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Spot dynamics of the volume preserving reaction-diffusion systems

Research Project

Project/Area Number 25610029
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionHokkaido University

Principal Investigator

NAGAYAMA Masaharu  北海道大学, 電子科学研究所, 教授 (20314289)

Co-Investigator(Renkei-kenkyūsha) NAKAMURA Ken-Ichi  金沢大学, 数物科学系, 准教授 (40293120)
TERAMOTO Takashi  旭川医科大学, 医学部, 准教授 (40382543)
Project Period (FY) 2013-04-01 – 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 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords体積保存型反応拡散系 / 振動進行スポット / 自励往復運動スポット / 楕円形状定常解 / ピーナッツ形状定常解 / 自励往復スポット / 反応拡散系 / スポット運動 / 分岐数値計算 / 液滴運動モデル / 計算機援用解析
Outline of Final Research Achievements

We have performed a mathematical analysis of model equations for fixed-form particle motions, as well as for one that utilizes droplet-like motions to incorporate shape deformations. In particular, droplet deformations are incorporated through the combination of a volume preserving phase-field equation within a two-component reaction diffusion system. By use of computer-aided analysis, we have also investigated the pattern dynamics within the mathematical model. We observe a parameter for which traveling spots bifurcate from stable standing spot solutions. Traveling spots, moreover, destabilize by means of a Hopf bifurcation, which leads to the appearance of an oscillatory travelling spot. We have also clarified the existence of stable elliptical-shaped and peanut-shaped equilibrium solutions.

Report

(3 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • Research Products

    (14 results)

All 2015 2014 2013 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 1 results) Presentation (8 results) (of which Invited: 5 results) Remarks (2 results)

  • [Journal Article] Physicochemical design and analysis of self-propelled objects that are characteristically sensitive to interfacial environments2015

    • Author(s)
      S. Nakata, M. Nagayama, H. Kitahata, N. J. Suematsu and T. Hasegawa
    • Journal Title

      Physical Chemistry Chemical Physics

      Volume: 7 Issue: 16 Pages: 10326-10338

    • DOI

      10.1039/c5cp00541h

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Appilcation of a center maifold theory to a reaction-diffusion system of collective motion of camphor disks and boats2014

    • Author(s)
      S.-I. Ei, K. Ikeda, M. Nagayama and A. Tomoeda
    • Journal Title

      Mathematica Bohemica

      Volume: 139(2) Pages: 363-371

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical study on the translation and rotation of an elliptic camphor particle2014

    • Author(s)
      Keita Iida, Hiroyuki Kitahata, Masaharu Nagayama
    • Journal Title

      physica D

      Volume: 272 Pages: 39-50

    • DOI

      10.1016/j.physd.2014.01.005

    • NAID

      120005457008

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical study on the translation and rotation of an elliptic camphor particle2014

    • Author(s)
      K.Iida, H.Kitahata and M.Nagayama
    • Journal Title

      Physica D

      Volume: 272 Pages: 39-50

    • NAID

      120005457008

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] The collective motion of camphor papers in a cylindrical channel2015

    • Author(s)
      長山雅晴
    • Organizer
      One-day Workshop on Applied Mathematics
    • Place of Presentation
      台北(台湾)
    • Year and Date
      2015-03-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 自走粒子の集団運動に対する数理解析2014

    • Author(s)
      長山雅晴
    • Organizer
      非線形数理セミナー
    • Place of Presentation
      明治大学(神奈川県川崎市)
    • Year and Date
      2014-09-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The collective motion of camphor papers in a cylindrical channel2014

    • Author(s)
      長山雅晴
    • Organizer
      The 10th AIMS Conference on Dynamical systems, Differential Equations and Applications
    • Place of Presentation
      マドリッド(スペイン)
    • Year and Date
      2014-07-07 – 2014-07-11
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 樟脳円盤の集団運動に対する数理解析2014

    • Author(s)
      西 慧
    • Organizer
      日本計算工学講演会
    • Place of Presentation
      広島国際会議場(広島県広島市)
    • Year and Date
      2014-06-11 – 2014-06-13
    • Related Report
      2014 Annual Research Report
  • [Presentation] The collective motion of camphor papers in a cylindrical channel2014

    • Author(s)
      長山雅晴
    • Organizer
      The 10th AIMS Conference on Dynamical systems, Differential Equations and Applications
    • Place of Presentation
      マドリッド(スペイン,Universidad Autonoma de Madrid )
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 樟脳粒の自発運動:粒子形状と運動の関係について2013

    • Author(s)
      飯田渓太
    • Organizer
      日本計算工学会
    • Place of Presentation
      東京大学(東京都)
    • Related Report
      2013 Research-status Report
  • [Presentation] Mathematical analysis of the collective motion of camphor disks2013

    • Author(s)
      長山雅晴
    • Organizer
      013 Northeastern Asian Symposium on High Performance Computing Method and Modeling, September
    • Place of Presentation
      成都(中国,Wangjiang Hotel)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 自己駆動粒子の集団運動に対する数理解析2013

    • Author(s)
      若井健
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県瀬田市)
    • Related Report
      2013 Research-status Report
  • [Remarks] Research Work

    • URL

      http://mmc01.es.hokudai.ac.jp/prof/research.html

    • Related Report
      2014 Annual Research Report
  • [Remarks] Research Work

    • URL

      http://mmc01.es.hokudai.ac.jp/prof/research.html

    • Related Report
      2013 Research-status Report

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

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