Objetivo This proposal deals with the development of quantitative tools in stochastic homogenization, and their applications to materials science. Three main challenges will be addressed.First, a complete quantitative theory of stochastic homogenization of linear elliptic equations will be developed starting from results I recently obtained on the subject combining tools originally introduced for statistical physics, such as spectral gap and logarithmic Sobolev inequalities, with elliptic regularity theory. The ultimate goal is to prove a central limit theorem for solutions to elliptic PDEs with random coefficients.The second challenge consists in developing an adaptive multiscale numerical method for diffusion in inhomogeneous media. Many powerful numerical methods were introduced in the last few years, and analyzed in the case of periodic coefficients. Relying on my recent results on quantitative stochastic homogenization, I have made a sharp numerical analysis of these methods, and introduced more efficient variants, so that the three academic examples of periodic, quasi-periodic, and random stationary diffusion coefficients can be dealt with efficiently. The emphasis of this challenge is put on the adaptivity with respect to the local structure of the diffusion coefficients, in order to deal with more complex examples of interest to practitioners.The last and larger objective is to make a rigorous connection between the continuum theory of nonlinear elastic materials and polymer-chain physics through stochastic homogenization of nonlinear problems and random graphs. Analytic and numerical preliminary results show the potential of this approach. I plan to derive explicit constitutive laws for rubber from polymer chain properties, using the insight of the first two challenges. This requires a good understanding of polymer physics in addition to qualitative and quantitative stochastic homogenization. Ámbito científico natural scienceschemical sciencespolymer sciencesnatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsnumerical analysissocial scienceslaw Programa(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Tema(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Convocatoria de propuestas ERC-2013-StG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-SG - ERC Starting Grant Institución de acogida UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6 Aportación de la UE € 360 284,73 Dirección Place Jussieu 4 75252 PARIS Francia Ver en el mapa Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Olivia Leroy (Mrs.) Investigador principal Antoine Kenneth Florent Gloria (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (3) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6 Francia Aportación de la UE € 360 284,73 Dirección Place Jussieu 4 75252 PARIS Ver en el mapa Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Olivia Leroy (Mrs.) Investigador principal Antoine Kenneth Florent Gloria (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE La participación finalizó Francia Aportación de la UE € 165 562,74 Dirección DOMAINE DE VOLUCEAU ROCQUENCOURT 78153 Le Chesnay Cedex Ver en el mapa Región Ile-de-France Ile-de-France Yvelines Tipo de actividad Research Organisations Contacto administrativo Mohamed Riffi Asri (Mr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos UNIVERSITE LIBRE DE BRUXELLES Bélgica Aportación de la UE € 517 324,53 Dirección AVENUE FRANKLIN ROOSEVELT 50 1050 Bruxelles / Brussel Ver en el mapa Región Région de Bruxelles-Capitale/Brussels Hoofdstedelijk Gewest Région de Bruxelles-Capitale/ Brussels Hoofdstedelijk Gewest Arr. de Bruxelles-Capitale/Arr. Brussel-Hoofdstad Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Anastasios Perimenis (Mr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
