Discrete surface theory for optimal mass transportation in porous materials

2021 Fiscal Year Final Research Report

• Project Area: Discrete Geometric Analysis for Materials Design
• Project/Area Number: 17H06465
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Tohoku University
• Principal Investigator: Kotani Motoko 東北大学, 材料科学高等研究所, 教授 (50230024)
• Co-Investigator(Kenkyū-buntansha): 楯 辰哉 東北大学, 理学研究科, 教授 (00317299)
• Project Period (FY): 2017-06-30 – 2022-03-31
• Keywords: 微分幾何学 / 離散幾何学 / 極小曲面

Outline of Final Research Achievements

"Discrete geometric analysis" is a mathematical framework, which enables us to describe and analyze the correlation between microscopic structures and macroscopic properties of various materials. In this project, both of the "forward problems" predicting materials properties from their structure and the "inverse problems" suggesting reasonable structures from desired properties are approached by developing such a framework cooperating with materials scientists. It was shown that mathematical findings on "curved surface" in the world of atoms and molecules work also for predicting and understanding the structures and properties of real materials such as nano carbon. A novel approach for design of the next generation materials was successfully proposed.

Free Research Field

数学、微分幾何学、離散幾何解析学

Academic Significance and Societal Importance of the Research Achievements

近年、データと人工知能（AI）を用いた物質材料の探索が盛んになっているが、ミクロな構造とマクロな性質との関係を調べ、求める性質を実現するための構造を予測する逆問題を解くことは簡単ではない。数学を用いて複雑な構造が持つ本質的な情報をデータ化し、ミクロとマクロの関係を階層横断的に理解して逆問題を解くための道すじを示せたことが、本研究成果の社会的意義である。また、具体例を考察することで「特異点を排除するのではなく、むしろ活用する工夫をする」などの発想の転換が数学の側に誘起されたことが学術的意義の例として挙げられる。