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Quantitative methods in stochastic homogenization

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.

Call for proposal

ERC-2013-StG
See other projects for this call

Host institution

UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6
Address
Place Jussieu 4
75252 Paris
France
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 360 284,73
Principal investigator
Antoine Kenneth Florent Gloria (Prof.)
Administrative Contact
Olivia Leroy (Mrs.)

Beneficiaries (3)

UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6
France
EU contribution
€ 360 284,73
Address
Place Jussieu 4
75252 Paris
Activity type
Higher or Secondary Education Establishments
Principal investigator
Antoine Kenneth Florent Gloria (Prof.)
Administrative Contact
Olivia Leroy (Mrs.)
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
Activity type
Research Organisations
Administrative Contact
Mohamed Riffi Asri (Mr.)
UNIVERSITE LIBRE DE BRUXELLES
Belgium
EU contribution
€ 517 324,53
Address
Avenue Franklin Roosevelt 50
1050 Bruxelles
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Anastasios Perimenis (Mr.)