Control of Self-organization Phenomena in Phase Transitions and Its Application to Nanotechnology

相变自组织现象的控制及其在纳米技术中的应用

• 批准号: 14550217
• 负责人: ISHIKAWA Masaaki
• 金额: $ 1.86万
• 依托单位: Yamaguchi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14550217/
• 关键词: Phase Transition; Order-disorder Transition; Phase boundary; Mean Curvature Flow; Growth with constant speed; Stochastic level set equation; Simulations; Self-organization; 確率等高面方程式; 相分離; 確立Ginzburg-Landau方程; 確率Cahn-Hilliard方程式; 等高面法

This study is concerned with the control of self-organization phenomena in phase transitions and its application to the nanotechnology. First, we have analyzed the phase transition phenomena quantitatively and qualitatively, i.e., the analysis by the mathematical model of the phase transitions phenomena and their simulation analyses. We found that the random noise played a very important role in the phase transition phenomena. The random noise accelerates the order-disorder transition and phase separation. Secondly, we studied the behavior of the phase boundary in phase transition, in particular, Stefan problems and mean curvature flow of the phase boundary in annealing of the metal. We analyzed the influence of the random noise on the behavior of phase boundaries.Finally, we studied self-organization phenomena in the chemical reaction and the material. The results obtained in this study are very important as the basic knowledge of analysis of self-organization in the phase transition phenomena and give the basic model of control of the phase transitions.

本论文主要研究相变自组织现象的控制及其在纳米技术中的应用。首先，我们定量和定性地分析了相变现象，即，相变现象的数学模型分析及其仿真分析。我们发现随机噪声在相变现象中起着非常重要的作用。随机噪声加速了有序-无序转变和相分离。其次，我们研究了相变过程中相边界的行为，特别是Stefan问题和金属退火过程中相边界的平均曲率流动。分析了随机噪声对相界行为的影响，最后研究了化学反应和材料中的自组织现象。本研究的结果作为分析相变现象中自组织现象的基础知识是非常重要的，并给出了控制相变的基本模型。

项目成果

M.Ishikawa, K.Miyajima, Takayuki Tanabe: "Analysis of the Influence of Random Disturbances on Turing Patterns in Bounded Domains"Abstracts of the 35th ISCIE International Symposium on Stochastic Systems Theory and Its Applications. 1. 106-107 (2003)

M.Ishikawa、K.Miyajima、Takayuki Tanabe：“有界域中随机扰动对图灵模式的影响分析”第35届ISCIE随机系统理论及其应用国际研讨会摘要。

M.Ishikawa, K.Miyajima, M.Hirano: "Behavior Analysis of Phase Boundaries by Level Set Methods -Application of Stochastic Viscosity Solutions"Proceedings of SICE2OO2(計測自動制御学会主催). (CD-ROM). (2002)

M.Ishikawa、K.Miyajima、M.Hirano：“通过水平集方法进行相边界的行为分析 - 随机粘度解决方案的应用”SICE2OO2 论文集（由仪器与控制工程师协会赞助）（CD-ROM）。 (2002)

Simulation Analysis of Motion of Phase Boundaries by the Stochastic Level Set Method

随机水平集法相边界运动的仿真分析

• 发表时间: 2004
• 期刊: Proceedings of the 4^<th> European Congress on Computational (CD-ROM)
• 作者: M.Ishikawa;K.Miyajima
• 通讯作者: K.Miyajima

石川昌明, 宮島啓一: "確率等高面方程式による相境界の運動解析"第46回自動制御連合講演会講演論文集. CD-ROM. (2003)

Masaaki Ishikawa、Keiichi Miyajima：“使用随机轮廓方程进行相边界的运动分析”第 46 届自动控制协会会议论文集（2003 年）。

Stochastic Modeling of the Behavior of Phase Boundaries in the Mean Curvature Flow and Simulation Analyses

平均曲率流中相边界行为的随机建模和仿真分析

• 发表时间: 2005
• 期刊: Proceedings of the 5^<th> International Conference on Control and Automation (印刷中)
• 作者: M.Ishikawa;K.Miyajima
• 通讯作者: K.Miyajima