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Symmetry of crystals and geometry of minimal surfaces

Research Project

Project/Area Number 25400072
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionNara Women's University

Principal Investigator

Matsuzawa Junichi  奈良女子大学, 自然科学系, 教授 (00212217)

Co-Investigator(Kenkyū-buntansha) 堂寺 知成  近畿大学, 理工学部, 教授 (30217616)
Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords極小曲面 / ジャイロイド曲面 / アルキメデスタイリング / 双曲平面 / Schwarzの3角群 / テータ関数 / Schwarzの三角群 / 空間群 / 三角群 / 離散曲面
Outline of Final Research Achievements

We have studied, from the points of view of mathematics and physics, basic theory of hyperbolic Archimedean tilings on triply periodic minimal surfaces appearing as the interfaces in soft matters or mesoporous materials of nanoscopic size. In particular, we have investigated many tilings on Schwarz minimal surfaces and Schoen’s Gyroid surface. Furthermore we have given concrete expressions of the mappings between these minimal surfaces and the hyperbolic plane.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (22 results)

All 2018 2017 2016 2015 2014 2013 Other

All Journal Article (4 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 2 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (17 results) (of which Int'l Joint Research: 5 results,  Invited: 2 results) Remarks (1 results)

  • [Journal Article] Bronze-mean hexagonal quasicrystal2017

    • Author(s)
      Dotera Tomonari、Bekku Shinichi、Ziherl Primoz
    • Journal Title

      Nature Materials

      Volume: 16 Issue: 10 Pages: 987-992

    • DOI

      10.1038/nmat4963

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Hexagulation numbers: the magic numbers of equal spheres on triply periodic minimal surfaces2016

    • Author(s)
      Tomonari Dotera, Hideaki Tanaka and Yusuke Takahashi
    • Journal Title

      Structural Chemistry

      Volume: 28 Issue: 1 Pages: 105-112

    • DOI

      10.1007/s11224-016-0833-7

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] ジャイロイドの迷宮2014

    • Author(s)
      堂寺知成
    • Journal Title

      現代化学

      Volume: 523 Pages: 32-32

    • Related Report
      2014 Research-status Report
  • [Journal Article] ソフトマター準結晶2013

    • Author(s)
      堂寺知成
    • Journal Title

      固体物理

      Volume: 48 Pages: 331-340

    • Related Report
      2013 Research-status Report
  • [Presentation] 青銅比準周期タイリングとその拡張 (Bronze-mean quasicrystalline tiling and its extensions2018

    • Author(s)
      堂寺知成 Tomonari Dotera
    • Organizer
      AIMaP 研究会「結晶構造と準結晶の数理」筑波大学
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 正6角形の自己組織化による切頭8面体の周期構造2018

    • Author(s)
      田中秀明, 堂寺知成
    • Organizer
      日本物理学会年次大会(東京理科大学野田)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 青銅比準結晶から派生する非周期的タイリング構造2018

    • Author(s)
      中蔵丈一郎, 堂寺知成, Primoz Ziherl
    • Organizer
      日本物理学会年次大会(東京理科大学野田)
    • Related Report
      2017 Annual Research Report
  • [Presentation] P、G、D曲面上の剛体球の相転移 I, II2017

    • Author(s)
      高橋佑輔, 田中秀明, 堂寺知成
    • Organizer
      日本物理学会秋季大会(岩手大学)
    • Related Report
      2017 Annual Research Report
  • [Presentation] アゲハチョウとエッシャーと保型関数2017

    • Author(s)
      松澤淳一
    • Organizer
      広島大学総合科学部数理情報セミナー
    • Related Report
      2017 Annual Research Report
  • [Presentation] Regular Arrangement on the P-Surface2016

    • Author(s)
      Yusuke Takahashi and Tomonari Dotera
    • Organizer
      Animal Vegetal Minearal? Boden Research Conference
    • Place of Presentation
      Yallingup,Australia
    • Year and Date
      2016-09-19
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Regular Arrangement on the D-Surface2016

    • Author(s)
      Hideaki Tanaka and Tomonari Dotera
    • Organizer
      Animal Vegetal Minearal? Boden Research Conference
    • Place of Presentation
      Yallingup,Australia
    • Year and Date
      2016-09-19
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Some double fibrations arising from quadric line complexes.2016

    • Author(s)
      Daisuke Tarama
    • Organizer
      Complex Geometry and Lie Groups
    • Place of Presentation
      奈良女子大学
    • Year and Date
      2016-03-23
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 3重周期極小曲面上の剛体球のアルダー転移に現れる魔法数2016

    • Author(s)
      堂寺知成、田中秀明、高橋佑輔
    • Organizer
      ソフトマター研究会
    • Place of Presentation
      北海道大学
    • Related Report
      2016 Research-status Report
  • [Presentation] P、G、D 曲面上の球状粒子がつくる結晶構造の相転移シミュレーション2016

    • Author(s)
      田中秀明、高橋佑輔、堂寺知成
    • Organizer
      高分子基礎物性研究会・高分子計算機科学研究会・高分子ナノテクノロジー研究会 合同討論会
    • Place of Presentation
      東京農工大
    • Related Report
      2016 Research-status Report
  • [Presentation] 周期的極小曲面と Schwarz の三角群2015

    • Author(s)
      松澤淳一
    • Organizer
      非可換代数幾何学の大域的問題とその周辺
    • Place of Presentation
      高知大学
    • Year and Date
      2015-12-19
    • Related Report
      2015 Research-status Report
  • [Presentation] ダイヤモンド曲面上の剛体球の配置2015

    • Author(s)
      田中秀明,堂寺知成
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      関西大学
    • Year and Date
      2015-09-17
    • Related Report
      2015 Research-status Report
  • [Presentation] プリミティブ曲面上の剛体球の配置2015

    • Author(s)
      高橋佑輔,堂寺知成
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      関西大学
    • Year and Date
      2015-09-17
    • Related Report
      2015 Research-status Report
  • [Presentation] Regular tessellations of hard spheres on the P-surface2015

    • Author(s)
      Tomonari Dotera
    • Organizer
      Gordon Research Conference, Soft Condensed Matter Physics
    • Place of Presentation
      Colby-Sawyer College, NH, USA
    • Year and Date
      2015-08-09
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Hard Spheres on the Primitive Surface2015

    • Author(s)
      Tomonari Dotera and Yusuke Takahashi
    • Organizer
      APS March Meeting
    • Place of Presentation
      Ssan Antonio, Texas (USA)
    • Year and Date
      2015-03-02
    • Related Report
      2014 Research-status Report
  • [Presentation] Simulation study of two-lengthscale quasicrystals2013

    • Author(s)
      堂寺知成
    • Organizer
      12th International Conference on Quasicrystals
    • Place of Presentation
      Krakow, Poland
    • Related Report
      2013 Research-status Report
  • [Presentation] まとめ

    • Author(s)
      堂寺知成
    • Organizer
      日本物理学会年会 領域6,7シンポジウム「複雑秩序 -準結晶と多様な物質分野の学融合-」29pCB-8
    • Place of Presentation
      東海大学湘南
    • Related Report
      2013 Research-status Report
    • Invited
  • [Remarks] The 4th Workshop "Complex Geometry and Lie Groups"

    • URL

      https://sites.google.com/site/annafino/the-4th-workshop-complex-geometry-and-lie-groups

    • Related Report
      2015 Research-status Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

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