Visualization-system of spatio-temporal patterns in natural sciences

自然科学时空格局可视化系统

• 批准号: 63840001
• 负责人: MIMURA Masayasu
• 金额: $ 6.14万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Developmental Scientific Research
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-63840001/
• 关键词: Numerical simulations of reaction-diffusion equations; Visualization of numerical simulations; Numerical study of Interfacial patterns; 数値シミュレーションの動画化処理; 界面パターンの数値計算

In 1988, we developed visualization system of numerical simulations which connected with mini-super computer under local network systems in the department of Mathematics at Hiroshima University. By using this system, our first study is to visualize spatio-temporal patterns dynamics in combustions, by numerically solving two mathematical models of reaction-diffusion type. The first example is to demonstrate the propagation of combustion waves in one dimension. We can observe that there occurs a bifurcation phenomenon in the wave velocity. That is, when we change the difference of the temperatures at the both side X = <plus-minus>*, the wave which propagates with constant velocity becomes unstable through Hopf-bifurcation and there appears a new wave which propagates with periodic velocity. This phenomenon can be also observed in real experiments. Another example is the pattern formation of cellular flame in a 2 dimensional annular domain. We find that radially symmetric flame patterns become unstable and then there appear cellular flame patterns through static bifurcatioIn 1989, we are interested in visualizing the phenomena of phase separation and coarsening process in binary alloy from a theoretical view point. We numerically solved several reaction-diffusion equation models which has been proposed so far to understand these phenomena. The results show so complex and beautiful patterns which has not been expected until now.

1988年，广岛大学数学系开发了与本地网络系统下的微型超级计算机连接的数值模拟可视化系统。通过使用该系统，我们的第一项研究是通过数值求解反应扩散类型的两个数学模型来可视化燃烧中的时空模式动力学。第一个例子是演示燃烧波在一维中的传播。我们可以观察到波速出现了分叉现象。也就是说，当我们改变两侧的温度差 X = <plus-minus>* 时，以等速传播的波通过 Hopf 分岔变得不稳定，并出现新的以周期速度传播的波。这种现象在实际实验中也可以观察到。另一个例子是二维环形域中细胞火焰的图案形成。我们发现径向对称的火焰图案变得不稳定，然后通过静态分叉出现细胞火焰图案。1989年，我们有兴趣从理论角度可视化二元合金中的相分离和粗化过程的现象。我们对迄今为止提出的几个反应扩散方程模型进行了数值求解，以理解这些现象。结果显示出如此复杂而美丽的图案，这是迄今为止所没有想到的。

项目成果

辻川亨: "Stability properties of traveling pulse solutions of the higher dimensional FutzHugh-Nagumo equations" Japan Journal of Applid Mathematics. 6. 341-366 (1989)

Toru Tsujikawa：“高维 FutzHugh-Nagumo 方程的行进脉冲解的稳定性”日本应用数学杂志 6. 341-366 (1989)。

藤越康祝: J.Multivariate Anal.27. 194-205 (1988)

藤越泰之：J.多元分析.27.194-205（1988）

藤越康祝: "Error bounds for asymptotic expansions of the maximums of the multivariable t-and F-variables with common dynominator" Hiroshima Mathematical Journal. 19. 319-327 (1989)

Yasuyuki Fujikoshi：“具有共同动力的多变量 t 变量和 F 变量的最大值的渐近展开的误差界”广岛数学杂志 19. 319-327 (1989)。

Tohru Tsujikawa: "Stability properties of traveling pulse solutions of the higher dimensional FitzHugh-Nagumo equations" Japan J. Appl. Math., 6, 341-366, 1989.

Tohru Tsujikawa：“高维 FitzHugh-Nagumo 方程的行进脉冲解的稳定性” Japan J. Appl。

西田孝明: Lecture Notes in Num.Apple.Anal.(1989)

Takaaki Nishida：《Num.Apple.Anal.》讲义（1989）