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

对于材料科学中熔化、凝固和生长过程的数学理解，我们从实验、建模和辅助计算机分析三个方面进行了理论研究。由于首席调查员在研究任期的第二年从东京大学搬到广岛大学，一些调查人员不得不从原来的成员进行更改，但执行研究计划没有任何困难。三村主要研究了非线性非平衡系统中的图案形成。特别是对生物和化学系统中的树枝状结构进行了研究，以揭示这种结构在自然科学中的普遍性。作为聚合物科学的基础理论，Ohta研究了微观相分离的动力学。石川在实验上研究了材料过程中的枝晶生长，特别是研究了微重力对胶体晶体生长的影响。Oharu已经开发了…进一步发展了非线性半群理论，推广了自由边界问题的基本理论。船木从概率的角度研究了界面动力学。Matano、Yanagida和Kimura研究了描述界面的解析和数值平均曲率方程。Yamada和Kusano发展了数值方法来求解球面上的反应扩散方程。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从理论和实验两个角度对形状表面进行了分形化，得到了超强拒水表面。石村用曲率流理论分析了材料在生长过程中产生的螺旋模式。Okuzono分析了液滴耗散系统中两相流动的动力学。Ueyama利用计算机辅助分析，从理论上理解了反应扩散系统中的自复制过程。上述结果在日本国内外的几个会议上都有报道。其中大多数都是在每年在日本举行的应用数学会议上发表的，并在会议记录中发表。较少

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