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 an explicit characterization of the complete set of model parameters.
Keywords: Euler-Langevin equations ; Hamilton-Langevin equations ; stationary measures ; polymer modeling ; Unique Tetranucleotide Sequences ; Fokker-Planck Equations ; Molecular-Dynamics ; Dna Oligonucleotides ; Base-Pair ; Simulations ; Elasticity ; Curvature ; Langevin ; Motion
Record created on 2011-12-16, modified on 2016-08-09