Twist and Writhe Dynamics of Stiff Polymers

I consider the dynamics of a stiff filament, in particular the coupling of twist and bend via writhe. The time dependence of the writhe of a filament of length $L$ is $〈\left[\mathrm{Wr}\right(t)-Wr(0){]}^2〉\sim {Lt}^{1/4}$. Simulations, on a simple model of a stiff polymer, are used to confirm scaling arguments. Fuller's theorem, and its relation with geometric phases, is reconsidered for open filaments.