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Mathematical Studies of melting, solidification and growth phenomena in material science

材料科学中熔化、凝固和生长现象的数学研究

基本信息

批准号：
09354001
负责人：
MIURA Masayasu
金额：
$ 10.18万
依托单位：
Hiroshima University (1998-1999)The University of Tokyo (1997)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09354001/
关键词：
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 界面ダイナミクスの数理コロイド結晶結晶成長の数値

项目摘要

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 … More 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

为了从数学上理解材料科学中的熔化、凝固和生长过程，我们从实验、建模和辅助的计算机分析等方面进行了理论研究。由于首席研究员在研究期的第二年从东京大学转到了广岛大学，一些研究员不得不改变原来的成员，但研究计划的执行没有遇到任何麻烦。三村主要研究非线性非平衡系统中的斑图形成。特别是研究了生物和化学系统中的树枝状模式，以揭示这种模式在自然科学中的普遍性。微相分离动力学是高分子科学的基础理论，Ohta等人对微相分离动力学进行了研究。石川对材料加工中的枝晶生长进行了实验研究，特别是对微重力对胶体晶体生长的影响进行了研究。小春发展了 ...更多信息艾德推广了自由边界问题的基本理论。Funaki从概率方法研究了界面动力学。Matano、Yanagida和Kimura研究了描述界面的平均曲率方程的解析和数值方法。Yamada和Kusano发展了求解球上反应扩散方程组的数值方法。Tsujikawa和Mimura用奇异极限方法研究了生物系统的生长过程。Sakamoto发展了奇异摄动方法，建立了高维的内层理论。Onda对形状表面进行了分形处理，从理论和实验的角度获得了超疏水表面。石村用曲率流理论分析了材料生长过程中出现的螺旋纹。Okuzono分析了液滴耗散系统中的两相流动力学。Ueyama通过使用计算机辅助分析给出了反应扩散系统中自复制过程的理论理解。上述结果已在日本国内外的几次会议上报告。他们中的大多数人都谈到了应用数学会议在日本举行，每年举行，并发表在他们的诉讼。少