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Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions.

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journal contribution
posted on 2018-01-10, 09:43 authored by R. L. Davidchack, T. E. Ouldridge, M. V. Tretyakov
We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces and hydrodynamic coupling. In the absence of non-conservative forces, the Langevin-type equations sample from the canonical ensemble. The rotational degrees of freedom are described using quaternions, the lengths of which are exactly preserved by the stochastic dynamics. For the proposed Langevin-type equations, we construct a weak 2nd order geometric integrator that preserves the main geometric features of the continuous dynamics. The integrator uses Verlet-type splitting for the deterministic part of Langevin equations appropriately combined with an exactly integrated Ornstein-Uhlenbeck process. Numerical experiments are presented to illustrate both the new Langevin model and the numerical method for it, as well as to demonstrate how inertia and the coupling of rotational and translational motion can introduce qualitatively distinct behaviours.

Funding

This work was partially supported by the Computer Simulation of Condensed Phases (CCP5) Collaboration Grant, which is part of the EPSRC Grant No. EP/J010480/1. T.E.O. is supported by a Royal Society University Research Fellowship and also acknowledges fellowships from University College, Oxford and Imperial College London. R.L.D. acknowledges a study leave granted by the University of Leicester. This research used the ALICE High Performance Computing Facility at the University of Leicester.

History

Citation

Journal of Chemical Physics, 2017, 147 (22), 224103

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • VoR (Version of Record)

Published in

Journal of Chemical Physics

Publisher

AIP Publishing

issn

0021-9606

eissn

1089-7690

Acceptance date

2017-11-26

Copyright date

2017

Available date

2018-12-12

Publisher version

http://aip.scitation.org/doi/pdf/10.1063/1.4999771

Notes

The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.

Language

en

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