MEthodes Géométriques et échantillonnage: Application à la Simulation moléculaire

 Geometric methods and sampling: applications to molecular simulation

2009 - 2012

This project is supported by the Agence Nationale de la Recherche, under grant ANR-09-BLAN-0216-01

Scientific scope :

Today's and tomorrow's materials are developed at a microscopic level, using information at ever smaller time and space scales. In many cases, these materials are described at the atomic level, based upon the physical theories of quantum physics and statistical physics. Recent examples of novel materials include: carbon nanotubes, which could be the building blocks of a whole generation of electronic devices exhibiting new mechanical, thermal and electrical properties ; in silico design of new drugs, where the chemical properties of new molecules are simulated on a computer instead of resorting to expensive synthesis ; surface chemistry in fuel cells.

These examples are only some of the most prominent instances of a now ubiquituous technique: molecular simulation. However, the methods developed originally in this field may also have applications in areas very different in nature, ranging from astronomy to financial mathematics.

The remarkable accuracy of numerical simulations at the microscopic scale has a counterpart: their numerical costs. The typical length and time scales now tractable are of the order of several billions of atoms  whose dynamics can be followed for a few nanoseconds. In any case, macroscopic time and length scales are beyond reach, even with the considerable increase in computational power witnessed in the past few years.  On the other hand, it is often the case that new physics, and that the identification of new phenomena both arise from the consideration of larger systems simulated on longer times. So, it is no surprise that molecular simulations represent today a huge part of the CPU time used by scientists.
However, this field is mostly unexplored to date by numerical analysts and experts in scientific computing. We believe that molecular simulations are the source of many new and interesting topics in numerical analysis and scientific computing. A mathematical understanding of the (hierarchy of) models and the problems arising in their simulation is one of the key for reducing the time/scale gap with the macroscopic world. A mathematical understanding is also important for validating and assessing the precision of the methods used.

The aim of this project is to investigate various aspects of the mathematical questions raised by molecular simulations, including : computation of free energy differences and improved sampling ; highly oscillating dynamics ; coarse-graining of dynamics ; steady-state non equilibrium sampling ; Quantum Monte-Carlo methods ; discrete to continuum coupling methods.


Some events of the ANR:
A few recent publications :

Journal articles:
Chapter of books, books:
Free Energy Computations: A mathematical perspective

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