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.

Hyperelastic constitutive model for rubber-like materials based on the first Seth strain measures invariant

Abstract: The mechanical behaviour of isotropic and incompressible vulcanized natural rubbers (NR's) and that of quasi-incompressible carbon black filled vulcanized natural rubbers (NR 70) are considered both theoretically and experimentally. We start by generalising the neo-Hookean model to derive an original form of the strain energy density function (W). W satisfies the hypothesis of the Valanis–Landel function, which allows reducing the number of needed experimental tests to identify the parameters of the model. In the present study, in the order to identity the analytical form of W, we undertake only simple tension tests. The two-dimensional field of in-plane homogeneous displacements is determined here using a home-developed image analysis cross-correlation technique. Our model is also identified using results taken from the literature in the case of (NR's) for different types of solicitations, including simple tension, equibiaxial tension and pure shear deformation. Comparison of numerical results with the experimental data indicates that the present model can characterise the hyperelastic behaviour of NR's and that of NR 70 for all the tested modes of deformation. Moreover, it seems to be valid over a wide range of deformation intervals.

Propagation of Gevrey regularity for solutions of the Boltzmann equation for Maxwellian molecules

Abstract: We prove that Gevrey regularity is propagated by the Boltzmann equation with Maxwellian molecules, with or without angular cut-off. The proof relies on the Wild expansion of the solution to the equation and on the characterization of Gevrey regularity by the Fourier transform.

On a variant of Korn's inequality arising in statistical mechanics

Abstract: We state and prove a Korn-like inequality for a vector field in a bounded open set of , satisfying a tangency boundary condition. This inequality, which is crucial in our study of the trend towards equilibrium for dilute gases, holds true if and only if the domain is not axisymmetric. We give quantitative, explicit estimates on how the departure from axisymmetry affects the constants; a Monge–Kantorovich minimization problem naturally arises in this process. Variants in the axisymmetric case are briefly discussed.

Affine plane curve evolution: a fully consistent scheme

Abstract: We present an accurate numerical scheme for the affine plane curve evolution and its morphological extension to grey-level images. This scheme is based on the iteration of a nonlocal, fully affine invariant and numerically stable operator, which can be exactly computed on polygons. The properties of this operator ensure that a few iterations are sufficient to achieve a very good accuracy, unlike classical finite difference schemes that generally require a lot of iterations. Convergence results are provided, as well as theoretical examples and experiments.

Model checking probabilistic timed automata with one or two clocks

Abstract: Probabilistic timed automata are an extension of timed automata with discrete probability distributions.We consider model-checking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic model-checking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIME-complete for one clock probabilistic timed automata, and are EXPTIME-complete for probabilistic timed automata with two clocks. Secondly, we show that the model-checking problem for the probabilistic timed temporal logic PTCTL is EXPTIME-complete for one clock probabilistic timed automata. However, the corresponding model-checking problem for the subclass of PTCTL which does not permit both (1) punctual timing bounds, which require the occurrence of an event at an exact time point, and (2) comparisons with probability bounds other than 0 or 1, is PTIME-complete.