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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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CiteScore 2016: 0.70

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1569-3961
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Volume 10, Issue 1

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Optimal Prediction in Molecular Dynamics

Benjamin Seibold
  • Department of Mathematics, Technical University of Kaiserslautern, Gottlieb-Daimler-Straße, 67653 Kaiserslautern, Germany
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Optimal prediction approximates the average solution of a large system of ordinary differential equations by a smaller system. We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in order to reduce the number of particles to be tracked in the computations. We consider a model problem, which describes a surface coating process, and show how asymptotic methods can be employed to approximate the high dimensional conditional expectations, which arise in optimal prediction. The thus derived smaller system is compared to the original system in terms of statistical quantities, such as diffusion constants. The comparison is carried out by Monte-Carlo simulations, and it is shown under which conditions optimal prediction yields a valid approximation to the original system.

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Published in Print: 2004-03-01


Citation Information: Monte Carlo Methods and Applications mcma, Volume 10, Issue 1, Pages 25–50, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/156939604323091199.

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[1]
Martin Frank and Benjamin Seibold
Kinetic and Related Models, 2011, Volume 4, Number 3, Page 717
[2]
Alexandre Chorin and Panagiotis Stinis
Communications in Applied Mathematics and Computational Science, 2006, Volume 1, Number 1, Page 1
[3]
Benjamin Seibold and Martin Frank
Continuum Mechanics and Thermodynamics, 2009, Volume 21, Number 6, Page 511

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