Objective Many models for materials rely on a microscopic description. In a classical regime and for a fixed temperature, atoms are described by particles that interact through a force field and evolve according to Newton’s equations of motion, with additional stochastic terms to model thermostating. This simulation technique is called molecular dynamics. Applications are ubiquitous, ranging from biology to materials science.The direct numerical simulation of these models is extremely computationally expensive, since the typical timescale at the microscopic level is orders of magnitude smaller than the macroscopic timescales of interest. Many algorithms used by practitioners have not yet been investigated by applied mathematicians. The aim of this proposal is to further develop the mathematical analysis of these methods and to build new and more efficient algorithms, validated by precise error estimates.The underlying theoretical questions are related to the mathematical definition and quantification of metastability for stochastic processes. Metastability refers to the fact that the stochastic process remains trapped in some regions of the configuration space for very long times. Using naive simulations, transitions between these states are very rarely observed, whereas these transition events are actually those which matter at the macroscopic level. Metastability is one of the major bottlenecks in making molecular simulations predictive for real life test cases.The main challenges motivating this proposal are: the design of efficient techniques to sample high-dimensional multimodal measures, the development and analysis of algorithms to sample metastable dynamics and the construction of coarse-graining techniques for high-dimensional problems.This project relies on strong collaborations with practitioners (biologists and physicists) in order to propose common benchmarks, to identify the methodological bottlenecks and to apply new algorithms to real life test cases. Fields of science natural sciencesmathematicspure mathematicsmathematical analysis Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-CG-2013-PE1 - ERC Consolidator Grant - Mathematics Call for proposal ERC-2013-CoG See other projects for this call Funding Scheme ERC-CG - ERC Consolidator Grants Coordinator ECOLE NATIONALE DES PONTS ET CHAUSSEES Address Avenue blaise pascal-cite descartes-champs-sur-marne 6-8 77455 Marne la vallee cedex 2 France See on map Region Ile-de-France Ile-de-France Seine-et-Marne Activity type Higher or Secondary Education Establishments Principal investigator Tony Gilbert Lelievre (Prof.) Administrative Contact Carolina Garcia-Olmedo (Ms.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution € 1 773 600,00 Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all ECOLE NATIONALE DES PONTS ET CHAUSSEES France EU contribution € 1 773 600,00 Address Avenue blaise pascal-cite descartes-champs-sur-marne 6-8 77455 Marne la vallee cedex 2 See on map Region Ile-de-France Ile-de-France Seine-et-Marne Activity type Higher or Secondary Education Establishments Principal investigator Tony Gilbert Lelievre (Prof.) Administrative Contact Carolina Garcia-Olmedo (Ms.) Links Contact the organisation Opens in new window Website Opens in new window
