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.

Etude numérique de la résolution par équations intégrales de la diffraction multiple par des disques

Abstract: Dans cet expose, nous presenterons une nouvelle methode de resolution du probleme de diffraction multiple par des cylindres circulaires, en particulier dans le cas ou la longueur d'ondes est petite devant la taille caracteristique des cylindres. En effet, il est bien connu que ce regime induit d'importantes difficultes numeriques, notamment parce qu'il conduit a la resolution de systemes lineaires de grande taille. Dans l'approche proposee, le champ diffracte est obtenu en resolvant une equation integrale via une projection dans une base de Fourier. Nous proposerons une methode de resolution robuste et efficace, obtenue en combinant une troncature judicieuse des series de Fourier et un solveur iteratif avec preconditonneur de type Krylov (GMRES) exploitant certaines proprietes remarquables de la matrice du systeme (Matrice Toeplitz). Enfin, nous presenterons des exemples de simulation numerique pour la diffraction multiple a haute frequence par des configurations aleatoires de disques.

Convergence of a normed eigenvector stochastic approximation process and application to online principal component analysis of a data stream

Abstract: Many articles were devoted to the problem of estimating recursively the eigenvectors and eigenvalues in decreasing order of the expectation of a random matrix using an i.i.d. sample of it. The present study makes the following contributions. The convergence of a normed process is proved under more general assumptions: the random matrices are not supposed i.i.d. and a new data mini-batch or all data until the current step are taken into account at each step without storing them; three types of processes are studied; this is applied to online principal component analysis of a data stream, assuming that data are realizations of a random vector Z whose expectation is unknown and must be estimated online, as well as possibly the metrics used when it depends on unknown characteristics of Z.

Modélisation de la croissance d'une tumeur après traitement par radiothérapie

Abstract: Nous avons propose dans cette these une nouvelle approche de modelisation des reponses cellulaire et tumorale durant la radiotherapie. Cette modelisation est fondee sur les chaines de Markov. Elle se situe dans le cadre de la theorie de cible qui suppose qu'il existe dans la cellule des regions sensibles appelees cibles, qui doivent toutes etre desactivees pour tuer la cellule. Un premier travail est consiste a proposer un modele a temps discret en tenant compte non seulement des phases de reparations cellulaires entre les fractions de dose mais egalement de l'heterogeneite des dommages cellulaires. Nous avons ensuite propose un modele stochastique de la duree de vie cellulaire. Cette modelisation fut egalement etendue a une population de cellules et a permis d'etablir de nouvelles expressions des probabilites d'eﰓcacite et de complication therapeutique. Nos derniers travaux portent sur le developpement d'un modele de type chaine de Markov a temps continu qui pourrait etre applique aux reponses des tumeurs traitees par la therapie photodynamique.

Numerical Study of Solutions of the 3D Generalized Kadomtsev-Petviashvili Equations for Long Times

Abstract: From a spectral method combined with a predictor-corrector scheme, we numerically study the behavior in time of solutions of the three-dimensional generalized Kadomtsev-Petviashvili equations. In a systematic way, the dispersion, the blow-up in finite time, the solitonic behavior and the transverse instabilities are numerically inspected.

Study of a system for the isothermal separation of components in a binary alloy with change of phase

Abstract: An isothermal model describing the separation of the components of a binary metallic alloy is considered. A process of phase transition is also assumed to occur in the solder; hence, the state of the material is described by two order parameters, i.e. the concentration c of the first component and the phase field ϕ. A physical derivation is provided starting from energy balance considerations. The resulting system of PDEs consists of a rather regular second-order parabolic equation for ϕ coupled with a fourth-order relation of Cahn-Hilliard type for c with constraint and solution-dependent mobility. Global existence of solutions is proved and several regularity properties are discussed under more restrictive assumptions on the physical parameters. Continuous dependence on data is shown in a special case. An asymptotic analysis of the model is also performed, yielding at the limit step a coupling of the original phase field equation with a Stefan-like system for c.