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Quantitative methods in stochastic homogenization

Ziel

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.

Wissenschaftliches Gebiet

Programm/Programme

Thema/Themen

Aufforderung zur Vorschlagseinreichung

ERC-2013-StG
Andere Projekte für diesen Aufruf anzeigen

Finanzierungsplan

ERC-SG - ERC Starting Grant

Gastgebende Einrichtung

UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6
EU-Beitrag
€ 360 284,73
Adresse
Place Jussieu 4
75252 PARIS
Frankreich

Auf der Karte ansehen
Aktivitätstyp
Higher or Secondary Education Establishments
Kontakt Verwaltung
Olivia Leroy (Mrs.)
Hauptforscher
Antoine Kenneth Florent Gloria (Prof.)
Links
Gesamtkosten
Keine Daten

Begünstigte (3)

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Letzte Aktualisierung: 25 Mai 2022

Mein Booklet

Permalink: https://cordis.europa.eu/project/id/335410/de

European Union, 2024