Accelerated dynamics: Mathematical foundations and algorithmic improvements
Université Paris-Est, CERMICS (ENPC), INRIA, 6-8 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France
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Received: 20 March 2015
Revised: 5 May 2015
Published online: 22 June 2015
We present a review of recent works on the mathematical analysis of algorithms which have been proposed by A.F. Voter and co-workers in the late nineties in order to efficiently generate long trajectories of metastable processes. These techniques have been successfully applied in many contexts, in particular in the field of materials science. The mathematical analysis we propose relies on the notion of quasi-stationary distribution.
The work of T. Lelièvre is supported by the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement number 614492. T. Lelièvre would like to thank very instructive discussions with D. Perez and A.F. Voter on accelerated dynamics, as well as his co-authors D. Aristoff, A. Binder, C. Le Bris, M. Luskin, F. Nier, D. Perez and G. Simpson.
© EDP Sciences, Springer-Verlag, 2015