ArticleProceedings of the National Academy of Sciences of the United States of America2022
Statistics and topology of fluctuating ribbons.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Reply to van der Heijden and Starostin: On the persistent helicity of fluctuating ribbons.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Biased statistical ensembles for developable ribbons.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
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4 authors.
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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.
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