Bittracher, Andreas and Hartmann, C. and Junge, O. and Koltai, Péter (2015) Pseudo generators for under-resolved molecular dynamics. The European Physical Journal Special Topics, 224 (12). pp. 2463-2490. ISSN 1951-6355
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Official URL: http://link.springer.com/article/10.1140%2Fepjst%2...
Many features of a molecule which are of physical interest (e.g. molecular conformations, reaction rates) are described in terms of its dynamics in configuration space. This article deals with the pro- jection of molecular dynamics in phase space onto configuration space. Specifically, we study the situation that the phase space dynamics is governed by a stochastic Langevin equation and study its relation with the configurational Smoluchowski equation in the three different scaling regimes: Firstly, the Smoluchowski equations in non-Cartesian geome- tries are derived from the overdamped limit of the Langevin equation. Secondly, transfer operator methods are used to describe the metastable behaviour of the system at hand, and an explicit small-time asymp- totics is derived on which the Smoluchowski equation turns out to govern the dynamics of the position coordinate (without any assump- tions on the damping). By using an adequate reduction technique, these considerations are then extended to one-dimensional reaction coordi- nates. Thirdly, we sketch three different approaches to approximate the metastable dynamics based on time-local information only.
|Subjects:||Mathematical and Computer Sciences > Mathematics > Mathematical Modelling|
|Divisions:||Other Institutes > Matheon|
Department of Mathematics and Computer Science > Institute of Mathematics
Department of Mathematics and Computer Science > Institute of Mathematics > Cellular Mechanics Group
Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
|Deposited By:||Carsten Hartmann|
|Deposited On:||27 Jan 2015 13:46|
|Last Modified:||13 Jan 2016 11:37|
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