Nicholas R Beaton, Kai Ishihara, Mahshid Atapour, Jeremy W Eng, Mariel Vazquez, Koya Shimokawa, Christine E Soteros
{"title":"A first proof of knot localization for polymers in a nanochannel","authors":"Nicholas R Beaton, Kai Ishihara, Mahshid Atapour, Jeremy W Eng, Mariel Vazquez, Koya Shimokawa, Christine E Soteros","doi":"10.1088/1751-8121/ad6c01","DOIUrl":null,"url":null,"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 <italic toggle=\"yes\">K</italic> 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 <italic toggle=\"yes\">K</italic>. 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, depending on how the size of a knot is measured. Here we outline the proof that the KE conjecture holds for polygons in the <inline-formula>\n<tex-math><?CDATA $\\infty\\times2\\times1$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi mathvariant=\"normal\">∞</mml:mi><mml:mo>×</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6c01ieqn1.gif\"></inline-graphic></inline-formula> lattice tube and show that knotting is localized when a connected-sum measure of knot size is used. Similar results are established for linked polygons. This is the first model for which the knot entropy conjecture has been proved.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"242 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics A: Mathematical and Theoretical","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1751-8121/ad6c01","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
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, depending on how the size of a knot is measured. Here we outline the proof that the KE conjecture holds for polygons in the ∞×2×1 lattice tube and show that knotting is localized when a connected-sum measure of knot size is used. Similar results are established for linked polygons. This is the first model for which the knot entropy conjecture has been proved.
期刊介绍:
Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.