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3次元トポロジーに基づく静的・動的ネットワークの提案

Planned

Project AreaDiscrete Geometric Analysis for Materials Design
Project/Area Number 17H06463
Research Category

Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)

Allocation TypeSingle-year Grants
Review Section Science and Engineering
Research InstitutionSaitama University

Principal Investigator

下川 航也  埼玉大学, 理工学研究科, 教授 (60312633)

Co-Investigator(Kenkyū-buntansha) 石原 海  山口大学, 教育学部, 准教授 (40634762)
伊藤 克司  東京工業大学, 理学院, 教授 (60221769)
出口 哲生  お茶の水女子大学, 基幹研究院, 教授 (70227544)
手塚 育志  東京工業大学, 物質理工学院, 教授 (80155457)
Project Period (FY) 2017-06-30 – 2022-03-31
Project Status Granted (Fiscal Year 2021)
Budget Amount *help
¥52,130,000 (Direct Cost: ¥40,100,000、Indirect Cost: ¥12,030,000)
Fiscal Year 2021: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2020: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2019: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2018: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2017: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Keywordsネットワーク / 3次元トポロジー / 高分子材料 / 共連続構造 / トポロジー / トポロジー高分子 / 結び目 / 3次元トポロジー / 3次元多様体 / ポリマー / 高分子 / 3次元ネットワーク
Outline of Annual Research Achievements

本年度は、これまでこの新学術領域研究として行って来た高分子のトポロジーに関する研究を、著書``Topology of Polymers''として石原氏、手塚氏とともにまとめ、Springer Monographから出版した。ここでは、多環状高分子の合成方法、そのトポロジーの数学的記述と命名法などをまとめている。また、金属とペプチドから構成される環が6つ絡まることで作られるカプセル状の分子のトポロジーを東大の藤田研究室とともに考察し、Nature Communicationsから2019年12月に出版した。この構造は交点数24を持つものであり、交点数が決定できる絡み目状の構造としては、これまでで世界で最も複雑なものとなっている。この絡み目は多面体から構成されるが、その構成方法を数学的に特徴付けた。この研究については、東京大学と埼玉大学からプレスリリースを発表した。また、共連続構造の数学的モデル化に関してもその分類成果を挙げ、論文として発表を準備している。ここでは、2つの共連続構造が与えられた場合に、どのような変形を行うと一方を他方に変形できるかを明らかにしている。
高分子に纏わる数学、化学、物理に関する国際会議を、2019年8月7日~9日に"Polymers and networks via topology and entanglement"として、お茶の水女子大学で開催した。この国際会議のアブストラクトは、小冊子としてまとめている。また、2019年12月に材料科学の大きな国際会議であるMRM2019において、招待講演を行った。

Current Status of Research Progress
Current Status of Research Progress

1: Research has progressed more than it was originally planned.

Reason

高分子のトポロジーに関して、当初の予定通りのペースで研究が進んでいる。特に今年度は研究成果を著書として出版することが出来たことは、大きな成果であると考えている。また、今年度も国際会議を開催し、大変有意義な情報交換を行うことが出来た。さらに、領域外の方とのコラボレーションとして、東京大学の藤田誠氏との共同研究を行い、その成果を今年度もNature Communicationsから出版することが出来た。これは、交点数24をもつ絡み目のトポロジーをもつ分子があり、これまで観測されたもので最も交点数が多いものとなっている。この成果は、東京大学、埼玉大学からプレスリリースとして発表を行った。またこの論文は、Nature Communicationsの2019年の``Top 50 Chemistry and Materials Sciences Articles''に選出された。この共同研究の成果は、当初の計画には無い部分であり、世界記録としてプレスリリースを発表出来た点でも、当初の計画を上回る成果と言える。

Strategy for Future Research Activity

引き続き、高分子とトポロジーの研究を行う。特に、3相共連続構造に関する成果を2つの論文にまとめ投稿予定である。その中で3相共連続構造のリスト作りを行っており、そのデータをもとに材料設計を行う予定である。現在までの成果を、新学術領域外の研究者へ伝えるためのweb pageを作成している。また、金属とペプチドからなる分子構造の解析も続け、これまでに構成されている構造の特徴付けを行う予定である。

Report

(3 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report

Research Products

(61 results)

All 2019 2018 2017 Other

All Int'l Joint Research (6 results) Journal Article (20 results) (of which Int'l Joint Research: 8 results,  Peer Reviewed: 19 results,  Open Access: 8 results,  Acknowledgement Compliant: 2 results) Presentation (24 results) (of which Int'l Joint Research: 23 results,  Invited: 24 results) Book (1 results) Remarks (6 results) Funded Workshop (4 results)

  • [Int'l Joint Research] University of California, Davis/University of Georgia(米国)

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

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] UNAM(メキシコ)

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

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] University of California, Davis(米国)

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

    • Related Report
      2017 Annual Research Report
  • [Journal Article] A metal-peptide capsule by multiple ring threading2019

    • Author(s)
      Sawada Tomohisa、Inomata Yuuki、Shimokawa Koya、Fujita Makoto
    • Journal Title

      Nature Communications

      Volume: 10 Pages: 5687-5687

    • DOI

      10.1038/s41467-019-13594-4

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Metal-peptide rings form highly entangled topologically inequivalent frameworks with the same ring- and crossing-numbers2019

    • Author(s)
      T. Sawada, A. Saito, K. Tamiya, K. Shimokawa, Y. Hisada, M. Fujita
    • Journal Title

      Nature Commun.

      Volume: 10 Pages: 921-921

    • DOI

      10.1038/s41467-019-08879-7

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [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] Bimodality in the knotting probability of semiflexible rings suggested by mapping with self-avoiding polygons2019

    • Author(s)
      Uehara Erica、Coronel Lucia、Micheletti Cristian、Deguchi Tetsuo
    • Journal Title

      Reactive and Functional Polymers

      Volume: 134 Pages: 141-149

    • DOI

      10.1016/j.reactfunctpolym.2018.11.008

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Programmed Polymer Folding with Periodically Positioned Tetrafunctional Telechelic Precursors by Cyclic Ammonium Salt Units as Nodal Points2019

    • Author(s)
      Kyoda Kohei、Yamamoto Takuya、Tezuka Yasuyuki
    • Journal Title

      J. Am. Chem. Soc.

      Volume: 141 Pages: 7526-7536

    • DOI

      10.1021/jacs.9b02459

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [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 Pages: 5775-5785

    • DOI

      10.1039/c8sm00734a

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Two-point correlation function of ring polymers: Experiments and numerical simulations for the case of circular DNA in 2 dimensions2018

    • Author(s)
      Ropelewski Sophia、Uehara Erica、Lehmann Caroline、Deguchi Tetsuo、Dietler Giovanni
    • Journal Title

      Reactive and Functional Polymers

      Volume: 133 Pages: 66-70

    • DOI

      10.1016/j.reactfunctpolym.2018.10.001

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Mean-square radius of gyration and the hydrodynamic radius for topological polymers expressed with graphs evaluated by the method of quaternions revisited2018

    • Author(s)
      Uehara Erica、Deguchi Tetsuo
    • Journal Title

      Reactive and Functional Polymers

      Volume: 133 Pages: 93-102

    • DOI

      10.1016/j.reactfunctpolym.2018.09.007

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Statistical properties of multi-theta polymer chains2018

    • Author(s)
      Uehara Erica、Deguchi Tetsuo
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 51 Pages: 134001-134001

    • DOI

      10.1088/1751-8121/aaae2d

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Macrocyclic poly(p-phenylenevinylene)s by ring expansion metathesis polymerisation and their characterisation by single-molecule spectroscopy2018

    • Author(s)
      Lidster Benjamin John、Hirata Shuzo、Matsuda Shoki、Yamamoto Takuya、Komanduri Venukrishnan、Kumar Dharam Raj、Tezuka Yasuyuki、Vacha Martin、Turner Michael L.
    • Journal Title

      Chem. Sci.

      Volume: 9 Pages: 2934-2941

    • DOI

      10.1039/c7sc03945j

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Recent advances in the construction of cyclic grafted polymers and their potential applications2018

    • Author(s)
      Zhang Shuangshuang、Tezuka Yasuyuki、Zhang Zhengbiao、Li Na、Zhang Wei、Zhu Xiulin
    • Journal Title

      Polymer Chemistry

      Volume: 9 Pages: 677-686

    • DOI

      10.1039/c7py01544e

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Synthesis, Isolation, and Properties of All Head-to-Tail Cyclic Poly(3-hexylthiophene): Fully Delocalized Exciton over the Defect-Free Ring Polymer2018

    • Author(s)
      Yamamoto Takuya、Hosokawa Masaaki、Nakamura Minato、Sato Shin-ichiro、Isono Takuya、Tajima Kenji、Satoh Toshifumi、Sato Masamichi、Tezuka Yasuyuki、Saeki Akinori、Kikkawa Yoshihiro
    • Journal Title

      Macromolecules

      Volume: 51 Pages: 9284-9293

    • DOI

      10.1021/acs.macromol.8b01681

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Enzyme action for topological entanglement in DNA and knot theory2018

    • Author(s)
      K. Ishihara
    • Journal Title

      Reactive and Functional Polymers

      Volume: 132 Pages: 74-80

    • DOI

      10.1016/j.reactfunctpolym.2018.09.006

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [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 Pages: 215601-215601

    • DOI

      10.1088/1751-8121/aa6a4f

    • Related Report
      2017 Annual Research 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 Pages: 1-11

    • DOI

      10.1038/s41598-017-12172-2

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A Twisting Ring Polymer: Synthesis and Thermally Induced Chiroptical Responses of a Cyclic Poly(tetrahydrofuran) Having Axially Chiral Units2017

    • Author(s)
      Honda Satoshi、Adachi Kaoru、Yamamoto Takuya、Tezuka Yasuyuki
    • Journal Title

      Macromolecules

      Volume: 50 Pages: 5323-5331

    • DOI

      10.1021/acs.macromol.7b00839

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Load-Induced Frictional Transition at a Well-Defined Alkane Loop Surface2017

    • Author(s)
      A. Shundo, K. Hori, Y. Tezuka, T. Yamamoto, and K. Tanaka
    • Journal Title

      Langmuir

      Volume: 33 Pages: 2396-2401

    • DOI

      10.1021/acs.langmuir.6b04042

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Topological Polymer Chemistry Designing Complex Macromolecular Graph Constructions2017

    • Author(s)
      Tezuka Yasuyuki
    • Journal Title

      Accounts of Chemical Research

      Volume: 50 Pages: 2661-2672

    • DOI

      10.1021/acs.accounts.7b00338

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Knotting probability of self-avoiding polygons under a topological constraint2017

    • Author(s)
      Uehara Erica、Deguchi Tetsuo
    • Journal Title

      The Journal of Chemical Physics

      Volume: 147 Pages: 094901-094901

    • DOI

      10.1063/1.4996645

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent2017

    • Author(s)
      Uehara Erica、Deguchi Tetsuo
    • Journal Title

      The Journal of Chemical Physics

      Volume: 147 Pages: 214901-214901

    • DOI

      10.1063/1.4999266

    • Related Report
      2017 Annual Research Report
  • [Presentation] 3-dimensional topology and polycontinuous pattern2019

    • Author(s)
      Koya Shimokawa
    • Organizer
      International Symposium “Polymers and networks via topology and entanglement”
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 3-dimensional topology and poly-continuous pattern2019

    • Author(s)
      Koya Shimokawa
    • Organizer
      MATERIALS RESEARCH MEETING 2019, Mathematical Materials Science -Mathematical Approaches for Materials Designs in the Data Driven Society-
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Handlebody decomposition of 3-manifolds and their application2019

    • Author(s)
      Koya Shimokawa
    • Organizer
      可微分写像の特異点論とその応用
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 3-dimensional topology and polycontinuous pattern2019

    • Author(s)
      Koya Shimokawa
    • Organizer
      The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [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] Poly-continuous pattern, networks and 3-dimensional topology2019

    • Author(s)
      Koya Shimokawa
    • Organizer
      International Symposium "Polymers meet Topology"
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rouse Dynamics of Topological Polymers through Gaussian Random Embeddings and Comparison with Experiments2019

    • Author(s)
      Tetsuo Deguchi
    • Organizer
      The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rouse Dynamics of Topological Polymers through Gaussian Random Graph Embeddings2019

    • Author(s)
      Tetsuo Deguchi
    • Organizer
      International Symposium "Polymers meet Topology"
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Knotting probability of self-avoiding polygons under a topological constraint: A sum rule derived from the factorization property2019

    • Author(s)
      T. Deguchi and E. Uehara
    • Organizer
      ``Topology of Biopolymers’’, Special Session at the Spring Eastern Sectional Meeting of AMS
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological Polymer Chemistry Designing Macromolecular Graph Constructions, International2019

    • Author(s)
      Y. Tezuka
    • Organizer
      International Symposium "Polymers meet Topology"
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Types of Multicyclic Graphs2019

    • Author(s)
      K. Ishihara
    • Organizer
      International Symposium "Polymers meet Topology"
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] First steps of unlinking pathways2019

    • Author(s)
      K. Ishihara
    • Organizer
      The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology
    • 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
      2018 Fall AMS Sectional Meeting
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / 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] Topological Polymer Chemistry with Programmed ESA-CF Polymer Folding Constructions2018

    • Author(s)
      Y. Tezuka
    • Organizer
      14th Japan-Belgium Symposium on Polymer Science
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological Chemistry Designing Novel Macromolecular Constructions2018

    • Author(s)
      Y. Tezuka
    • Organizer
      2018 Taiwan-Japan Bilateral Polymer Symposium
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On chirality of molecular graphs2018

    • Author(s)
      Koya Shimokawa
    • Organizer
      Cyclic & Topologically Complex Polymers, Spring 2018 American Chemical Society Meeting
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 3-dimensional topology and network analysis in soft materials2018

    • Author(s)
      Koya Shimokawa
    • Organizer
      International kick-off workshop "Discrete Geometric Analysis for Materials Design"
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Statistical and hydrodynamic properties of graph-shaped polymers and quaternions2018

    • Author(s)
      T. Deguchi and E. Uehara
    • Organizer
      Cyclic & Topologically Complex Polymers, Spring 2018 American Chemical Society Meeting
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological Chemistry Designing Macromolecular Graph Constructions2017

    • Author(s)
      Yasuyuki Tezuka
    • Organizer
      Japan-Taiwan Bilateral Polymer Symposium (JTBPS 2017)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Designing Cyclic and Topological Polymer Constructions by Innovative Synthetic Protocols2017

    • Author(s)
      Yasuyuki Tezuka
    • Organizer
      International Workshop “Ring Polymers”
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Statistical and Hydrodynamic Properties of Graph-Shaped Polymers and Quaternions2017

    • Author(s)
      Tetsuo Deguchi
    • Organizer
      International workshop``Knots and polymers: aspects of topological enanglement in DNA, proteins and graph-shaped polymers''
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Statistical Mechanics of Theta-shaped and Ring-shaped Polymer Chains2017

    • Author(s)
      E. Uehara and T. Deguchi
    • Organizer
      International workshop``Knots and polymers: aspects of topological enanglement in DNA, proteins and graph-shaped polymers''
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Additivity of Topological Balance Length and a Slow Growth in the Effective Scaling Exponent of Knotted Random Polygons2017

    • Author(s)
      T. Deguchi and E. Uehara
    • Organizer
      CMO-BIRS Workshop: “The Geometry and Topology of Knotting and Entanglement in Proteins
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Book] Topology of Polymers2019

    • Author(s)
      Shimokawa, Koya, Ishihara, Kai, Tezuka, Yasuyuki
    • Total Pages
      89
    • Publisher
      Springer, SpringerBriefs in the Mathematics of Materials
    • ISBN
      9784431568865
    • Related Report
      2019 Annual Research Report
  • [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
      2019 Annual Research Report
  • [Remarks] ペプチド鎖が精密に編み込まれたナノカプセルの合成に初成功

    • URL

      http://www.saitama-u.ac.jp/topics_archives/2019-1211-1337-18.html

    • Related Report
      2019 Annual Research Report
  • [Remarks] 国際会議ホームページ

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/kshimoka/polymersandnetworks2019.html

    • Related Report
      2019 Annual Research Report
  • [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
      2017 Annual Research Report
  • [Remarks] 国際ワークショップ Knots and Polymers

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/kshimoka/knotsandpolymers2017J.html

    • Related Report
      2017 Annual Research Report
  • [Remarks] 新学術領域「次世代物質探索のための離散幾何学」

    • URL

      https://www.math-materials.jp

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] 国際シンポジウム "Polymers and networks via topology and entanglement"2019

    • Related Report
      2019 Annual Research Report
  • [Funded Workshop] 国際シンポジウム「Polymers meet Topology」2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] Knots and Polymers: Aspects of topological entanglement in DNA, proteins and graph-shaped polymers2017

    • Related Report
      2017 Annual Research Report

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Published: 2017-07-04   Modified: 2022-02-28  

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