Objetivo 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. Ámbito científico natural sciencesphysical scienceselectromagnetism and electronicsoptoelectronicsnatural sciencesphysical sciencesquantum physicsnatural sciencesphysical scienceselectromagnetism and electronicssemiconductivitynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programa(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) Tema(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Convocatoria de propuestas ERC-2010-AdG_20100224 Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-AG - ERC Advanced Grant Institución de acogida FORSCHUNGSVERBUND BERLIN EV Aportación de la UE € 1 390 000,00 Dirección RUDOWER CHAUSSEE 17 12489 Berlin Alemania Ver en el mapa Región Berlin Berlin Berlin Tipo de actividad Research Organisations Contacto administrativo Volker Knoll-Hoyer (Mr.) Investigador principal Alexander Mielke (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo FORSCHUNGSVERBUND BERLIN EV Alemania Aportación de la UE € 1 390 000,00 Dirección RUDOWER CHAUSSEE 17 12489 Berlin Ver en el mapa Región Berlin Berlin Berlin Tipo de actividad Research Organisations Contacto administrativo Volker Knoll-Hoyer (Mr.) Investigador principal Alexander Mielke (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
