Reply to Comment on "Statistical mechanics of developable ribbons"

TL;DR

This paper defends previous findings of spontaneous helical structures in developable ribbons against claims of systematic errors caused by Frenet frame rotation, clarifying misconceptions about the Monte Carlo sampling process.

Contribution

It clarifies that the Frenet frame rotation at inflection points does not bias Monte Carlo sampling, reaffirming the original results on ribbon helicity.

Findings

Frenet frame rotation does not bias Monte Carlo sampling.

Original results on spontaneous helical structures are valid.

Misconceptions about inflection point effects are addressed.

Abstract

Starostin and van der Heijden [arXiv:1111.2029] question the validity of the results reported in our Letter [Phys. Rev. Lett. 104, 238104 (2010)] regarding the existence of spontaneous helical structure in finite-temperature developable ribbons. According to the authors of the Comment, our setting is affected by a systematic error in the calculation of the torsion \tau\ that results in a bias of the Monte Carlo sampling toward helical configurations, and originates from the fact that the Frenet frame, used by us to describe the centerline of the ribbons, rotates by 180^{\circ} about the direction of the tangent vector every time an inflection point (i.e. a point where the curvature \kappa\ changes in sign) is encountered. While the rotation of the frame at infection points is a well known property of Frenet frame, the conclusions of Starostin and van der Heijden on how this phenomenon would affect the Monte Carlo sampling are incorrect, as are many of the other statements that they make.