Project 4: Dynamic Large Deviations:
Nucleation and Growth in Phase Transitions and Avalanches in Random Hamiltonian Systems
Participants
Jürgen Gärtner, Stephan Luckhaus, Max von Renesse, Matthias Röger
Summary
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.
Some related earlier preprints
Achievements of the Research Group