Multi-resolution polymer Brownian dynamics with hydrodynamic interactions

A polymer model given in terms of beads, interacting through Hookean springs and hydrodynamic forces, is studied. A Brownian dynamics description of this bead-spring polymer model is extended to multiple resolutions. Using this multiscale approach, a modeller can efficiently look at different regions of the polymer in different spatial and temporal resolutions with scalings given for the number of beads, statistical segment length, and bead radius in order to maintain macro-scale properties of the polymer filament. The Boltzmann distribution of a Gaussian chain for differing statistical segment lengths gives a diffusive displacement equation for the multi-resolution model with a mobility tensor for different bead sizes. Using the pre-averaging approximation, the translational diffusion coefficient is obtained as a function of the inverse of a matrix and then in closed form in the long-chain limit. This is then confirmed with numerical experiments.