CORDIS
EU research results

CORDIS

English EN

Quantitative methods in stochastic homogenization

Project information

Grant agreement ID: 335410

Status

Closed project

  • Start date

    1 February 2014

  • End date

    31 August 2019

Funded under:

FP7-IDEAS-ERC

  • Overall budget:

    € 1 043 172

  • EU contribution

    € 1 043 172

Hosted by:

UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6

France

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.

Principal Investigator

Antoine Kenneth Florent Gloria (Prof.)

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

INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE

France

EU Contribution

€ 165 562,74

UNIVERSITE LIBRE DE BRUXELLES

Belgium

EU Contribution

€ 517 324,53

Project information

Grant agreement ID: 335410

Status

Closed project

  • Start date

    1 February 2014

  • End date

    31 August 2019

Funded under:

FP7-IDEAS-ERC

  • Overall budget:

    € 1 043 172

  • EU contribution

    € 1 043 172

Hosted by:

UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6

France