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 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 a...

• Type: Journal
• Year: 2010
• Where: MMAS
• Authors: J. Walter, O. Gonzalez, J. H. Maddocks
• Keywords: Equations, Intelligent Agents, MMAS 2010, Polymer, Various Associated Measures