Research: Large Deviations and Non Equilibrium Phase Transitions for Turbulent Flows, Climate, and the Solar System
The aim of this project is to predict and compute extremely rare but essential trajectories in complex physical systems. We will compute rare transitions trajectories, first between two different turbulent attractors in models of planetary jet dynamics, and second between two configurations of ocean currents for a model of the thermohaline circulation. We will compute the dynamics and the probability for collisions between two planets in the solar system, on time scales of order of billions of years. We will evaluate rare events that lead to extremely large drags or torques on objects embedded in turbulent flows, directly from the dynamics. Because of the huge range of time scales, all those trajectories are not accessible through direct numerical simulations. The project's unity stems from the methodology based on large-deviations theory. Large deviation rate functions generalize the concept of entropy or free energy in non-equilibrium extended systems: they provide a global characterization of their most probable state, their large fluctuations and their phase transitions. Impressive explicit computations of large deviation rate functions have been recently performed in simple non-equilibrium systems. The main aim of this project is to bridge the gap between those extremely interesting new concepts and algorithms, and complex dynamical systems such as turbulent flows, semi-realistic models of fluids related to climate dynamics, or the long time behavior of the solar system. In order to achieve this goal, we will use macroscopic fluctuation theory, instanton theory, and other analytical methods in order to compute explicitly large deviation rate functions for essential macroscopic quantities (the velocity or density fields). We will also develop and use algorithms specifically dedicated at computing the statistics of extremely rare trajectories, based on the generalization of importance sampling implemented through cloning or multilevel splitting methods.
Max ERC Funding
1 178 760 €
Start date: 2014-03-01, End date: 2019-02-28
ERC Consolidator Grant
ERC Consolidator Grants support promising researchers who are at the beginning of an independent research career. The consolidation of their own research team will be funded with the grant. For the evaluation of the researcher profile several benchmarks according to research domain and career development are taken into account. For instance, applicants should have several important publications without their PhD supervisor. Other benchmarks include publications as first author in high-ranking international journals, (translated) monographs, patents, conference presentations or (inter)national prizes and awards.