Model reduction in multiscale problems focusing on polar ice (James K. Knowles Lecture).
Résumé
Solid materials are, by nature or by construction, multiscale objets. Polycrystalline polar ice is a typical example of such a material with many different scales and will be used to motivate this talk. Understanding the interplay between features at different scales is a challenging intellectual problem, one of those that Jim Knowles would certainly have encouraged young researchers to address, most probably opening the way himself. In many cases it also sheds light on specific aspects of material behavior. Unfortunately, the truth is that there exists no rigorous scale-decoupling in nonlinear problems and the practical answer to such problems involves approximations which are often contradicted by experimental evidence. This talk will survey some recent improvements to these approximations, accounting for instance for field fluctuations in mean-field theories, or using model-reduction techniques inspired by observations made possible by recent progress in experimental techniques or numerical simulations.