Understanding of singularities arising in nonlinear nonequilibrium phenomena

理解非线性非平衡现象中出现的奇点

• 批准号: 11214101
• 负责人: MIMURA Masauasu
• 金额: $ 18.37万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11214101/
• 关键词: Singular limit method; Multi-dimensional dissipative system; Transient dynamics; Pattern formation in biological systems; Singularities in flow; Computer aided analysis; Dynamical system; Free boundary problem; 特異極限法自由境界問題; 界面ダイナミクス; 生物系のパターン形成

Investigators of this project consist of the group leaders of the team projects : Nonlinear physics group (Kuramoto), Experimental and theoretical group of biological systems (Matsushita), Mathematical analysis group (Nishiura), Nonlinear waves group (Nishida), Fundamental mathematical analysis group (Matano). The results obtained by these groups are introduced in their research reports. Speaking in key-word way, these are(1) Theoretical analysis of complex patterns in dissipative systems ; (2) Analysis of patterns in nonlinear nonequilibrium systems ; (3) Diversity of patterns in biological systems ; (4) Numerical aided analysis of singularities in flows ; (5) Reductive methods of infinite dimensional dynamical systems.The activity of the project is not only to support these research groups, but also to publish "News letter" every 4 months and to organize the symposium (every year), international conferences, workshops and schools.

该项目的研究人员包括团队项目的组长：非线性物理组（仓本），生物系统的实验和理论组（松下），数学分析组（西浦），非线性波组（西田），基础数学分析组（松野）。这些小组的研究报告介绍了他们取得的成果。按关键词讲，它们是：（1）耗散系统复杂斑图的理论分析，（2）非线性非平衡系统斑图的分析，（3）生物系统斑图的多样性，（4）流动奇异性的数值辅助分析，（5）非线性非平衡系统斑图的分析，（6）非线性非平衡系统斑图的分析，（7）非线性非平衡系统斑图的分析，（8）非线性非平衡系统斑图的分析，（9）非线性非线性非平衡系统斑图的分析，（10）非线性非平衡系统斑图的分析，（10）非线性非平衡系统斑图的分析，（11）非线性非线性非平衡系统斑图的分析，（12）非线性非线性非平衡系统斑图的分析，（13）非线性非线性非平衡系统斑图的分析，（14）非线性非平衡系统斑图的分析，（15）非线性非平衡系统斑图的分析，（16）非线性非平衡系统斑图的（5）无穷维动力系统的约化方法。该项目的活动不仅是为了支持这些研究小组，还每4个月出版一次《新闻快报》，并组织研讨会（每年）、国际会议、讲习班和学校。

项目成果

Y.Kuramoto: "Reduction methods applied to nonlocally coupled oscillator systems, in "Nonlinear Dynamics and Chaos : Where do we go from here?""J.Hogan et al.. (In press). (2002)

Y.Kuramoto：“应用于非局部耦合振荡器系统的归约方法，在“非线性动力学和混沌：我们从这里到哪里去？”中。”J.Hogan 等人（正在出版）。

M.Matsushita: "Periodic colony formation by bacterial species Bacillus subtilis"Phys. Soc. Jpn.. 70. 911-919 (2001)

M.Matsushita：“枯草芽孢杆菌细菌的周期性菌落形成”Phys。

H.Matano: "Dynamical structure of some nonlinear degenerate diffusion equations"J. Dynamics and Differential Equations. (In press). (2003)

H.Matano：“一些非线性简并扩散方程的动力学结构”J。

T. Nishida: "A numerical verification of bifurcated solutions for the heat convection problems"J. Mathematical Fluid Mechanics. in press. (2003)

T. Nishida：“热对流问题分叉解的数值验证”J。

Y.Nishiura: "2n-splitting or Edge-splitting-A manner of splitting in dissipative systems"Japan J. of Ind. Appl. Math.. 18. 181-200 (2001)

Y.Nishiura：“2n-分裂或边缘分裂-耗散系统中的一种分裂方式”Japan J. of Ind. Appl。