Project/Area Number  09650074 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Engineering fundamentals

Research Institution  HOKKAIDO UNIVERSITY 
Principal Investigator 
KOBAYASHI Ryo Hokkaido Univ., Res. Inst. for Electronic Sci., Asso. Pro., 電子科学研究所, 助教授 (60153657)

CoInvestigator(Kenkyūbuntansha) 
TANAGATA Tatsuo Hokkaido Univ., Res. Inst. For Electronic Sci., Inst., 電子科学研究所, 助手 (80242262)
NISHIURA Yasumasa Hokkaido Univ., Res. Inst. For Electronic Sci., Pro., 電子科学研究所, 教授 (00131277)

Project Fiscal Year 
1997 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,700,000 (Direct Cost : ¥3,700,000)
Fiscal Year 1999 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1998 : ¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1997 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Keywords  grain boundary / phase field model / recrystallization / singular diffusivity / spiral steps / segregation / granular materials / selfreplicating pattern / 粒界 / フェーズフィールドモデル / 再結晶 / 特異拡散 / スパイラルステップ / 偏析 / 粉粒体 / 自己分裂パターン / grain boundarg migration / grain rotation / step dynamics / screw dislocation / spiral step / bunching / polycrystal / nonlinear semigroup theory / selfreplicating / 反応拡散系 / フェーズフィールド / 多結晶 / 相分離 / CahnHilliard / ブロックコポリマー / 散逸系 
Research Abstract 
(a) Usual phase field models have an essential short coming that they cannot describe the formation of polycrystals since they are lacking in the information of orientation. We proposed a vectorized phase field model which enables us to simulate a simultaneous crystallization of many particles with various orientations and a formation of grain boundaries. (b) Recrystallization takes place through the two basic processes, say, (I) grain boundary migration and (ii) grain rotation. Almost all the model of recrystallization handle the process (I) only. We proposed a totally new phase field model which can treat both of the processes (I) and (il) simultaneously. c In the above recrystallization model the equation for the evolution of angle variable expresses a nonlocal interaction by introducing a new mathematical concept "singular diffusivity" We justified this new equation and analyzed it mathematically. (d) It is well known that the mixture of granular materials can segregate in the rotating cylinder. We investigated this phenomena through experiments and modeling and found that it is caused by the property of strong segregation in the suface flow of binary mixture of granular materials. (e) A mathematical model of step dynamics on the facet of growing crystals are presented. This model is able to describe the motion of steps caused by the arbitrary number of screw dislocations. (f) Mathematical structure which produces selfreplicating patterns were made clear by the approach of experimental mathematics. We demonstrated that the ordered saddle node bifurcation branches and the paths connecting them are essential for the formation of selfreplicating patterns.
