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，我们研究了数学和互补的数值方法的建模，分析和发展，以便在瞬态过程中了解非线性 - 非平衡现象。（1）研究了使用数学模型（2）使用VELAINTIFF ROCONTION的反应（2）使用VELIFF的反应（2）使用VELIFF的反应。载体假设。（3）描述粘液模具的数学模型的建议和模拟，以了解实验中观察到的合并和分离过程。这是细胞智能（4）的理论研究的第一步，是在短暂过程，建议和分析中描述生物学个体在异质培养基中的空间分散的概率模型的问题，以及分析个体之间特异性相互作用在空间分散体中速度的反应和SPOTS研究（5）研究的影响（5）。通过奇异极限分析在交叉扩散系统中的空间分离模式。

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