Twist and writhe dynamics of stiff filaments

TL;DR

This paper investigates the coupled twist and bend dynamics of stiff filaments, revealing how writhe evolves over time and analyzing the roles of different motion types through simulations and theoretical considerations.

Contribution

It introduces new insights into the time-dependent behavior of writhe in stiff filaments and revisits Fuller's theorem in the context of open filaments.

Findings

Writhe squared scales as L t^{1/4} for linear filaments.

Writhe squared scales as t^{1/2} / L for curved filaments.

Simulations highlight the roles of crankshaft and tube-like motions in twist dynamics.

Abstract

This letter considers 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 is $W_r^2\sim L t^{1/4}$ for a linear filament and $W_r^2\sim t^{1/2} / L $ for a curved filament. Simulations are used to study the relative importance of crankshaft motion and tube like motion in twist dynamics. Fuller's theorem, and its relation with the Berry phase, is reconsidered for open filaments