Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

Energy release rate and stress intensity factors in planar elasticity in presence of smooth cracks

Abstract: In this work we first analyze the singular behavior of the displacement u of a linearly elastic body in dimension 2 close to the tip of a smooth crack, extending the well-known results for straight fractures to general smooth ones. As conjectured by Griffith (Phys Eng Sci 221:163–198, 1921), u behaves as the sum of an $$H^{2}$$ -function and a linear combination of two singular functions whose profile is similar to the square root of the distance from the tip. The coefficients of the linear combination are the so called stress intensity factors. Afterwards, we prove the differentiability of the elastic energy with respect to an infinitesimal fracture elongation and we compute the energy release rate, enlightening its dependence on the stress intensity factors.

Determination of the Mechanical Properties of a Solid Elastic Medium from a Seismic Wave Propagation Using Two Statistical Estimators

Abstract: In this paper, we study an inverse problem consisting in the determination of the mechanical prop- erties of a layered solid elastic medium in contact with a fluid medium by measuring the variation of the pressure in the fluid while propagating a seismic/acoustic wave. The estimation of mechanical parameters of the solid is obtained from the simulation of a seismic wave propagation model governed by a system of par- tial differential equations. Two stochastic methods, Markov chain Monte Carlo with an accelerated version and simultaneous per- turbation stochastic approximation, are implemented and compared with respect to cost and accuracy.

A counterexample to the Cantelli conjecture through the Skorokhod embedding problem

Abstract: In this paper, we construct a counter-example to a question by Cantelli, asking whether there exists a non-constant positive measurable function $\varphi$ such that for i.i.d. r.v. $X,Y$ of law $\mN(0,1)$, the r.v. $X+\varphi(X)\cdot Y$ is also Gaussian. For the construction that we propose, we introduce a new tool, the Brownian mass transport: the mass is transported by Brownian particles that are stopped in a specific way. This transport seems to be interesting by itself, turning out to be related to the Skorokhod and Stefan problems.

Mass endomorphism, surgery and perturbations

Abstract: We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

Diffusions under a local strong Hörmander condition. Part II: tube estimates

Abstract: We study lower and upper bounds for the probability that a diffusion process in R^n remains in a tube around a skeleton path up to a fixed time. We assume that the diffusion coefficients σ_1 ,. .. , σ_d may degenerate but they satisfy a strong Hormander condition involving the first order Lie brackets around the skeleton of interest. The tube is written in terms of a norm which accounts for the non-isotropic structure of the problem: in a small time δ, the diffusion process propagates with speed √ δ in the direction of the diffusion vector fields σ_j and with speed δ = √ δ × √ δ in the direction of [σ_i , σ_j ]. The proof consists in a concatenation technique which strongly uses the lower and upper bounds for the density proved in the part I.