Objectif Many complex phenomena in the sciences are described by nonlinear partial differential equations, the solutions of which exhibit oscillations and concentration effects on multiple temporal or spatial scales. Our aim is to use methods from applied analysis to contribute to the understanding of the interplay of effects on different scales. The central question is to determine those quantities on the microscale which are needed to for the correct description of the macroscopic evolution.We aim to develop a mathematical framework for analyzing and modeling coupled systems with multiple scales. This will include Hamiltonian dynamics as well as different types of dissipation like gradient flows or rate-independent dynamics. The choice of models will be guided by specific applications in material modeling (e.g. thermoplasticity, pattern formation, porous media) and optoelectronics (pulse interaction, Maxwell-Bloch systems, semiconductors, quantum mechanics). The research will address mathematically fundamental issues like existence and stability of solutions but will mainly be devoted to the modeling of multiscale phenomena in evolution systems. We will focus on systems with geometric structures, where the dynamics is driven by functionals. Thus, we can go much beyond the classical theory of homogenization and singular perturbations. The novel features of our approach are- the combination of different dynamical effects in one framework,- the use of geometric and metric structures for coupled partial differential equations,- the exploitation of Gamma-convergence for evolution systems driven by functionals. Champ scientifique natural sciencesphysical scienceselectromagnetism and electronicsoptoelectronicsnatural sciencesphysical sciencesquantum physicsnatural sciencesphysical scienceselectromagnetism and electronicssemiconductivitynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Appel à propositions ERC-2010-AdG_20100224 Voir d’autres projets de cet appel Régime de financement ERC-AG - ERC Advanced Grant Institution d’accueil FORSCHUNGSVERBUND BERLIN EV Contribution de l’UE € 1 390 000,00 Adresse RUDOWER CHAUSSEE 17 12489 Berlin Allemagne Voir sur la carte Région Berlin Berlin Berlin Type d’activité Research Organisations Contact administratif Volker Knoll-Hoyer (Mr.) Chercheur principal Alexander Mielke (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire FORSCHUNGSVERBUND BERLIN EV Allemagne Contribution de l’UE € 1 390 000,00 Adresse RUDOWER CHAUSSEE 17 12489 Berlin Voir sur la carte Région Berlin Berlin Berlin Type d’activité Research Organisations Contact administratif Volker Knoll-Hoyer (Mr.) Chercheur principal Alexander Mielke (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée
