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、分析以及数学和互补数值方法的发展，以理解瞬态过程中的非线性非平衡现象。（1）利用数学方法研究趋化细菌的群体模式的多样性。 (2)利用反应扩散假设和载体假设下的两种反应扩散模型来理解叶片脉络形成的机制。(3)描述粘菌的数学模型的提出和模拟，以理解粘菌的合并和传播实验中观察到的分离过程。这是细胞智能理论研究的第一步(4)作为瞬态过程中出现的问题，描述生物个体在异质介质中空间分散的概率模型的提出和分析，以及个体间种间相互作用的影响分析(5)反应扩散系统中锋面和斑点相互作用的研究(6)通过奇​​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

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。

Pathogens can slow down or reverse invasion fronts of their hosts

• DOI: 10.1007/s10530-005-5215-9
• 发表时间: 2005-09-01
• 期刊: BIOLOGICAL INVASIONS
• 影响因子: 2.9
• 作者: Hilker, FM;Lewis, MA;Malchow, H
• 通讯作者: Malchow, H