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Mathematical approach to materials science by using non-commutative geometry

Research Project

Project/Area Number 23654020
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionTohoku University

Principal Investigator

KOTANI Motoko  東北大学, 理学(系)研究科(研究院), 教授 (50230024)

Co-Investigator(Renkei-kenkyūsha) AKAMA Yohji  東北大学, 大学院理学研究科, 准教授 (30272454)
ODA Tadao  東北大学, 大学院理学研究科, 名誉教授 (60022555)
Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords非可換幾何学 / 準結晶 / 格子欠陥 / 量子ホール効果 / 結晶格子 / 非可換幾何
Outline of Final Research Achievements

One of the fundamental questions of solid state physics is to understand relations between microscopic structures and macroscopic properties of matter. One can computer properties in principle if the matter assumes periodic structure. It however often happens that periodic structures are broken under various physical environment such as with impieties, magnetic fields, boundaries. In this project we challenge to establish a new mathematical approach to those problems by using non-commutative geometry.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (47 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article (19 results) (of which Peer Reviewed: 19 results,  Open Access: 1 results) Presentation (28 results) (of which Invited: 19 results)

  • [Journal Article] Geometric measures of finite carbon nanotube molecules : A proposal for length index and filling indexes2014

    • Author(s)
      Taisuke Matsuno, Hisashi Naito, Sunpei Hitotsugi, Sota Sato, Motoko Kotani and Hiroyuki Isobe
    • Journal Title

      Pure and Applied Chemistry

      Volume: 86 Issue: 4 Pages: 489-495

    • DOI

      10.1515/pac-2014-5006

    • Related Report
      2014 Annual Research Report 2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Negatively curved cubic carbon crystals with octahedral symmetry2014

    • Author(s)
      MakotoTagami, Yunye Liang, Hisashi Naito, Yoshiyuki Kawazoe, Motoko Kotani
    • Journal Title

      Carbon

      Volume: 76 Pages: 266-274

    • DOI

      10.1016/j.carbon.2014.04.077

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Mesoscopic Dynamics of Laser-Induced Phase Separation in Water and 2-Butoxyethanol Mixtures Revealed by Nanosecond Time-Resolved Light Scattering2014

    • Author(s)
      Shuichi Toyouchi, Shinji Kajimoto, Masatoshi Toda, Toshihiro Kawakatsu, Yohji Akama, Motoko Kotani, Hiroshi Fukumura
    • Journal Title

      Chemistry Letters

      Volume: 43(12) Issue: 12 Pages: 1838-1840

    • DOI

      10.1246/cl.140698

    • NAID

      130004687279

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantization of interface currents2014

    • Author(s)
      Motoko Kotani, Hermann Schultz-Baldes, Carlos Villegas-Blas
    • Journal Title

      Journal of Mathematical Physics

      Volume: 55(12) Issue: 12 Pages: 1219011-9

    • DOI

      10.1063/1.4902377

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 炭素の新しい結晶 K4 と代数学2014

    • Author(s)
      小田 忠雄
    • Journal Title

      数理科学

      Volume: 611 Pages: 49-54

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric frustration of icosahedron in metallic glasses2013

    • Author(s)
      A.Hirata, L. J. Kang, T. Fujita, B. Klumov, K. Matsue, M. Kotani, A. R. Yavari, M. W. Chen
    • Journal Title

      Science

      Volume: 341巻No. 6144 Issue: 6144 Pages: 376-379

    • DOI

      10.1126/science.1232450

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 離散幾何学から提案する新物質創成・物性発現の解明2013

    • Author(s)
      小谷 元子
    • Journal Title

      応用数理

      Volume: Vol.23 No.4 Pages: 6-9

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (I) - a special tiling by congruent concave quadrangles.2013

    • Author(s)
      Yohji AKAMA
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 43 Pages: 285-304

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Algebro-geometry stability and crystals2013

    • Author(s)
      Tadao ODA
    • Journal Title

      Journal of Ramanujan Mathematical Society

      Volume: 28A Pages: 353-408

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 巻頭言 数学・数理科学の新たな潮流―諸科学との連携を求めて2013

    • Author(s)
      小谷 元子
    • Journal Title

      表面科学

      Volume: 34

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] 材料科学と離散幾何解析学の連携による挑戦2013

    • Author(s)
      小谷 元子
    • Journal Title

      表面科学

      Volume: 34

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Voronoi tilings hidden in crystals --- the case of maximal abelian coverings ---2013

    • Author(s)
      Tadao Oda
    • Journal Title

      Tohoku Math. J.

      Volume: 65 Pages: 1-30

    • NAID

      130005147681

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Convex polyhedral tilings hidden in crystals and quasicrystals2013

    • Author(s)
      Tadao Oda
    • Journal Title

      RACSAM

      Volume: 107 Issue: 1 Pages: 123-143

    • DOI

      10.1007/s13398-012-0078-2

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (I) -- a special tiling by congruent concave quadrangles2013

    • Author(s)
      Yohji Akama
    • Journal Title

      Hiroshima Math. J.

      Volume: 43

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] New Growth Mechanism of Cubic Rh Clusters Composed of 8–12 Atoms Found by the Method of Euclidean Designs2012

    • Author(s)
      Makoto Tagami, Yunye Liang, Yoshiyuki Kawazoe and Motoko Kotani
    • Journal Title

      MATERIALS TRANSACTIONS

      Volume: 53 Issue: 3 Pages: 459-462

    • DOI

      10.2320/matertrans.N-M2011859

    • NAID

      10030259381

    • ISSN
      1345-9678, 1347-5320
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] ラボラトリーズ「東北大学数学連携の取り組み」2012

    • Author(s)
      小谷 元子
    • Journal Title

      応用数理

      Volume: 22 Pages: 73-75

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Random Fields on Model Sets with Localized Dependency and Their Diffraction2012

    • Author(s)
      Yohji Akama and Shinji Iizuka
    • Journal Title

      Journal of Statistical Physics

      Volume: 149 Issue: 3 Pages: 478-495

    • DOI

      10.1007/s10955-012-0588-5

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] New Growth Mechanism of Cubic Rh Clusters Composed of 8-12 Atoms Found by Euclidean Designs2012

    • Author(s)
      M. Tagami, Y. Y. Liang, Y. Kawazoe and M. Kotani
    • Journal Title

      Materials Transactions

      Volume: 53巻 Pages: 459-462

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Set systems: order types, continuous nondeterministic deformations, and quasi-orders2011

    • Author(s)
      Yoji Akama
    • Journal Title

      Theoret. Comput. Sci.

      Volume: 412巻 Pages: 6235-6251

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Mathematical challenge to structural understanding of materials2015

    • Author(s)
      小谷 元子
    • Organizer
      2015 East Asian Core Doctorial Forum on Mthematics
    • Place of Presentation
      国立台湾大学(台北,台湾)
    • Year and Date
      2015-01-19
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Discrete geometric analysis applied to structural understanding of materials2014

    • Author(s)
      小谷 元子
    • Organizer
      Inverse Problems and Spectral Theory
    • Place of Presentation
      Texas A&M University(カレッジステーション,アメリカ)
    • Year and Date
      2014-10-17
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 材料科学へのトポロジーの応用2014

    • Author(s)
      小谷 元子
    • Organizer
      幾何学とインターネットの数理2014
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県沼田市)
    • Year and Date
      2014-07-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The rigidity, deformation and tile-transitivity of spherical tilings2014

    • Author(s)
      赤間 陽二
    • Organizer
      Japan Conference on Graph Theory and Combinatorics
    • Place of Presentation
      日本大学(東京都世田谷区)
    • Year and Date
      2014-05-19
    • Related Report
      2014 Annual Research Report
  • [Presentation] Solution to spherical Hilbert eighteenth problem and the deformation of spherical tilings2014

    • Author(s)
      赤間 陽二
    • Organizer
      Canberra - Japan Meeting, “Pattern Formation: Mathematics and Materials”.
    • Place of Presentation
      Australia National University, Canberra, Australia
    • Year and Date
      2014-04-29
    • Related Report
      2014 Annual Research Report
  • [Presentation] Discrete Geometric Analysis applied to structural understanding of Materials2013

    • Author(s)
      M. Kotani
    • Organizer
      Joint International Meeting of the AMS and the Romanian Mathematical Society
    • Place of Presentation
      University of Alba Iulia, Rumania
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Discrete Geometric Analysis applied to structural understanding of Materials2013

    • Author(s)
      M. Kotani
    • Organizer
      Tohoku University Forum at UCL
    • Place of Presentation
      University College London, London, UK
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Discrete Geometric Analysis applied to structural understanding of Materials2013

    • Author(s)
      M. Kotani
    • Organizer
      Tsinghua Sanya International Mathematics Forum
    • Place of Presentation
      Mathematical Sciences Center, Sanya, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] (Semi)stability and (quasi)crystals2012

    • Author(s)
      小田 忠雄
    • Organizer
      研究集会「CMI-IMSc International Mathematics Colloquium」(招待講演)
    • Place of Presentation
      チェンナイ数学研究所(インド)
    • Related Report
      2011 Research-status Report
  • [Presentation] (Semi)stability and (quasi)crystals2012

    • Author(s)
      小田 忠雄
    • Organizer
      研究集会「Arithmetic and Algebraic Geometry 2012」(招待講演)
    • Place of Presentation
      東京大学(東京)
    • Related Report
      2011 Research-status Report
  • [Presentation] 材料科学への数学の挑戦2012

    • Author(s)
      小谷 元子
    • Organizer
      The 6th Hokkaido Univ. Pure & Applied Physics Salon(招待講演)
    • Place of Presentation
      北海道大学(札幌)
    • Related Report
      2011 Research-status Report
  • [Presentation] A Mathematical Challenge to a new phase of materials science2012

    • Author(s)
      小谷 元子
    • Organizer
      MANA Symposium 2012(招待講演)
    • Place of Presentation
      MANA(筑波)
    • Related Report
      2011 Research-status Report
  • [Presentation] Algebro-geometric stability, (quasi)crystals and tropical geometry2011

    • Author(s)
      小田 忠雄
    • Organizer
      研究集会「特異点論とそのひろがり」(招待講演)
    • Place of Presentation
      京都大学理学部大会議室(京都)
    • Related Report
      2011 Research-status Report
  • [Presentation] A Mathematical Challenge to a new phase of materials science2011

    • Author(s)
      小谷 元子
    • Organizer
      Korea Institute For advanced Study Seminar(招待講演)
    • Place of Presentation
      KIAS(ソウル、韓国)
    • Related Report
      2011 Research-status Report
  • [Presentation] 離散幾何学から提案する新物質創成・物性発現の解明2011

    • Author(s)
      小谷 元子
    • Organizer
      CREST領域シンポジウム(招待講演)
    • Place of Presentation
      東京
    • Related Report
      2011 Research-status Report
  • [Presentation] Discrete Geometric Analysis applied to structural understanding of Materials

    • Author(s)
      M. Kotani
    • Organizer
      The 1st WPI workshop on materials science 10th France-Japan Workshop on Nanomaterials
    • Place of Presentation
      京都大学(京都府京都市)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] A mathematical challenge to a new phase of materials science

    • Author(s)
      M. Kotani
    • Organizer
      Connections 2013 Symposium: Crossing Boundaries with Informatics - from Basic Science to Social Infrastructure
    • Place of Presentation
      Cosmos Club, Washington DC, USA
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Discrete Geometric Analysis applied to structural understanding of Materials

    • Author(s)
      M. Kotani
    • Organizer
      CAMP opening symposium
    • Place of Presentation
      CAMP, NIMS, Daejeon, Korea
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 球面的ヒルベルトの第18問題の解決と球面タイリングの変形

    • Author(s)
      赤間 陽二
    • Organizer
      直観幾何学
    • Place of Presentation
      熊本大学(熊本市)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] SPHERICAL TILINGS BY CONGRUENT POLYGONS

    • Author(s)
      Yohji Akama
    • Organizer
      Student-Faculty Colloquium, Department of Mathematics, Hong Kong University of Science and Technology
    • Place of Presentation
      Hong Kong, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] A mathematical challenge to materials science

    • Author(s)
      Motoko Kotani
    • Organizer
      TOHOKU-FUDAN WORKSHOP ON THE OCCASION OF THE CENTENNIAL OF THE FACULTY OF SCIENCE
    • Place of Presentation
      ホテル松島大観荘 (松島)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A mathematical challenge to materials science

    • Author(s)
      Motoko Kotani
    • Organizer
      Topology and Functional Analysis 2012
    • Place of Presentation
      復旦大学 (上海)中国
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A mathematical challenge to materials science

    • Author(s)
      Motoko Kotani
    • Organizer
      理研研究会「物質科学の数学的手法と数理物理」
    • Place of Presentation
      理化学研究所(和光)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A mathematical challenge to materials science

    • Author(s)
      Motoko Kotani
    • Organizer
      RIMS研究集会「Discrete Geometric Analysis」
    • Place of Presentation
      京都大学(京都)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A mathematical challenge to materials science

    • Author(s)
      Motoko Kotani
    • Organizer
      第18回複素幾何シンポジウム
    • Place of Presentation
      信州菅平高原プチホテルゾンタック(上田)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A mathematical challenge to materials science

    • Author(s)
      Motoko Kotani
    • Organizer
      2012 International Conference on Modeling, Analysis and Simulation「現象数理学の展開」(ICMAS)
    • Place of Presentation
      明治大学(東京)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A mathematical challenge to materials science

    • Author(s)
      Motoko Kotani
    • Organizer
      Workshop on Stochastic Analysis and Related Topics
    • Place of Presentation
      AMSS, Chinese Academy of Sciences (北京)中国
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A mathematical challenge to materials science

    • Author(s)
      Motoko Kotani
    • Organizer
      The Seventh General Meeting of Asian Consortium on Computational Materials Science-Virtual Organization
    • Place of Presentation
      ホテル松島大観荘 (松島)
    • Related Report
      2012 Research-status Report
    • Invited

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Published: 2011-08-05   Modified: 2019-07-29  

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