Author
Listed:
- Le Bris Claude
(CERMICS, École des Ponts ParisTech, 6 & 8, avenue Blaise Pascal, 77455 Marne-La-Vallée; and INRIA Rocquencourt, MICMAC Project Team, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France)
- Lelièvre Tony
(CERMICS, École des Ponts ParisTech, 6 & 8, avenue Blaise Pascal, 77455 Marne-La-Vallée; and INRIA Rocquencourt, MICMAC Project Team, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay, France)
- Luskin Mitchell
(School of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN 55455, USA)
- Perez Danny
(Theoretical Division T-1, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA)
Abstract
We propose a mathematical analysis of a well-known numerical approach used in molecular dynamics to efficiently sample a coarse-grained description of the original trajectory (in terms of state-to-state dynamics). This technique is called parallel replica dynamics and has been introduced by Arthur F. Voter. The principle is to introduce many replicas of the original dynamics, and to consider the first transition event observed among all the replicas. The effective physical time is obtained by summing up all the times elapsed for all replicas. Using a parallel implementation, a speed-up of the order of the number of replicas can thus be obtained, allowing longer time scales to be computed. By drawing connections with the theory of Markov processes and, in particular, exploiting the notion of quasi-stationary distribution, we provide a mathematical setting appropriate for assessing theoretically the performance of the approach, and possibly improving it.
Suggested Citation
Le Bris Claude & Lelièvre Tony & Luskin Mitchell & Perez Danny, 2012.
"A mathematical formalization of the parallel replica dynamics,"
Monte Carlo Methods and Applications, De Gruyter, vol. 18(2), pages 119-146, January.
Handle:
RePEc:bpj:mcmeap:v:18:y:2012:i:2:p:119-146:n:2
DOI: 10.1515/mcma-2012-0003
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:mcmeap:v:18:y:2012:i:2:p:119-146:n:2. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
We have no bibliographic references for this item. You can help adding them by using this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.