonstrates that the M-L_X relation is well described by a single power law, α = 0.64 ± 0.03, over two decades in mass, M_(200) ~ 10^(13.5)-10^(15.5) h^(–1)_72 M_☉. These results are inconsistent at the 3.7σ level with the self-similar prediction of α = 0.75. We examine the redshift dependence of the M-L_X relation and find little evidence for evolution beyond the rate predicted by self-similarity from z ~ 0.25 to z ~ 0.

s-Tetrazines as Building Blocks for New Functional Molecules and Molecular Materials

Abstract: 4. Physical Chemistry of Tetrazines 3303 4.1. Electrochemistry of Tetrazines 3303 4.2. Photophysical Properties of Simple Tetrazines 3305 4.3. Computational Chemistry on Tetrazines 3307 5. Applications of Tetrazines 3309 5.1. Energetic Materials from Tetrazines 3309 5.2. NLO-phores with Tetrazine 3309 5.3. Active Polymers Including Tetrazines 3309 5.4. Supermolecular Tetrazines and Supramolecular Applications 3310

Entropy Dissipation and Long-Range Interactions

Abstract: We study Boltzmann's collision operator for long-range interactions, i.e., without Grad's angular cut-off assumption. We establish a functional inequality showing that the entropy dissipation controls smoothness of the distribution function, in a precise sense. Our estimate is optimal, and gives a unified treatment of both the linear and the nonlinear cases. We also give simple and self-contained proofs of several useful results that were scattered in previous works. As an application, we obtain several helpful estimates for the Cauchy problem, and for the Landau approximation in plasma physics.