Repository: Freie Universität Berlin, Math Department

Pseudogenerators of spatial transfer operators

Bittracher, Andreas and Koltai, Péter and Junge, Oliver (2015) Pseudogenerators of spatial transfer operators. SIAM Journal on Applied Dynamical Systems, 14 (3). pp. 1478-1517. ISSN 1536-0040

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Metastable behavior in dynamical systems may be a significant challenge for a simulation based analysis. In recent years, transfer operator based approaches to problems exhibiting metastability have matured. In order to make these approaches computationally feasible for larger systems, various reduction techniques have been proposed: For example, Schu ̈tte introduced a spatial transfer operator which acts on densities on configuration space, while Weber proposed to avoid trajectory simulation (like Froyland et al.) by considering a discrete generator. In this manuscript, we show that even though the family of spatial transfer operators is not a semigroup, it possesses a well defined generating structure. What is more, the pseudo generators up to order 4 in the Taylor expansion of this family have particularly simple, explicit expressions involving no momentum averaging. This makes collocation methods particularly easy to implement and computationally efficient, which in turn may open the door for further efficiency improvements in, e.g., the computational treatment of conforma- tion dynamics. We experimentally verify the predicted properties of these pseudo generators by means of two academic examples.

Item Type:Article
Subjects:Physical Sciences > Physics > Mathematical & Theoretical Physics > Computational Physics
Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Mathematical and Computer Sciences > Mathematics > Mathematical Methods
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Comp. Proteomics Group
Department of Mathematics and Computer Science > Institute of Mathematics
Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:1550
Deposited By: BioComp Admin
Deposited On:01 Jun 2015 09:06
Last Modified:03 Mar 2017 14:41

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