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2005 Fiscal Year Final Research Report Summary

Mathematical Approach to Nonlinear-Non-equilibrium Phenomena - Understanding of Transient Spatio-temporal Patterns-

Research Project

Project/Area Number 15204006
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionMeiji University (2004-2005)
Hiroshima University (2003)

Principal Investigator

MIMURA Masayasu  Meiji University, School of Science and Technology, Professor, 理工学部, 教授 (50068128)

Co-Investigator(Kenkyū-buntansha) MASUDA Kyuya  Meiji University, School of Science and Technology, Professor, 理工学部, 教授 (10090523)
MOCHIZUKI Atsushi  National Institute for Basic Biology, Division of Theoretical Biology, Associate Professor, 理論生物学研究部門, 助教授 (10304726)
KOBAYASHI Ryo  Hiroshima University, Graduate School of Mathematical and Life Sciences, Professor, 大学院・理学研究科, 教授 (60153657)
SENO Hiromi  Hiroshima University, Graduate School of Mathematical and Life Sciences, Associate Professor, 大学院・理学研究科, 助教授 (50221338)
EI Shin-ichiro  Kyushu University, Graduate School of Mathematics, Professor, 大学院・数理学研究院, 教授 (30201362)
Project Period (FY) 2003 – 2005
KeywordsNonlinear-non-equilibrium system / Transient dynamics / Reaction-diffusion system theory / Cell intelligence / Ecological models / Venation formation / Formation of bacterial colonies / Interaction of fronts and spots
Research Abstract

Among diverse nonlinear phenomena, we have studied modeling, analysis and the development of mathematical and complementarily numerical methods in order to understand nonlinear-non-equilibrium phenomena in the transient process.
(1)Investigation of diversity of colonial patterns in chemotactic bacteria by using mathematical models.
(2)Understanding of mechanism of venation formation of leafs by using two reaction-diffusion models under reaction-diffusion hypothesis and carrier hypothesis.
(3)Proposal and simulation of mathematical models describing slime mold in order to understand merge and separation processes observed in experiments. This is the first step of theoretical study of cell-intelligence
(4)As a problem arising in transient processes, proposal and analysis of probabilistic models describing spatial dispersion of biological individuals in heterogeneous medium, and analysis of influence of inter-specific interaction between individuals on velocity in spatial dispersion.
(5)Study of interaction of fronts and spots arising in reaction-diffusion systems
(6)Investigation of dynamics of spatially segregated patterns in cross-diffusion systems by singular limit analysis.

  • Research Products

    (11 results)

All 2006 2005 2004 Other

All Journal Article (10 results) Book (1 results)

  • [Journal Article] Traveling front solutions in a chemotaxis-growth model2006

    • Author(s)
      M.Mimura
    • Journal Title

      J. Free Boundaries and Interfaces (to appear)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A mathematical consideration for the optimal shell change of hermit crab.2006

    • Author(s)
      H.Seno
    • Journal Title

      J. Math. Biol. 52

      Pages: 70-92

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A mathematical consideration for the optimal Shell change of hermit crab2006

    • Author(s)
      H.Seno
    • Journal Title

      J.Math.Biol. 62

      Pages: 70-92

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Self-organization of the vascular system in plant leaves : Inter-dependent dynamics of auxin flux and carrier proteins2005

    • Author(s)
      A.Mochizuki
    • Journal Title

      J. theor. Biol. 236

      Pages: 366-375

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A coupled-oscillator model with a conservation law for the rhythmic amoeboid movements of plasmodial slime molds2005

    • Author(s)
      R.Kobayashi
    • Journal Title

      Physica D 205

      Pages: 125-135

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A variational approach to singular perturbation problems in reaction-diffusion systems2005

    • Author(s)
      S.Ei
    • Journal Title

      Physica D 207

      Pages: 171-219

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Self-organization of vascular system in Plant leaves : Inter-dependent dynamics of auxis flux and carrier proteins2005

    • Author(s)
      A.Mochizuki
    • Journal Title

      J.theor.Biol. 236

      Pages: 366-375

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Pattern formation in consumer-finite resource reaction-diffusion systems2004

    • Author(s)
      M.Mimura
    • Journal Title

      Publ. RIMS, Kyoto Univ., 40

      Pages: 1413-1431

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Pattern formation in consumer-finite resource reaction-diffusion systems2004

    • Author(s)
      M.Mimura
    • Journal Title

      Publ.RIMS, Kyoto Univ. 40

      Pages: 1413-1431

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Traveling front solutions in a chemotaxis-growth Model

    • Author(s)
      M.Mimura
    • Journal Title

      J.Free Boundaries and Interfaces (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] パターン形成とダイナミクス-非線形。非平衡現象の数理(4)2006

    • Author(s)
      三村 昌泰
    • Total Pages
      194
    • Publisher
      東大出版会
    • Description
      「研究成果報告書概要(和文)」より

URL: 

Published: 2007-12-13  

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