Obiettivo 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. Campo scientifico scienze naturaliscienze fisicheelettromagnetismo ed elettronicaoptoelettronicascienze naturaliscienze fisichefisica quantisticascienze naturaliscienze fisicheelettromagnetismo ed elettronicasemiconduttivitàscienze naturalimatematicamatematica puraanalisi matematicaequazioni differenzialiequazioni differenziali parziali Programma(i) 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) Argomento(i) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Invito a presentare proposte ERC-2010-AdG_20100224 Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-AG - ERC Advanced Grant Coordinatore FORSCHUNGSVERBUND BERLIN EV Indirizzo Rudower chaussee 17 12489 Berlin Germania Mostra sulla mappa Regione Berlin Berlin Berlin Tipo di attività Research Organisations Contatto amministrativo Volker Knoll-Hoyer (Mr.) Ricercatore principale Alexander Mielke (Prof.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Contributo UE Nessun dato Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto FORSCHUNGSVERBUND BERLIN EV Germania Contributo UE € 1 390 000,00 Indirizzo Rudower chaussee 17 12489 Berlin Mostra sulla mappa Regione Berlin Berlin Berlin Tipo di attività Research Organisations Contatto amministrativo Volker Knoll-Hoyer (Mr.) Ricercatore principale Alexander Mielke (Prof.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Altri finanziamenti Nessun dato
