XFEM based fictitious domain method for linear elasticity model with crack

Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid re-meshing, we propose a new finite element approach for the numerical simulation of discontinuities of displacements generated by cracks inside elastic media. The approach is based on a fictitious domain method originally developed for Dirichlet conditions for the Poisson problem and for the Stokes problem, which is adapted to the Neumann boundary conditions of crack problems. The crack is represented by level-set functions. Numerical tests are made with a mixed formulation to emphasize the accuracy of the method, as well as its robustness with respect to the geometry enforced by a stabilization technique. In particular an inf-sup condition is theoretically proven for the latter. A realistic simulation with a uniformly pressurized fracture inside a volcano is given for illustrating the applicability of the method.Comment: 27 pages, 15 figure

Local Convex Hull support and boundary estimation

International audienceIn this paper we introduce a new estimator for the support of a multivariatedensity. It is defined as a union of convex hulls of observations contained in balls of fixed radius.We study the asymptotic behavior of this ``local convex hull" for the estimation of the support and its boundary.When the support is smooth enough, the proposed estimator is proved to be, eventually almost surely, homeomorphic to the support.Numerical simulations on both simulated and real data illustrate the performance of our estimator

Lendemains économiques de la guerre en Irak : un "remake" de 1991 ?

Depuis le début de l’attaque américaine contre l’Irak, la perspective d’une reprise économique une fois le conflit terminé est de plus en plus évoquée. Si reprise il y a, celle-ci risque cependant d’être lente et graduelle !

Nominal wage rigidities in a new Keynesian model with frictional unemployment

In this paper, we propose a search and matching model with nominal stickiness à la Calvo in the wage bargaining. We analyze the properties of the model, first, in the context of a typical real business cycle model driven by stochastic productivity shocks and second, in a fully specified monetary DSGE model with various real and nominal rigidities and multiple shocks. The model generates realistic statistics for the important labor market variablesDSGE, Search and Matching, Nominal Wage Rigidity, Monetary Policy

A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions

In this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form ∂ny + f(y)=0 are considered. The problem leads to an analysis of a special type of nonlinear null controllability problem. A sharp study of the linear case and a later application of an appropriate fixed point argument constitute the scheme of the proof of the main result. The boundary conditions we are dealing with lead us to seek a fixed point, and thus also control functions, in certain H¨older spaces. The main strategy in this paper is the construction of controls with H¨olderian regularity starting from L2-controls in the linear case. Sufficient regularity in the data and appropriate assumptions on the right-hand side term ξ of the equation are required.Ministerio de Educación y Cienci

Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity

In this paper we consider a semilinear heat equation (in a bounded domain Ω of IRN ) with a nonlinearity that has a superlinear growth at infinity. We prove the existence of a control, with support in an open set ω ⊂ Ω, that insensitizes the L2−norm of the observation of the solution in another open subset O ⊂ Ω when ω ∩ O 6= ∅, under suitable assumptions on the nonlinear term f(y) and the right hand side term ξ of the equation. The proof, involving global Carleman estimates and regularizing properties of the heat equation, relies on the sharp study of a similar linearized problem and an appropriate fixed-point argument. For certain superlinear nonlinearities, we also prove an insensitivity result of a negative nature. The crucial point in this paper is the technique of construction of L r–controls (r large enough) starting from insensitizing controls in L 2.Ministerio de Educación y Cienci

Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient

In this paper we present two results on the existence of insensitizing controls for a heat equation in a bounded domain of IRN . We first consider a semilinear heat equation involving gradient terms with homogeneous Dirichlet boundary conditions. Then a heat equation with a nonlinear term F(y) and linear boundary conditions of Fourier type is considered. The nonlinearities are assumed to be globally Lipschitz-continuous. In both cases, we prove the existence of controls insensitizing the L2−norm of the observation of the solution in an open subset O of the domain, under suitable assumptions on the data. Each problem boils down to a special type of null controllability problem. General observability inequalities are proved for linear systems similar to the linearized problem. The proofs of the main results in this paper involve such inequalities and rely on the study of these linear problems and appropriate fixed point arguments.Ministerio de Ciencia y Tecnologí

Tracking dynamic interactions between structural and functional connectivity : a TMS/EEG-dMRI study

Transcranial magnetic stimulation (TMS) in combination with neuroimaging techniques allows to measure the effects of a direct perturbation of the brain. When coupled with high-density electroencephalography (TMS/hd-EEG), TMS pulses revealed electrophysiological signatures of different cortical modules in health and disease. However, the neural underpinnings of these signatures remain unclear. Here, by applying multimodal analyses of cortical response to TMS recordings and diffusion magnetic resonance imaging (dMRI) tractography, we investigated the relationship between functional and structural features of different cortical modules in a cohort of awake healthy volunteers. For each subject, we computed directed functional connectivity interactions between cortical areas from the source-reconstructed TMS/hd-EEG recordings and correlated them with the correspondent structural connectivity matrix extracted from dMRI tractography, in three different frequency bands (alpha, beta, gamma) and two sites of stimulation (left precuneus and left premotor). Each stimulated area appeared to mainly respond to TMS by being functionally elicited in specific frequency bands, that is, beta for precuneus and gamma for premotor. We also observed a temporary decrease in the whole-brain correlation between directed functional connectivity and structural connectivity after TMS in all frequency bands. Notably, when focusing on the stimulated areas only, we found that the structure-function correlation significantly increases over time in the premotor area controlateral to TMS. Our study points out the importance of taking into account the major role played by different cortical oscillations when investigating the mechanisms for integration and segregation of information in the human brain