2005 Fiscal Year Final Research Report Summary
Mathematical Approach to Nonlinear-Non-equilibrium Phenomena - Understanding of Transient Spatio-temporal Patterns-
| Project/Area Number |
15204006
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Meiji University (2004-2005)
Hiroshima University (2003) |
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Principal Investigator |
MIMURA Masayasu Meiji University, School of Science and Technology, Professor, 理工学部, 教授 (50068128)
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| 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)
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| Project Period (FY) |
2003 – 2005
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| Keywords | Nonlinear-non-equilibrium system / Transient dynamics / Reaction-diffusion system theory / Cell intelligence / Ecological models / Venation formation / Formation of bacterial colonies / Interaction of fronts and spots |
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| 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.
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