Integrated Studies towards New Development in Mathematical Sciences

数学科学新发展的综合研究

基本信息

批准号：
07304017
负责人：
MIURA Masayasu
金额：
$ 3.9万
依托单位：
University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07304017/
关键词：
Bifurcation theory of flow problems Algorithm of parallel computing Theooretical study of domain decomposition methods Computer aided analysis Methods to mathematical sciences 数理科学的概論 Industrial Mathematics 数理ファイナンスソフトサイエンス

项目摘要

Towards new development in mathematical sciences, we have considered mathematical understanding of several topics in engineering, natual sciences etc. For instance, Tabata and Okamoto have studied bifurcation theories, numerical algorithm, application to several concrete problems, parallel computing in large scale systems in fluid dynamics problems. Ikeda and Nishiura have analycally and complementarily numerically nvestigated to reveal the mecanism of phase seperation and interfacial problems in physical science, by using reaction-diffuison model systems. Mori, Kawarada and Mitsui have discussed mathemathematical topics arising in Industrial mathematics. Especially, they have developed new numerical algorithm of domain decomposition methods, which is known as one of effective scientific numerical methods. Nishida, Nakao and Tsutsumi have studied qualitative properites of nonlinear partial differential equations, from the numerical aided analysis standing point, and proposed a new analytical methods to understand nonlinear phenomena. Mimura and his group have discussed biological problems, especially aggregation, segregation of biological individuals described by reaction-diffusion systems, by integrating analytical methods, numerical simulations and visualization. This appraoch is a trial to develop new methods in mathematical sciences. The results obtained above were reperented in the meeting of Applied Mathematics in Japan which was held on December everyyear and published in the forms of proceedings.

为了在数学科学领域进行新的发展，我们考虑了对工程，生态科学等的几个主题的数学理解等。 Ikeda和Nishiura通过使用反应 - 散热器模型系统在分析和互补的数值上进行了互补的识别，以揭示物理科学中相位分离和界面问题的生物。莫里（Mori），川田（Kawarada）和三井（Mitsui）讨论了工业数学中出现的数学主题。特别是，他们开发了域分解方法的新数值算法，该算法被称为有效的科学数值方法之一。 Nishida，Nakao和Tsutsumi从数值辅助分析站立点研究了非线性偏微分方程的定性适当位，并提出了一种新的分析方法来了解非线性现象。 Mimura和他的小组通过整合分析方法，数值模拟和可视化来讨论了由反应扩散系统描述的生物学个体的生物学问题，尤其是聚集的生物学个体。此评估是开发数学科学方法的新方法的试验。上面获得的结果在日本的应用数学会议上记录了，该数学于12月举行，每年都以诉讼的形式出版。