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TRANSITION Report Summary

Project ID: 616811
Funded under: FP7-IDEAS-ERC
Country: France

Mid-Term Report Summary - TRANSITION (Large Deviations and Non Equilibrium Phase Transitions for Turbulent Flows, Climate, and the Solar System)

The aim of the project is to develop theoretical and computational tools in order to compute rare events in complex non equilibrium dynamical systems, and to apply them to phenomena in several fields: climate, turbulence and the large time dynamics of the solar system.
The theoretical part, mainly based on tools from large deviation theory, has led to several new theoretical and mathematical results. First a generalization of the Eyring--Kramers formula, that describes the transition rate of rare transitions between metastable states, to non equilibrium dynamics. Second a theory for computing non-equilibrium quasipotentials (or free energies) for complex systems, like for example particle systems with long range interactions. Those essential theoretical aspects have been completed by the development and use of rare event algorithms in order to directly compute rare transitions, or other classes of rare events, for complex dynamical systems. We have demonstrated that algorithms from statistical mechanics can be used successfully with stochastic partial differential equation, for instance describing turbulent flows or the dynamics of turbulent atmospheres with a climate perspective.
In terms of applications, we have for the first time been able to study multistability and extremely rare transitions from numerical simulations in turbulent flows. We have for instance been able to discuss the existence of an Arrhenius law for the non equilibrium dynamics of ultra rare transitions between jets related the Jupiter’s troposphere jet dynamics.

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