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

非线性非平衡现象的数学方法-瞬态时空模式的理解-

• 批准号: 15204006
• 负责人: MIMURA Masayasu
• 金额: $ 14.98万
• 依托单位: Meiji University (2004-2005)Hiroshima University (2003)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15204006/
• 关键词: 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; 大腸菌コロニー形成; パルス相互作用; 反応拡散系; 特異極限法

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.

在各种非线性现象中，我们研究了建模，分析和数学和补充数值方法的发展，以了解瞬态过程中的非线性非平衡现象。（1）利用数学模型研究趋化性细菌菌落形态的多样性。（2）在反应扩散假说和载体假说下，利用两个反应扩散模型对叶片脉序形成机理的认识。（3）提出并模拟描述黏菌的数学模型，以理解实验中观察到的合并和分离过程。（4）作为瞬态过程中的问题，提出并分析了描述生物个体在非均匀介质中空间离散的概率模型，分析了个体间种间相互作用对空间离散速度的影响。（5）研究反应扩散系统中的锋和斑的相互作用（6）用奇异极限分析研究交叉扩散系统中空间分离模式的动力学。

项目成果

A mathematical consideration for the optimal shell change of hermit crab.

寄居蟹最佳换壳的数学考虑。

• 发表时间: 2006
• 期刊: J. Math. Biol. 52
• 作者: YOSHIDA;Fumikazu;KITABATAKE;Yosifusa (eds.);H.Seno
• 通讯作者: H.Seno

Self-organization of the vascular system in plant leaves: Inter-dependent dynamics of auxin flux and carrier proteins

• DOI: 10.1016/j.jtbi.2005.03.017
• 发表时间: 2005-10-21
• 期刊: JOURNAL OF THEORETICAL BIOLOGY
• 影响因子: 2
• 作者: Feugier, FG;Mochizuki, A;Iwasa, Y
• 通讯作者: Iwasa, Y

A coupled-oscillator model with a conservation law for the rhythmic amoeboid movements of plasmodial slime molds

• DOI: 10.1016/j.physd.2005.01.010
• 发表时间: 2005-06
• 期刊: Physica D: Nonlinear Phenomena
• 作者: A. Tero;R. Kobayashi;T. Nakagaki

Emergence of adaptability to time delay in bipedal locomotion

双足运动对时间延迟的适应性的出现

• 发表时间: 2004
• 期刊: Biol. Cybern. 90
• 作者: Q.Wang;G.Gu;Y.Higano;T. Katsura;S.-I.Ei
• 通讯作者: S.-I.Ei

T.Ohta: "Phase Ordering in the Time-Dependent Ginzburg-Landau Equation with a Global Coupling"Journal of the Physical Society of Japan. 72. 1315-1317 (2003)

T.Ohta：“具有全局耦合的瞬态 Ginzburg-Landau 方程中的相序”日本物理学会杂志。