Project Details
Projekt
Dynamic large deviations: nucleation and growth in phase transitions and avalanches in random hamiltonian systems
Applicant
Professor Dr. Matthias Röger
Subject Area
Mathematics
Term
from 2009 to 2014
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 20967890
Stochastic perturbations allow for large deviations from the deterministic evolutions, as for example the escape from (deterministically) stationary states. We investigate dynamic large deviations in two different contexts: mesoscale models for the evolution of phase boundaries in multi-phase materials, and overdamped Langevin dynamics with a 'wiggly' potential as a possible model for avalanches.The focus of the first problem is on the existence and qualitative properties of good rate functionals and the characterisation of minimisers under constraints on the macroscopic evolution. A particular example is the switching (tunneling) between stationary states of the deterministic evolution.The aim of the second problem is to identify a stochastic dynamic in a suitable large deviations scaling of a simplified random Hamiltonian system with a potential that has a highly oscillating ('wiggly') part. The main question is whether this can serve as a model for avalanches.
DFG Programme
Research Units
Participating Persons
Professor Dr. Jürgen Gärtner; Professor Dr. Max-Konstantin von Renesse
