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Title: Statistics and topology of fluctuating ribbons
Authors: Yong, Ee Hou 
Dary, Farisan
Giom, Luca
Mahadevan, L.
Keywords: Science::Physics
Issue Date: 2022
Source: Yong, E. H., Dary, F., Giom, L. & Mahadevan, L. (2022). Statistics and topology of fluctuating ribbons. Proceedings of the National Academy of Sciences of the United States of America, 119(32), e2122907119-.
Project: 04INS000175C230
Journal: Proceedings of the National Academy of Sciences of the United States of America
Abstract: Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases-a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase-that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.
ISSN: 0027-8424
DOI: 10.1073/pnas.2122907119
Schools: School of Physical and Mathematical Sciences 
Rights: © 2022 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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