Statistics and topology of fluctuating ribbons
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 t...
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sg-ntu-dr.10356-1640812023-02-28T19:21:59Z Statistics and topology of fluctuating ribbons Yong, Ee Hou Dary, Farisan Giom, Luca Mahadevan, L. School of Physical and Mathematical Sciences Science::Physics Statistical Mechanics Polymer Physics 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. Nanyang Technological University Published version E.H.Y. and F.D. acknowledge support from Nanyang Technological University, Singapore, under its Start Up Grant Scheme(04INS000175C230). L.G. is supported by the European Union via the ERC-CoG Grant HexaTissue and by Netherlands Organization for Scientific Research (Ministry of Education, Culture & Science), as part of the Vidi scheme. L.M. thanks the NSF Harvard MRSEC DMR 2011754, NSF EFRI 1830901, the Simons Foundation, and the Henri Seydoux Fund for partial financial support. 2023-01-04T04:55:25Z 2023-01-04T04:55:25Z 2022 Journal Article 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-. https://dx.doi.org/10.1073/pnas.2122907119 0027-8424 https://hdl.handle.net/10356/164081 10.1073/pnas.2122907119 35917354 2-s2.0-85135540412 32 119 e2122907119 en 04INS000175C230 Proceedings of the National Academy of Sciences of the United States of America © 2022 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). application/pdf |
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Science::Physics Statistical Mechanics Polymer Physics Yong, Ee Hou Dary, Farisan Giom, Luca Mahadevan, L. Statistics and topology of fluctuating ribbons |
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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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Yong, Ee Hou Dary, Farisan Giom, Luca Mahadevan, L. |
format |
Article |
author |
Yong, Ee Hou Dary, Farisan Giom, Luca Mahadevan, L. |
author_sort |
Yong, Ee Hou |
title |
Statistics and topology of fluctuating ribbons |
title_short |
Statistics and topology of fluctuating ribbons |
title_full |
Statistics and topology of fluctuating ribbons |
title_fullStr |
Statistics and topology of fluctuating ribbons |
title_full_unstemmed |
Statistics and topology of fluctuating ribbons |
title_sort |
statistics and topology of fluctuating ribbons |
publishDate |
2023 |
url |
https://hdl.handle.net/10356/164081 |
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1759857287822835712 |