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

Davidchack, R.L.; Ouldridge, T.E.; Tretyakov, M.V.

Authors

R.L. Davidchack

T.E. Ouldridge

M.V. Tretyakov Michael.Tretyakov@nottingham.ac.uk



Abstract

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 which 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.

Journal Article Type Article
Journal Journal of Chemical Physics
Print ISSN 0021-9606
Electronic ISSN 1089-7690
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 147
Issue 22
Article Number 224103
APA6 Citation Davidchack, R., Ouldridge, T., & Tretyakov, M. (in press). Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions. Journal of Chemical Physics, 147(22), doi:10.1063/1.4999771
DOI https://doi.org/10.1063/1.4999771
Keywords rigid body dynamics; quaternions; hydrodynamic interactions; Stokesian dynamics; canonical
ensemble; Langevin equations; stochastic differential equations; weak approximation; ergodic limits; stochastic
geometric integrators
Publisher URL http://aip.scitation.org/doi/full/10.1063/1.4999771
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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