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Topology and entropy of polymers

Research Project

Project/Area Number 16K13751
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionSaitama University

Principal Investigator

SHIMOKAWA Koya  埼玉大学, 理工学研究科, 教授 (60312633)

Research Collaborator ISHIHARA Kai  山口大学
SOTEROS Chris  University of Saskatchewan
Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords結び目 / ポリマー / エントロピー / 格子結び目 / 局所結び目 / 結び目解消操作
Outline of Final Research Achievements

It has been conjectured that that the exponential growth rate of the number of lattice polygons with knot-type K is the same as that for unknotted polygons. We proved this conjecture for a subset of simple cubic lattice polygons confined to the smallest tube which admits knotting, the 2x1-tube. As part of the proof, we characterize unknotting operations on diagrams of 4-plat knots.
We also define one way to characterize different configurations of a given knot as either “local” or “non-local” and, for several tube regions we provide both theoretical and numerical evidence that, at equilibrium, the non-local configurations are more likely than the local ones.

Academic Significance and Societal Importance of the Research Achievements

紐状のポリマーに結び目の構造が含まれると、その物性が変化することが分かっている。この研究では、どのような結び目の構造が現れやすいか、という問題に取り組んでいる。今回の研究では、細い筒状領域にある長いポリマーについては、どの結び目の形も指数関数的には同程度の確率で現れることを示している。また、細い筒状領域内のポリマーの結び目の構造が、局在化して現れるか、それとも大きな構造として現れるかについての考察を行った。これらの結果は、DNAの形状の研究、ポリマー材料の物性の研究への応用が期待される。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (23 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (5 results) Journal Article (6 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 6 results,  Open Access: 4 results,  Acknowledgement Compliant: 3 results) Presentation (8 results) (of which Int'l Joint Research: 2 results,  Invited: 8 results) Remarks (1 results) Funded Workshop (3 results)

  • [Int'l Joint Research] University of Saskatchewan(カナダ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] University of Melbourne(オーストラリア)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] University of Saskatchewan(カナダ)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] University of Melbourne(オーストラリア)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] University of Saskatchewan(カナダ)

    • Related Report
      2016 Research-status Report
  • [Journal Article] Neighborhood equivalence for multibranched surfaces in 3-manifolds2019

    • Author(s)
      Ishihara Kai、Koda Yuya、Ozawa Makoto、Shimokawa Koya
    • Journal Title

      Topology and its Applications

      Volume: 257 Pages: 11-21

    • DOI

      10.1016/j.topol.2019.02.005

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characterising knotting properties of polymers in nanochannels2018

    • Author(s)
      N. R. Beaton, J. W. Eng, K. Ishihara, K. Shimokawa, C. E. Soteros
    • Journal Title

      Soft Matter

      Volume: 14 Issue: 28 Pages: 5775-5785

    • DOI

      10.1039/c8sm00734a

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Bounds for minimum step number of knots confined to tubes in the simple cubic lattice2017

    • Author(s)
      Ishihara, Kai; Pouokam, Maxime; Suzuki, Atsumi; Scharein, Robert; Vazquez, Mariel; Arsuaga, Javier; Shimokawa, Koya
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 50 Issue: 21 Pages: 1-28

    • DOI

      10.1088/1751-8121/aa6a4f

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Pathways of DNA unlinking: A story of stepwise simplification2017

    • Author(s)
      Stolz Robert、Yoshida Masaaki、Brasher Reuben、Flanner Michelle、Ishihara Kai、Sherratt David J.、Shimokawa Koya、Vazquez Mariel
    • Journal Title

      Scientific Reports

      Volume: 7 Issue: 1 Pages: 12420-12420

    • DOI

      10.1038/s41598-017-12172-2

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Band surgeries and crossing changes between fibered links2016

    • Author(s)
      Dorothy Buck, Kai Ishihara, Matt Rathbun, and Koya Shimokawa
    • Journal Title

      J. London Math. Soc.

      Volume: 94(2) Issue: 2 Pages: 557-582

    • DOI

      10.1112/jlms/jdw049

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Dehn surgery and Seifert surface system2016

    • Author(s)
      Makoto Ozawa and Koya Shimokawa
    • Journal Title

      Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)

      Volume: - Pages: 267-276

    • DOI

      10.2422/2036-2145.201410_008

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] トポロジーと高分子科学2019

    • Author(s)
      下川航也
    • Organizer
      日本数学会 2019年度年会企画特別講演
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 結び目理論の高分子科学への応用 -- DNA組換え酵素、高分子化学、 材料科学、統計力学的エントロピー--2018

    • Author(s)
      下川航也
    • Organizer
      名古屋大学多元数理科学研究科談話会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Knots, links and spatial graphs in the simple cubic lattice2018

    • Author(s)
      Koya Shimokawa
    • Organizer
      2018 Fall AMS Sectional Meeting, San Francisco State University
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Knots, links and spatial graphs in the simple cubic lattice2018

    • Author(s)
      Koya Shimokawa
    • Organizer
      研究集会「トポロジーとコンピュータ2018」
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Lattice knots and links in tube regions2018

    • Author(s)
      Koya Shimokawa
    • Organizer
      33rd Summer Conference on Topology and its Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Lattice knots and links confined in tube region2017

    • Author(s)
      Koya Shimokawa
    • Organizer
      Conference on Means, Methods and Results in the Statistical Mechanics of Polymeric Systems II
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] トポロジーの高分子化学への応用2016

    • Author(s)
      下川航也
    • Organizer
      ナノ学会主催 ナノ構造・物性- ナノ機能・応用部会 合同シンポジウム
    • Place of Presentation
      グランドパレス川端(秋田県大仙市)
    • Year and Date
      2016-12-27
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 結び目理論の応用について -DNA組換え酵素、高分子化学、統計力学的エントロピー-2016

    • Author(s)
      下川航也
    • Organizer
      第63回トポロジーシンポジウム
    • Place of Presentation
      神戸大学(兵庫県神戸市)
    • Year and Date
      2016-07-07
    • Related Report
      2016 Research-status Report
    • Invited
  • [Remarks] 下川航也ホームページ

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/KoyaShimokawa.html

    • Related Report
      2018 Annual Research Report 2017 Research-status Report 2016 Research-status Report
  • [Funded Workshop] International Symposium “Polymers meet Topology”2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] 国際ワークショップ “The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology” (19w5226)2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] 国際ワークショップ"Topology and graphs in polymer chemistry"2016

    • Place of Presentation
      東京工業大学(東京都目黒区)
    • Year and Date
      2016-08-06
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2020-03-30  

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