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.
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14 December 2017
Research Article|
December 12 2017
Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions
R. L. Davidchack
;
R. L. Davidchack
a)
1
Department of Mathematics, University of Leicester
, Leicester LE1 7RH, United Kingdom
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T. E. Ouldridge
;
T. E. Ouldridge
b)
2
Department of Bioengineering, Imperial College London
, London SW7 2AZ, United Kingdom
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M. V. Tretyakov
M. V. Tretyakov
c)
3
School of Mathematical Sciences, University of Nottingham
, Nottingham NG7 2RD, United Kingdom
Search for other works by this author on:
R. L. Davidchack
1,a)
T. E. Ouldridge
2,b)
M. V. Tretyakov
3,c)
1
Department of Mathematics, University of Leicester
, Leicester LE1 7RH, United Kingdom
2
Department of Bioengineering, Imperial College London
, London SW7 2AZ, United Kingdom
3
School of Mathematical Sciences, University of Nottingham
, Nottingham NG7 2RD, United Kingdom
a)
Electronic mail: [email protected]
b)
Electronic mail: [email protected]
c)
Electronic mail: [email protected]
J. Chem. Phys. 147, 224103 (2017)
Article history
Received:
August 10 2017
Accepted:
November 26 2017
Citation
R. L. Davidchack, T. E. Ouldridge, M. V. Tretyakov; Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions. J. Chem. Phys. 14 December 2017; 147 (22): 224103. https://doi.org/10.1063/1.4999771
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