Objective 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. Fields of science natural scienceschemical sciencespolymer sciencesnatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsnumerical analysissocial scienceslaw Programme(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) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2013-StG See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Coordinator UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6 Address Place jussieu 4 75252 Paris France See on map Activity type Higher or Secondary Education Establishments Administrative Contact Olivia Leroy (Mrs.) Principal investigator Antoine Kenneth Florent Gloria (Prof.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution € 360 284,73 Beneficiaries (3) Sort alphabetically Sort by EU Contribution Expand all Collapse all UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6 France EU contribution € 360 284,73 Address Place jussieu 4 75252 Paris See on map Activity type Higher or Secondary Education Establishments Administrative Contact Olivia Leroy (Mrs.) Principal investigator Antoine Kenneth Florent Gloria (Prof.) Links Contact the organisation Opens in new window Website Opens in new window INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE Participation ended France EU contribution € 165 562,74 Address Domaine de voluceau rocquencourt 78153 Le chesnay cedex See on map Region Ile-de-France Ile-de-France Yvelines Activity type Research Organisations Administrative Contact Mohamed Riffi Asri (Mr.) Links Contact the organisation Opens in new window Website Opens in new window UNIVERSITE LIBRE DE BRUXELLES Belgium EU contribution € 517 324,53 Address Avenue franklin roosevelt 50 1050 Bruxelles / brussel See on map Region Région de Bruxelles-Capitale/Brussels Hoofdstedelijk Gewest Région de Bruxelles-Capitale/ Brussels Hoofdstedelijk Gewest Arr. de Bruxelles-Capitale/Arr. Brussel-Hoofdstad Activity type Higher or Secondary Education Establishments Administrative Contact Anastasios Perimenis (Mr.) Links Contact the organisation Opens in new window Website Opens in new window
