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Global analysis of phase transition by using nano-minimal surface theory

Planned Research

Project AreaDiscrete Geometric Analysis for Materials Design
Project/Area Number 17H06466
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 InstitutionNagoya University

Principal Investigator

Naito Hisashi  名古屋大学, 多元数理科学研究科, 准教授 (40211411)

Co-Investigator(Kenkyū-buntansha) 納谷 信  名古屋大学, 多元数理科学研究科, 教授 (70222180)
Project Period (FY) 2017-06-30 – 2022-03-31
Project Status Completed (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離散幾何解析 / 極小曲面 / グラフ理論 / 炭素構造 / MOF / 材料科学 / グラフェン / 離散材料幾何学 / 幾何解析学 / 離散幾何解析学 / 微分幾何学 / 数値解析
Outline of Final Research Achievements

A novel crystal structure represented by a carbon structure was analyzed using discrete geometry analysis.
In order to analyze the crystal structure, which is a typical example of the carbon structure from the viewpoint of discrete geometry analysis, Define a trivalent discrete surface, define its Gaussian curvature and mean curvature, It shows the negative curvature of the structure that was conventionally called ``negative curvature carbon structure'', etc. It was shown that the structure that appears in material science can be described by the method of discrete geometry analysis. In addition, by improving the energy of the graph, we proposed a high-speed calculation method for the curved graphene structure.
An example is shown in which there is a strong correlation between the curvature of a curved surface and its physical properties.

Academic Significance and Societal Importance of the Research Achievements

従来とは異なる離散幾何解析的なアプローチによって材料物性を解析できる可能性を示した. 従来の材料科学では経験的な手法によって望ましい物性を探索することが多く, また近年のデータ駆動型アプローチでも, 多くの既存のデータを用いることが多い. 一方, 我々が行なった離散幾何解析的アプローチは, 材料の幾何学的性質を考察することにより,
望ましい物性・新奇な物性をもつ材料を探索する可能性を開拓した.

Report

(6 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (29 results)

All 2022 2021 2020 2019 2018 2017 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 3 results) Presentation (22 results) (of which Int'l Joint Research: 6 results,  Invited: 20 results) Remarks (2 results)

  • [Journal Article] Geometric model of 3D curved graphene with chemical dopants2021

    • Author(s)
      Dechant Andreas、Ohto Tatsuhiko、Ito Yoshikazu、Makarova Marina V.、Kawabe Yusuke、Agari Tatsufumi、Kumai Hikaru、Takahashi Yasufumi、Naito Hisashi、Kotani Motoko
    • Journal Title

      Carbon

      Volume: 182 Pages: 223-232

    • DOI

      10.1016/j.carbon.2021.06.004

    • NAID

      120007180740

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Construction of continuum from a discrete surface by its iterated subdivisions2021

    • Author(s)
      Motoko Kotani, Hisashi Naito, Chen Tao
    • Journal Title

      Tohoku Mathematical Journal (掲載決定済)

      Volume: -

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A nitrogen-doped nanotube molecule with atom vacancy defects2020

    • Author(s)
      K. Ikemoto, S. Yang, H. Naito, M. Kotani, S. Sato, H. Sato
    • Journal Title

      Nature Communications

      Volume: 11, 1807 Issue: 1 Pages: 1807-1807

    • DOI

      10.1038/s41467-020-15662-6

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A discrete surface theory2017

    • Author(s)
      Motoko Kotani, Hisashi Naito, Toshiaki Omori
    • Journal Title

      Computer Aided Geometric Design

      Volume: 58 Pages: 24-54

    • DOI

      10.1016/j.cagd.2017.09.002

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Fixed-point property for affine actions on a Hilbert space2017

    • Author(s)
      Shin Nayatan
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 66

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] 離散幾何解析とその物性科学への応用2022

    • Author(s)
      内藤久資
    • Organizer
      ワークショップ「物性と離散幾何学」
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Topological Crystallography2021

    • Author(s)
      Hisashi Naito
    • Organizer
      MoSI Meeting
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Carbon structures and Geometry of Trivalent Discrete Surfaces2021

    • Author(s)
      Hisashi Naito
    • Organizer
      International Conference on Discrete Geometric Analysis for Materials Design
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Carbon structures and a discrete surface theory2021

    • Author(s)
      Hisashi Naito
    • Organizer
      Mathematical Sciences of Visualization and Deeping of Symmetry and Moduli
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 3分岐離散曲面と炭素構造2021

    • Author(s)
      内藤久資
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Carbon structures and a discrete surface theory2021

    • Author(s)
      Hisashi Naito
    • Organizer
      Mathematical Sciences of Visualization and Deeping of Symmetry and Moduli, Osaka City University
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 離散曲面論とその材料科学への応用2020

    • Author(s)
      内藤久資,小谷元子
    • Organizer
      化学工学会第51回秋季大会
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] 次世代物質探索のための離散幾何学2020

    • Author(s)
      内藤久資
    • Organizer
      第14回凝縮系科学領域横断研究
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] 離散曲面論とその材料科学への応用2020

    • Author(s)
      内藤久資,小谷元子
    • Organizer
      化学工学会第51回秋季大会,材料・界面部会シンポジウム:次世代物質・材料探索のための新たなアプローチ
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] 次世代物質探索のための離散幾何学2020

    • Author(s)
      内藤久資
    • Organizer
      第14回凝縮系科学領域横断研究会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] 離散曲面論とその材料科学への応用2020

    • Author(s)
      内藤久資
    • Organizer
      日本物理学会第76回年次大会,シンポジウム:次世代物質探索のための離散幾何学
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Discrete geometric analysis -- crystal structure, a discrete surface theory and its applications to physics and chemistry --2019

    • Author(s)
      Hisashi NAITO
    • Organizer
      Introductory workshop on discrete differential geometry
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Analysus of phase transitions using minimal surfaces2018

    • Author(s)
      内藤久資
    • Organizer
      次世代物質探索のための離散幾何学・領域会議
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] ナノ極小曲面論による相分離過程の大域解析2018

    • Author(s)
      内藤久資
    • Organizer
      次世代物質探索のための離散幾何学・班会議
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 炭素構造・結晶格子・離散曲面2018

    • Author(s)
      内藤久資
    • Organizer
      名古屋大学,物質と幾何セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] Analysis of phase transitions using minimal surfaces2018

    • Author(s)
      Hisashi Naito
    • Organizer
      Discrete Geometric Analysis for Materials Design
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] ラプラシアンの第1固有値を最大化する種数2閉曲面上の計量2018

    • Author(s)
      納谷 信
    • Organizer
      日本数学会2018年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 三分岐離散調和曲面の収束2017

    • Author(s)
      内藤久資
    • Organizer
      多様体上の微分方程式
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 炭素構造と離散幾何解析2017

    • Author(s)
      内藤久資
    • Organizer
      幾何学を指標とする化学構造と機能物性
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian2017

    • Author(s)
      Shin Nayatani
    • Organizer
      The 3rd Japan-China Geometry Conference
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Hersch-Yang-Yauの不等式と閉曲面上の第1固有値の最大化について2017

    • Author(s)
      納谷 信
    • Organizer
      Geometric Analysis in Geometry and Topology 2017
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] ラプラシアンの第1固有値を最大化する閉曲面上の計量について2017

    • Author(s)
      納谷 信
    • Organizer
      リーマン幾何と幾何解析
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Remarks] 数学を取り入れたシミュレーションで材料設計を加速

    • URL

      https://www.nagoya-u.ac.jp/researchinfo/result/2021/07/-10.html

    • Related Report
      2021 Annual Research Report
  • [Remarks] 世界初 窒素ドープ型ナノチューブ分子登場

    • URL

      https://www.s.u-tokyo.ac.jp/ja/press/2020/6741/

    • Related Report
      2020 Annual Research Report

URL: 

Published: 2017-07-04   Modified: 2023-01-30  

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