Twirling and Whirling: Viscous Dynamics of Rotating Elastica
Abstract
Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.
Cite
@article{arxiv.cond-mat/9912360,
title = {Twirling and Whirling: Viscous Dynamics of Rotating Elastica},
author = {Charles W. Wolgemuth and Thomas R. Powers and Raymond E. Goldstein},
journal= {arXiv preprint arXiv:cond-mat/9912360},
year = {2009}
}
Comments
To be published in Physical Review Letters