The stochastic spectral dynamics of bending and tumbling

Abstract

Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in terms of the natural eigenfunctions. This formulation separates tumbling and bending dynamics, clearly showing their interrelation, naturally orders the bending dynamics according to the characteristic decay rate of its modes, and displays coupling among bending modes in a general flow. This hierarchy naturally yields a low dimensional stochastic dynamical system which recovers and extends previous numerical results and which leads to a fast and efficient numerical method for studying the stochastic nonlinear dynamics of semiflexible polymers in general flows. This formulation will be useful for studying other physical systems described by constrained stochastic partial differential equations.