| Project/Area Number |
09354001
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 展開研究 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hiroshima University (1998-1999)
The University of Tokyo (1997) |
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Principal Investigator |
MIURA Masayasu Faculty of Science, Hiroshima University, Professor, 理学部, 教授 (50068128)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAMOTO Kunimochi Faculty of Science, Hiroshima University, Associate Professor, 理学部, 助教授 (40243547)
FUNAKI Naohisa Graduate School of Mathematical Sciences, The University of Tokyo, Professor, 大学院・数理科学研究科, 教授 (60112174)
OHTA Takao Faculty of Science, Hiroshima University, Professor, 理学部, 教授 (50127990)
KIMURA Masato Faculty of Science, Hiroshima University, Lecture, 理学部, 講師 (70263358)
OKUZONO Tohru Faculty of Science, Hiroshima University, Lecture, 理学部, 講師 (10314725)
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| Project Period (FY) |
1997 – 1999
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| Keywords | Dendritic growth pattern / Singular limit methods / Phase se ration / Free boundary problem / complex liquid / Interfacial dynamics / Numerical analysis of melting and solidification problem / singular purturbation methods |
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| Research Abstract |
Towards mathematical understanding of melting, solidification and growth processes in material sciences, we have carried theoretical research from experiments, modeling and complementarily computer analysis. Since the head investigator had moved from the university of Tokyo to Hiroshima University at the second year of the research term, some investigators had to he altered from the original members but there was no trouble to carry out the research plan. Mimura has mainly studied pattern formation arising in nonlinear non equilibrium systems. In particular, has investigated dendritic patterns in biological and chemical systems, in order to reveal the universality in mechanism of such patterns in natural sciences. Ohta has studied dynamics of micro phase separation, as the basic theory in polymer science. Ishikawa has experimentally studied dendritic growth in material process and in particular, and has studied the effect of micro gravity on growth of colloid crystal. Oharu has develop
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ed nonlinear semi group theory to extend basic theory of free boundary problems. Funaki has studied interfacial dynamics from probabilistic approach. Matano, Yanagida and Kimura have investigated analytically and numerically mean curvature equations which describe interfaces. Yamada and Kusano have developed numerical methods to solve reaction-diffusion systems on a sphere. Tsujikawa and Mimura has studied growth process in biological systems by using singular limit methods. Sakamoto has developed singular perturbation methods and established the internal layer theory in higher dimensions. Onda has made fractalization of the surface of shapes and has obtained super water -repellent surfaces from theoretic and experimenrtal standing points. Ishimura has analyzed spiral patterns which arises in growth process in materials by using curvature flow theory. Okuzono has analyzed dynamics of two phase flow in droplet dissipative systems. Ueyama has given theoretical understanding of self-replication process in reaction-diffusion systems by using computer aided analysis. The above results have been reported in several conferences inside and outside of Japan. Most of them were talked at the Applied Mathematics Meeting in Japan which is held every year and were published in their proceedings. Less
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