ERC Starting Grant QUANTHOM 2014--2019 Quantitative methods in stochastic homogenization |
Home Research Publications and Preprints Cours ERC QUANTHOM |
Description of the project The purpose of this project is to develop a quantitative theory of stochastic homogenization. Primary applications concern the analysis and computations for random models in physics and materials science, such as numerical methods for diffusion in heterogeneous media and the mathematical derivation of nonlinear elasticity theory from polymer-chain networks models. The mathematical fields of concern are:
The first part is devoted to the development of a quantitative theory of stochastic homogenization. The far-reaching goal is to quantitatively relate the statistics of the solution of a PDE with random coefficients to the statistics of its coefficients for the largest class of PDEs and coefficients possible. The prototypical equation considered is a linear elliptic equation in divergence form. The second part is devoted to the development and the analysis of numerical methods to solve PDEs with rapidly oscillating coefficients, which are consistent and optimal with respect to the quantitative stochastic homogenization theory. The third part is devoted to the mathematical derivation of nonlinear elasticity theory from polymer-chain networks models. The aim is threefold:
Scientific results See Publications and Preprints Team and collaborators Coordinator of the project:
Events Here is a list of events organized or sponsored by the ERC project. Workshop on Relaxation, homogenization and dimensional reduction in hyperelasticity Organized by Gilles Francfort (Paris 13), Martin Kruzik (Prague), and Antoine Gloria Université Paris-Nord, March 25-27, 2014 Minisymposium on stochastic homogenization at EQUADIFF 2015 Organized by Scott Armstrong (Paris Dauphine) and Antoine Gloria Université Lyon, July 6-7, 2015 Workshop on Multiscale problems and relaxation in nonlinear elasticity Organized by Antoine Gloria and Stefan Neukamm (Dresden). TU Dresden (Department of Mathematics), July 4–5, 2017. |