Applied mathematics of pattern formation in material sciences

材料科学中模式形成的应用数学

• 批准号: 13554001
• 负责人: OHTA Takao
• 金额: $ 8.83万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13554001/
• 关键词: pattern formation; material sciences; mathematical model; reaction-diffusion system; numerical analysis; phase separation; phase field model; internal layer; 有限要素法; 数理解析; 数値シミュレーション; 反応拡散; 特異極限法; ポリマーアロイ; 高分子共重合体; 計算機シミュレーション; 自己無撞着平均場理論 /

We have carried out theoretical analysis and development of numerical method for studying various macroscopic and microscopic pattern formation in material sciences. In particular, we have investigated both numerically and analytically(1) structural transitions of mesophases in block copolymer melts(2) ordering dynamics of charged colloidal particles(3) dynamics of grain boundaries(4) domains dynamics of reactive phase separating systems and(5) formation of bacteria colony with chemotacsis.Some of these works have been performed in collaboration with experimentalists.Together with these studies, we have also developed fundamental theories of interface/grain boundary dynamics by means of singular perturbation and reduction method.

我们已经进行了理论分析和发展数值方法，用于研究物质科学中各种宏观和微观模式的形成。特别是，我们已经在数值和分析上（1）块共聚物熔体中中间酶的结构过渡（2）订购电荷胶体颗粒的动态（3）晶界动力学（4）域的动力学（4）反应相分离的动力学动力学和（5）与这些化学作用的somections somections.sportions.sportions.sportients.sportients.sportients.sportions.sportions.研究，我们还通过奇异的扰动和还原方法开发了界面/晶界动力学的基本理论。

项目成果

T.Ohta: "Theory of rubber-like elasticity in shape memory alloys"Material Science and Engenering A. 321・1-2. 57-65 (2001)

T.Ohta：“形状记忆合金的橡胶弹性理论”材料科学与工程A. 321・1-65（2001）。

M.Nonomura: "Kinetics of Morphological Transitions between Mesophases"J.Physics : Condensed Matter. 13. 9089-9112 (2001)

M.Nonomura：“中间相之间形态转变的动力学”J.Physics：Condensed Matter。

D.Hilhorst: "A competition-diffusion system approximation to the classical two-phase Stefan problem,"Japan J. Indsutrial and Appl. Mathematics. 18. 161-180 (2001)

D.Hilhorst：“近似于经典两相 Stefan 问题的竞争扩散系统”，Japan J. Indsutorial and Appl。

M.Nonomura, K.Yamada, T.Ohta: "Formation and stability of double gyroid in microphase separated diblock copolymers"J.Phys.:Condens.Matter. 15. L423-L430 (2003)

M.Nonomura、K.Yamada、T.Ohta：“微相分离二嵌段共聚物中双螺旋体的形成和稳定性”J.Phys.：Condens.Matter。

T.Okuzono: "Time-modulated oscillatory structures in phase-separating reactive mixtures"Phys. Rev. E66. 066216-066225 (2002)

T.Okuzono：“相分离反应混合物中的时间调制振荡结构”Phys。