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

为了了解材料科学中熔化，凝固和生长过程的数学理解，我们从实验，建模和完全计算机分析中进行了理论研究。由于研究任期的第二年，调查员已从东京大学搬到广岛大学，因此一些调查人员不得不从原始成员进行了更改，但执行研究计划并没有麻烦。 Mimura主要研究了在非线性非平衡系统中产生的模式形成。特别是，已经研究了生物学和化学系统中的树突状模式，以揭示自然科学中这种模式的宇宙。 OHTA研究了微相分离的动力学，作为聚合物科学的基本理论。 Ishikawa在材料过程中，尤其是在实验中研究了树突状的生长，并研究了微重力对胶体晶体生长的影响。 OHRA已经开发了……更多的非线性半群体理论，以扩展自由边界问题的基本理论。 Funaki从有问题的方法研究了界面动力学。 Matano，Yanagida和Kimura在分析和基本上是描述界面的均值曲率方程。 Yamada和Kusano开发了数值方法来解决球体上的反应扩散系统。 Tsujikawa和Mimura已使用奇异极限方法研究了生物系统中的生长过程。 Sakamoto开发了奇异的扰动方法，并在更高的维度上建立了内部层理论。 Onda已将形状表面分形，并从理论和专家站立点获得了超级水的表面。 Ishimura通过使用曲率流理论分析了材料生长过程中产生的螺旋模式。 Okuzono分析了液滴耗散系统中两个相流的动力学。 Ueyama通过使用计算机辅助分析对反应扩散系统中的自我复制过程给出了理论上的理解。上述结果已在日本内外的几个会议上报道。他们中的大多数人在日本的应用数学会议上进行了讨论，该会议每年举行，并在诉讼中发表。较少的