Cel 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. Dziedzina nauki natural sciencesphysical scienceselectromagnetism and electronicsoptoelectronicsnatural sciencesphysical sciencesquantum physicsnatural sciencesphysical scienceselectromagnetism and electronicssemiconductivitynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Program(-y) 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) Temat(-y) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Zaproszenie do składania wniosków ERC-2010-AdG_20100224 Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-AG - ERC Advanced Grant Instytucja przyjmująca FORSCHUNGSVERBUND BERLIN EV Wkład UE € 1 390 000,00 Adres RUDOWER CHAUSSEE 17 12489 Berlin Niemcy Zobacz na mapie Region Berlin Berlin Berlin Rodzaj działalności Research Organisations Kontakt administracyjny Volker Knoll-Hoyer (Mr.) Kierownik naukowy Alexander Mielke (Prof.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych Beneficjenci (1) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko FORSCHUNGSVERBUND BERLIN EV Niemcy Wkład UE € 1 390 000,00 Adres RUDOWER CHAUSSEE 17 12489 Berlin Zobacz na mapie Region Berlin Berlin Berlin Rodzaj działalności Research Organisations Kontakt administracyjny Volker Knoll-Hoyer (Mr.) Kierownik naukowy Alexander Mielke (Prof.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych
