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Construction of theory for a link between microscopic and macroscopic models related to biological phenomena

Research Project

Project/Area Number 16KT0135
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section特設分野
Research Field Mathematical Sciences in Search of New Cooperation
Research InstitutionUniversity of Miyazaki

Principal Investigator

Izuhara Hirofumi  宮崎大学, 工学部, 准教授 (50515096)

Project Period (FY) 2016-07-19 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords数理モデル / ミクロモデル / マクロモデル / パターン形成 / ミクロとマクロ / 大腸菌 / 階層性 / 応用数学
Outline of Final Research Achievements

Many phenomena observed in nature have hierarchical structures. E.coli which is one of bacteria have a simple movement that each individual repeats straight motion and rotation motion alternately. However, when they are cultivated on a nutrient agar, it is well known that a very regular colony pattern is formed in a macroscopic level. From the viewpoint of experiments and numerical simulations of mathematical models, there are so many studies on E.coli motion in a microscopic level and colony patterns in a macroscopic level. But, a relation between a simple microscopic motion of each individual and a regular macroscopic colony pattern is not known. In this research, we revealed the microscopic and macroscopic relation from a mathematical point of view.

Academic Significance and Societal Importance of the Research Achievements

古くから複雑な物事でも、それを構成する要素に分解し、個別の要素を理解すれば、全体の性質や振る舞いを理解できると思われていたが、ミクロの情報だけでは、マクロの振る舞いを予想できない創発性が認識されるようになり、ミクロとマクロの橋渡しとなる新たな手法の確立が必要となっていた。そのため、本研究は階層を超えたミクロとマクロの関係性解明に挑戦した研究であり、これからの創発現象解明への一つのブレイクスルーとして意義があると考えている。

Report

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

    (43 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (9 results) Journal Article (6 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 6 results,  Acknowledgement Compliant: 2 results) Presentation (27 results) (of which Int'l Joint Research: 11 results,  Invited: 25 results) Remarks (1 results)

  • [Int'l Joint Research] パリ南大学/モンペリエ大学(フランス)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] ローマ第2大学(イタリア)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] 国立台南大学(その他の国・地域 台湾)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] パリ南大学/モンペリエ大学(フランス)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] モンペリエ大学(イタリア)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] リムリック大学(アイルランド)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] ローマ第2大学(イタリア)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] パリ南大学/モンペリエ大学(フランス)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] リムリック大学(アイルランド)

    • Related Report
      2016 Research-status Report
  • [Journal Article] A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic Fisher KPP equation,2019

    • Author(s)
      Bertsch Michiel、Hilhorst Danielle、Izuhara Hirofumi、Mimura Masayasu、Wakasa Tohru
    • Journal Title

      Discrete and Continuous Dynamical Systems Series A

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Standing and traveling waves in a parabolic-hyperbolic system2019

    • Author(s)
      Bertsch Michiel、Izuhara Hirofumi、Mimura Masayasu、Wakasa Tohru
    • Journal Title

      Discrete and Continuous Dynamical Systems Series A

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Bifurcation structure of stationary solutions for a chemotaxis system with bistable growth2018

    • Author(s)
      Hiroshi Izuhara, Kouske Kuto and Tohru Tsujikawa
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 35 Issue: 2 Pages: 441-475

    • DOI

      10.1007/s13160-017-0298-0

    • NAID

      210000164399

    • Related Report
      2018 Annual Research Report 2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] On a nonlocal system for vegetation in drylands2018

    • Author(s)
      M. Alfaro, H. Izuhara and M. Mimura
    • Journal Title

      J. Math. Biol.

      Volume: 77 Issue: 6-7 Pages: 1-33

    • DOI

      10.1007/s00285-018-1215-0

    • Related Report
      2018 Annual Research Report 2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Traveling waves in a reaction-diffusion system describing smoldering combustion2017

    • Author(s)
      Ekeoma R. Ijioma, Hirofumi Izuhara, Masayasu Mimura
    • Journal Title

      SIAM Journal on Applied Mathematics

      Volume: 77 Issue: 2 Pages: 614-637

    • DOI

      10.1137/16m1089915

    • Related Report
      2017 Research-status Report 2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Diffusion-driven destabilization of spatially homogeneous limit cycles in reaction-diffusion systems2017

    • Author(s)
      Masataka Kuwamura, Hirofumi Izuhara
    • Journal Title

      Chaos: An Interdisciplinary Journal of Nonlinear Science

      Volume: 27 Issue: 3 Pages: 033112-033112

    • DOI

      10.1063/1.4978924

    • NAID

      120006318793

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Traveling waves in a nonlinear parabolic-hyperbolic system for contact inhibition2019

    • Author(s)
      Izuhara Hirofumi
    • Organizer
      Transition from hunter-gatherers to farmers in the Neolithic age
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spatio-temporal coexistence in the cross-diffusion competition system2019

    • Author(s)
      出原浩史
    • Organizer
      反応拡散系のパターン形成とその応用
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Computational study on combustion wave in a narrow channel2019

    • Author(s)
      出原浩史
    • Organizer
      数学と現象 in 那須塩原
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On a reaction-diffusion system describing smoldering combustion2018

    • Author(s)
      Izuhara Hirofumi
    • Organizer
      Seminar at National University of Tainan
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spatiotemporal coexistence in the cross-diffusion competition system2018

    • Author(s)
      Izuhara Hirofumi
    • Organizer
      2018 China-Japan Workshop on Nonlinear Diffusion Problems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Time periodic coexistence in the cross-diffusion competition system2018

    • Author(s)
      Izuhara Hirofumi
    • Organizer
      ReaDiNet 2018 Recent Progresses in Mathematical Theories for Biological Phenomena
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Computational study of flame spread in a narrow channel2018

    • Author(s)
      Izuhara Hirofumi
    • Organizer
      Journee d'Analyse Non Lineaire
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On a nonlocal system for vegetation in drylands2018

    • Author(s)
      Izuhara Hirofumi
    • Organizer
      The 12th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 交差拡散-競争方程式における周期解2018

    • Author(s)
      出原浩史
    • Organizer
      反応拡散系の理論と応用
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 非局所項をもつ微分方程式について2018

    • Author(s)
      出原浩史
    • Organizer
      数学と現象 in 長瀞
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 反応拡散系に現れる弛緩振動2018

    • Author(s)
      出原浩史
    • Organizer
      松江セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] パターンを遷移する弛緩振動について2018

    • Author(s)
      出原浩史
    • Organizer
      研究集会:パターン形成の数理とその周辺
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 燃焼モデルの数値シミュレーション解析2018

    • Author(s)
      出原浩史
    • Organizer
      数学と現象 in 清里
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Mathematical analysis on a nonlinear system for contact inhibition of cell growth2017

    • Author(s)
      Hirofumi Izuhara
    • Organizer
      MIMS workshop on Modeling and Numerical Analysis of Nonlinear Phenomena: Fluid Dynamics, Motion of Interfaces, and Cell Biology
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Smoldering combustion in a narrow channel2017

    • Author(s)
      Hirofumi Izuhara
    • Organizer
      ReaDiNet 2017 International Conference on Mathematical Biology
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 増殖項をもつ走化性方程式のパターン形成2017

    • Author(s)
      出原浩史
    • Organizer
      京都大学数理解析研究所共同研究(公開型) 非線形現象と反応拡散方程式
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] くすぶり燃焼の数理モデルからの接近2017

    • Author(s)
      出原浩史
    • Organizer
      明治大学MIMS研究集会 火災における不安定性の数理
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] 半乾燥地域に現れる植生パターンと砂漠化2017

    • Author(s)
      出原浩史
    • Organizer
      明治大学MIMS研究集会 自然界に現れる紋様, 形態の統合的理解
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] 反応拡散系における周期解について2017

    • Author(s)
      出原浩史
    • Organizer
      数学と現象 in 奥多摩
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] 接触抑制と正常細胞と異常細胞のダイナミクス2017

    • Author(s)
      出原浩史
    • Organizer
      北海道大学社会創造数学セミナーシリーズHMMCセミナー
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] 走化性と増殖の効果がつくりだす時空間パターン2017

    • Author(s)
      出原浩史
    • Organizer
      明治大学MIMS研究集会 時空間ダイナミクス~生命現象における時間変化を伴う空間秩序
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Narrow channelにおけるくすぶり燃焼と再燃2017

    • Author(s)
      出原浩史
    • Organizer
      日本応用数理学会2017年度年会
    • Related Report
      2017 Research-status Report
  • [Presentation] 微小重力環境におけるすす燃焼の数理解析2017

    • Author(s)
      出原浩史
    • Organizer
      数学と現象 in 清里
    • Place of Presentation
      明治大学清里セミナーハウス
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Vegetation and desertification in arid and semiarid ecosystems2016

    • Author(s)
      Hirofumi Izuhara
    • Organizer
      Mathematical Biology Workshop for Ecology and Evolutionary Problems
    • Place of Presentation
      NIMS, Daejeon, Korea
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Traveling wave solutions in a nonlinear system for contact inhibition of cells2016

    • Author(s)
      Hirofumi Izuhara
    • Organizer
      Reaction-Diffusion Systems in Mathematics and Biomedicine A GDRI ReaDiNet Conference in Frejus
    • Place of Presentation
      Villa Clythia, Frejus, France
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Vegetation patterns in arid ecosystems2016

    • Author(s)
      Hirofumi Izuhara
    • Organizer
      Patterns and Waves 2016
    • Place of Presentation
      北海道大学
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] A link between microscopic and macroscopic models of self-organized aggregation2016

    • Author(s)
      出原浩史
    • Organizer
      数学と現象 in 奥多摩
    • Place of Presentation
      奥多摩町福祉会館
    • Related Report
      2016 Research-status Report
    • Invited
  • [Remarks] Hirofumi Izuhara's webpage

    • URL

      https://sites.google.com/site/hirofumiizuhara/

    • Related Report
      2016 Research-status Report

URL: 

Published: 2016-07-20   Modified: 2023-03-08  

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