Abstract

Transitions between metastable states are important in many aspects of science, from phase transitions, over the onset of turbulence, to tipping points in Earth’s climate. All of them feature multiple locally stable states with basins of attraction, with edge states on their boundaries that facilitate the transition. The nature of these edge states (or transition states) often gives insight into the structure, likelihood, and mechanisms of the transition itself. In this talk, I will give an overview over different notions of edge states in complex systems and numerical algorithms to compute them. I will show examples from phase separation in the Cahn-Hilliard equation, transitional pipe flow and the tranition to turbulence, atmospheric jet formation, and metastable climate regimes in Earth’s climate.