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Study on the strong interaction among spatially localized patterns in dissipative systems

Research Project

Project/Area Number 21340019
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTohoku University (2011-2012)
Hokkaido University (2009-2010)

Principal Investigator

NISHIURA Yasumasa  東北大学, 原子分子材料科学高等研究機構, 教授 (00131277)

Co-Investigator(Kenkyū-buntansha) UEDA Keiichi  富山大学, 大学院・理工学研究部, 准教授 (00378960)
TERAMOTO Takashi  旭川医科大学, 医学部, 准教授 (40382543)
IIMA Makoto  広島大学, 大学院・理学研究科, 准教授 (90312412)
Co-Investigator(Renkei-kenkyūsha) NAKAGAKI Toshiyuki  公立はこだて未来大学, 複雑系知能学科, 教授 (70300887)
TAKAGI Seiji  北海道大学, 電子科学研究所, 助教 (80372259)
EI Shinichiro  九州大学, マス・フォア・インダストリ研究所, 教授 (30201362)
NAGAYAMA Masaharu  北海道大学, 電子科学研究所, 教授 (20314289)
Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥16,900,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥3,900,000)
Fiscal Year 2012: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2010: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2009: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Keywords空間局在解 / 大域分岐 / 応用数学 / 真正粘菌 / 自己組織化 / 反応拡散系 / 対流 / パターン形成 / 反応拡散 / ヘテロクリニック軌道 / スポット解
Research Abstract

Spatially localized traveling patterns appear ubiquitously in nature such as neural system, gas-discharge phenomena, chemical reaction, binary convection, and motion of true slime mold. They display a variety of dynamic patterns like annihilation, coalescence,and splitting via collisions or interaction with environments. For the comprehensive understanding of these phenomena, we combine several theoretical and numerical approaches like local bifurcation analysis of higher codimension, numerical path-tracking, and reduction to finite dimensional systems, which allow us to clarify the mathematical mechanism controlling behind those dynamics.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (50 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (28 results) (of which Peer Reviewed: 23 results) Presentation (11 results) (of which Invited: 1 results) Book (4 results) Remarks (7 results)

  • [Journal Article] Dynamics of two interfaces in a hybrid system with jump-type heterogeneity2013

    • Author(s)
      K.Nishi, Y.Nishiura, T.Teramoto
    • Journal Title

      Japan J. Indust. Appl. Math

      Volume: Vol.30 Issue: 2 Pages: 351-395

    • DOI

      10.1007/s13160-013-0100-x

    • NAID

      10031185313

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spontaneous formation of travelling localized structures and their asymptotic behaviours in binary fluid convection2012

    • Author(s)
      T. Watanabe, M. Iima and Y. Nishiura
    • Journal Title

      Journal of Fluid Mechanics

      Volume: Vol.712 Pages: 219-243

    • DOI

      10.1017/jfm.2012.413

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tacticdirection determined by the interaction betweenoscillatory chemical waves and rheologicaldeformation in an amoeba2012

    • Author(s)
      K. Ueda, S. Takagi, and T. Nakagaki
    • Journal Title

      Physical Review

      Volume: E86 Issue: 1 Pages: 11927-11927

    • DOI

      10.1103/physreve.86.011927

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Refraction, Reflection and Splitting : With thanksto all the people who allowed us to continue to make a research2012

    • Author(s)
      Y. Nishiura, T. Teramoto
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: Vol.B31 Pages: 167-194

    • URL

      http://ci.nii.ac.jp/naid/110009460972

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Heterogeneity-induced spot dynamics for a three-component reaction-diffusion system2012

    • Author(s)
      Y.Nishiura, T.Teramoto, X.Yuan
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: Vol.11 Issue: 1 Pages: 307-338

    • DOI

      10.3934/cpaa.2012.11.307

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A mathematical mechanism for instabilities in stripe formation on growing domains2012

    • Author(s)
      K.-I.Ueda, Y.Nishiura
    • Journal Title

      Physica D

      Volume: Vol.241 Issue: 1 Pages: 37-59

    • DOI

      10.1016/j.physd.2011.09.016

    • NAID

      120003702849

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Behaviors of a Front-Back Pulse Arising in a Bistable Medium with Jump-Type Heterogeneity2012

    • Author(s)
      Kei Nishi, Yasumasa Nishiura, Takashi Teramoto
    • Journal Title

      to appear in Advanced Studies in Pure Mathematics

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 二成分混合流体対流に現れる空間局在解の安定性2011

    • Author(s)
      渡辺毅、飯間信、西浦廉政
    • Journal Title

      日本流体力学会年会2011講演要旨集

    • URL

      http://rnavi.ndl.go.jp/books/2012/12/000011273069.php

    • Related Report
      2012 Final Research Report
  • [Journal Article] Collision dynamics in dissipative systems2011

    • Author(s)
      Y. Nishiura, T. Teramoto
    • Journal Title

      Theoretical and Applied Mechanics Japan

      Volume: Vol.59 Pages: 13-25

    • NAID

      130004463762

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Time-periodic traveling solutions of localized convection cells in binary fluid mixture2011

    • Author(s)
      T. Watanabe, K. Toyabe, M. Iima and Y.Nishiura
    • Journal Title

      Theoretical and Applied Mechanics Japan

      Volume: Vol.59 Pages: 211-219

    • NAID

      130004463770

    • URL

      https://www.jstage.jst.go.jp/browse/nctam/59/0/_contents

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Chaotic motion of propagating pulses in the Gray-Scott model2011

    • Author(s)
      M. Yadome, K. Ueda, M. Nagayama
    • Journal Title

      Physical Review E

      Volume: Vol.83, Issue 5 Issue: 5 Pages: 83-83

    • DOI

      10.1103/physreve.83.056207

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mathematical model for contemplative amoeboid locomotion2011

    • Author(s)
      K.-I.Ueda, S.Takagi, Y.Nishiura, T.Nakagaki
    • Journal Title

      Physical Review E

      Volume: Vol.83 Issue: 2 Pages: 21916-21916

    • DOI

      10.1103/physreve.83.021916

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Time-periodic traveling solutions of localized convection cells in binary fluid mixture2011

    • Author(s)
      T.Watanabe, K.Toyabe, M.Iima, Y.Nishiura
    • Journal Title

      Theoretical and Applied Mechanics Japan

      Volume: 59 Pages: 211-219

    • NAID

      130004463770

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A mathematical model for contemplative amoeboid locomotion2011

    • Author(s)
      K.Ueda, S.Takagi, Y.Nishiura, T.Nakagaki
    • Journal Title

      Physical Review E

      Volume: 83(2)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pinned fronts in heterogeneous media of jump type2010

    • Author(s)
      P.van Heijster, A.Doelman, T.J.Kaper, Y.Nishiura, K.-I.Ueda
    • Journal Title

      Nonlinearity

      Volume: Vol.24 Issue: 1 Pages: 127-157

    • DOI

      10.1088/0951-7715/24/1/007

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Morphological characterization of the diblock copolymer problem with topological computation2010

    • Author(s)
      T.Teramoto, Y.Nishiura
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: Vol.27 Issue: 2 Pages: 175-190

    • DOI

      10.1007/s13160-010-0014-9

    • NAID

      10026699997

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical approach to transient dynamics of oscillatory pulses in abistable reaction-diffusion system2010

    • Author(s)
      M. Nagayama, K. Ueda and M. Yadome
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: Vol.27, Issue 2 Issue: 2 Pages: 295-322

    • DOI

      10.1007/s13160-010-0015-8

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 二成分混合流体対流における漸近挙動:局在構造の自発的発現と集団運動2010

    • Author(s)
      渡辺毅、鳥谷部和孝、飯間信、西浦廉政
    • Journal Title

      日本流体力学会年会2010講演論文集

      Volume: 34

    • URL

      http://ci.nii.ac.jp/naid/110008460026

    • Related Report
      2012 Final Research Report
  • [Journal Article] 二成分混合流体対流に現れる様々な流れとその性質2010

    • Author(s)
      渡辺毅、鳥谷部和孝、飯間信、西浦廉政
    • Journal Title

      第59回 理論応用力学講演会講演論文集

      Pages: 167-168

    • NAID

      130004604627

    • Related Report
      2012 Final Research Report
  • [Journal Article] Pinned fronts in heterogeneous media of jump type2010

    • Author(s)
      P.V.Heijster, A.Doelman, T.J.Kaper, Y.Nishiura, K.Ueda
    • Journal Title

      Nonlinearity

      Volume: 24(1) Pages: 127-157

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rotational motion of traveling spots in dissipative systems2009

    • Author(s)
      T.Teramoto, K.Suzuki, Y.Nishiura
    • Journal Title

      Physical Review E

      Volume: Vol.80 Issue: 4

    • DOI

      10.1103/physreve.80.046208

    • NAID

      120001672681

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pulse dynamics for reaction-diffusion systems in the neighborhood of codimension two singularity2009

    • Author(s)
      S. Ei, Y. Nishiura and K. Ueda
    • Journal Title

      Journalof Math-for-industry

      Volume: Vol.1, Issue 2009B-2 Pages: 91-95

    • NAID

      120001633478

    • URL

      http://hdl.handle.net/2324/15583

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 二成分混合流体中に現れる局在型対流解の分岐構造と相互作用2009

    • Author(s)
      渡辺毅、鳥谷部和孝、飯間信、西浦廉政
    • Journal Title

      日本流体力学会年会2009講演論文集

      Pages: 50-50

    • URL

      http://ci.nii.ac.jp/naid/110008459730

    • Related Report
      2012 Final Research Report
  • [Journal Article] Dynamics of Particle Patterns in Dissipative Systems: Splitting ・Destruction ・ Scattering2009

    • Author(s)
      Y. Nishiura
    • Journal Title

      Sugaku expositions

      Volume: Vol.22, No.1 Pages: 37-55

    • NAID

      120001821837

    • URL

      http://hdl.handle.net/2115/42600

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Onset of unidirectional pulse propagation in an excitable medium with asymmetric heterogeneity2009

    • Author(s)
      T.Teramoto, X.Yuan, M.Bar, Y.Nishiura
    • Journal Title

      Physical Review E

      Volume: Vol.79 Issue: 4

    • DOI

      10.1103/physreve.79.046205

    • NAID

      120001342683

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Onset of unidirectional pulse propagation in an excitable medium with asymmetric heterogeneity2009

    • Author(s)
      Takashi Teramoto, Xiaohui Yuan, Markus Baer, Yasumasa Nishiura
    • Journal Title

      Physical Review E 79

    • NAID

      120001342683

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rotational motion of traveling spots in dissipative systems2009

    • Author(s)
      Takashi Teramoto, Katsuya Suzuki, Yasumasa Nishiura
    • Journal Title

      Physical Review E 80

    • NAID

      120001672681

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 反応拡散系に対する大域的分岐構造の数値計算法とその応用2009

    • Author(s)
      矢留雅亮, 長山雅晴, 上田肇一
    • Journal Title

      数理解析研究所講究録 1633

      Pages: 39-61

    • Related Report
      2009 Annual Research Report
  • [Presentation] Heterogeneity-induced spot dynamics in dissipative systems2012

    • Author(s)
      T. Teramoto and Y. Nishiura
    • Organizer
      2012 SIAM Conference on Nonlinear Waves and Coherent Structures,Geometric Methods for Advection- reactiondiffusion Systems - Part I of II
    • Place of Presentation
      Seattle, USA
    • Year and Date
      2012-06-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Deformations, Internal Dynamics and Network of Unstable Patterns2011

    • Author(s)
      Y. Nishiura
    • Organizer
      ICIAM2011
    • Place of Presentation
      Vancouver, Canada
    • Year and Date
      2011-07-18
    • Related Report
      2012 Final Research Report
  • [Presentation] Deformations, Internal Dynamics and Network of Unstable Patterns2011

    • Author(s)
      Y.Nishiura
    • Organizer
      ICIAM2011
    • Place of Presentation
      Vancouver, Canada(招待講演)
    • Year and Date
      2011-07-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] 遷移ダイナミクスにおける不安定性の思想2010

    • Author(s)
      西浦 廉政
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学東山キャン パス(名古屋市)
    • Year and Date
      2010-09-24
    • Related Report
      2012 Final Research Report
  • [Presentation] 遷移ダイナミクスにおける不安定性の思想2010

    • Author(s)
      西浦廉政
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学東山キャンパス(名古屋市) 招待講演
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] 二成分混合流体対流における漸近挙動:局在構造の自発的発現と集団運動2010

    • Author(s)
      渡辺毅、鳥谷部和孝、飯間信、西浦廉政
    • Organizer
      日本流体力学会年会2010
    • Place of Presentation
      北海道大学高等教育機能開発センター(札幌市)
    • Year and Date
      2010-09-09
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] Collision dynamics and rotational motion of dissipative particles2010

    • Author(s)
      Y. Nishiura
    • Organizer
      Japanese French Meeting ReaDiLab 2010 Spatio-Temporal Patternsfrom Mathematics to Biomedical Applications
    • Place of Presentation
      Archamps,France
    • Year and Date
      2010-03-17
    • Related Report
      2012 Final Research Report
  • [Presentation] Collision dynamics and rotational motion of dissipative particles2010

    • Author(s)
      Yasumasa Nishiura
    • Organizer
      Japanese French Meeting ReaDiLab 2010 Spatio-Temporal Patterns from Mathematics to Biomedical Applications
    • Place of Presentation
      ARCHAMPS, FRANCE
    • Year and Date
      2010-03-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] Collision dynamics in dissipative systems, International Workshop on Self-organization inChemical and Biological Systems: Modeling2009

    • Author(s)
      Y. Nishiura
    • Organizer
      Analysis and Simulation
    • Place of Presentation
      明治大学駿河台キャン パス(東京都)
    • Year and Date
      2009-07-08
    • Related Report
      2012 Final Research Report
  • [Presentation] Collision dynamics in dissipative systems2009

    • Author(s)
      Yasumasa Nishiura
    • Organizer
      International Workshop on Self-organization in Chemical and Biological Systems : Modeling, Analysis and Simulation
    • Place of Presentation
      明治大学駿河台キャンパス(東京都)
    • Year and Date
      2009-07-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Heterogeneity-induced spot dynamics in dissipative systems

    • Author(s)
      T. Teramoto and Y. Nishiura
    • Organizer
      2012 SIAM Conference on Nonlinear Waves and Coherent Structures,Geometric Methods for Advection-reaction-diffusion Systems - Part I of II
    • Place of Presentation
      Seattle, Washington, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Book] 越境する数学2013

    • Author(s)
      西浦廉政
    • Publisher
      岩波書店
    • Related Report
      2012 Final Research Report
  • [Book] 臨時別冊・数理科学『現象から方程式を創り出す』(砂漠化問題のバスタブモデル)2012

    • Author(s)
      西浦廉政、寺本敬
    • Publisher
      サイエンス社
    • Related Report
      2012 Final Research Report
  • [Book] 臨時別冊・数理科学『現象から方程式を創り出す』2012

    • Author(s)
      西浦廉政、寺本敬(分担執筆)
    • Publisher
      サイエンス社
    • Related Report
      2011 Annual Research Report
  • [Book] 現代界面コロイド科学の事典(生成・伝搬・崩壊のパターンダイナミクス)2010

    • Author(s)
      西浦廉政
    • Publisher
      丸善株式会社
    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://researchmap.jp/ynishiura/

    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://www.wpi-aimr.tohoku.ac.jp/

    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://researchmap.jp/ynishiura/

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www-nsc.es.hokudai.ac.jp/~nishiura/

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://researchmap.jp/ynishiura/

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.jst.go.jp/en/researchdirector/scientificworks/scientificworks_pl.html

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www-nsc.es.hokudai.ac.jp/~nishiura/

    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2019-07-29  

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