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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Official URL: http://epubs.siam.org/doi/abs/10.1137/14099872X?jo...

## Abstract

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 |
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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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