Journal article
A first proof of knot localization for polymers in a nanochannel
NR Beaton, K Ishihara, M Atapour, JW Eng, M Vazquez, K Shimokawa, CE Soteros
Journal of Physics A Mathematical and Theoretical | IOP Publishing Ltd | Published : 2024
Abstract
Based on polymer scaling theory and numerical evidence, Orlandini, Tesi, Janse van Rensburg and Whittington conjectured in 1996 that the limiting entropy of knot-type K lattice polygons is the same as that for unknot polygons, and that the entropic critical exponent increases by one for each prime knot in the knot decomposition of K. This Knot Entropy (KE) conjecture is consistent with the idea that for unconfined polymers, knots occur in a localized way (the knotted part is relatively small compared to polymer length). For full confinement (to a sphere or box), numerical evidence suggests that knots are much less localized. Numerical evidence for nanochannel or tube confinement is mixed, de..
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Grants
Awarded by National Science Foundation
Funding Acknowledgements
N R B was supported by Australian Research Council Grants DE170100186 and DP230100674. K I was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP17K14190, JP23K03114. K S is partially supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP16H03928, JP16K13751, JP19K21827, JP21H00978, JP23K20791. C E S acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number RGPIN-2020-06339], as well as Compute Canada resource allocations and past CRG support from the Pacific Institute for the Mathematical Sciences (PIMS). M V was supported by the National Science Foundation (NSF) Division of Mathematical Sciences (DMS) Grants 1817156 and 2054347.