On the Stochastic Modeling of Rigid Body Systems with Application to Polymer Dynamics

The stochastic equations of motion for a system of interacting rigid bodies in a solvent are formulated and studied. Three-dimensional bodies of arbitrary shape, with arbitrary couplings between translational and rotational degrees of freedom, as arise in coarse-grained models of polymers, are consi...

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Bibliographic Details
Published in:Multiscale modeling & simulation 2010-01, Vol.8 (3), p.1018-1053
Main Authors: Walter, J, Gonzalez, O, Maddocks, J H
Format: Article
Language:English
Subjects:
Dynamical systems
Dynamics
Equations of motion
Mathematical analysis
Mathematical models
Polymers
Rigid-body dynamics
Rotational
Stochastic models
Stochasticity
Studies
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Summary:The stochastic equations of motion for a system of interacting rigid bodies in a solvent are formulated and studied. Three-dimensional bodies of arbitrary shape, with arbitrary couplings between translational and rotational degrees of freedom, as arise in coarse-grained models of polymers, are considered. Beginning from an Euler-Langevin form of the equations, two different, properly invariant, Hamilton-Langevin forms are derived and studied together with various associated measures. Under different conditions depending on the choice of rotational coordinates, the canonical measure is shown to be a stationary solution of an associated Fokker-Planck equation and to always factorize into independent measures on configuration and velocity spaces. Explicit expressions are given for these measures, along with a certain Jacobian factor associated with the three-dimensional rotation group. When specialized to a fully coupled, quadratic model of a stiff polymer such as DNA, our results yield an explicit characterization of the complete set of model parameters. [PUBLICATION ABSTRACT]
ISSN:1540-3459
1540-3467
DOI:10.1137/090765705