Journal
MULTISCALE MODELING & SIMULATION
Volume 8, Issue 3, Pages 1018-1053Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090765705
Keywords
Euler-Langevin equations; Hamilton-Langevin equations; stationary measures; polymer modeling
Funding
- Swiss National Science Foundation
- U.S. National Science Foundation
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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.
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