Global analysis of phase transition by using nano-minimal surface theory

2021 Fiscal Year Final Research Report

• Project Area: Discrete Geometric Analysis for Materials Design
• Project/Area Number: 17H06466
• 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: Nagoya University
• Principal Investigator: Naito Hisashi 名古屋大学, 多元数理科学研究科, 准教授 (40211411)
• Co-Investigator(Kenkyū-buntansha): 納谷 信 名古屋大学, 多元数理科学研究科, 教授 (70222180)
• Project Period (FY): 2017-06-30 – 2022-03-31
• Keywords: 離散幾何解析 / 極小曲面 / グラフ理論 / 炭素構造

Outline of Final Research Achievements

A novel crystal structure represented by a carbon structure was analyzed using discrete geometry analysis.
In order to analyze the crystal structure, which is a typical example of the carbon structure from the viewpoint of discrete geometry analysis, Define a trivalent discrete surface, define its Gaussian curvature and mean curvature, It shows the negative curvature of the structure that was conventionally called ``negative curvature carbon structure'', etc. It was shown that the structure that appears in material science can be described by the method of discrete geometry analysis. In addition, by improving the energy of the graph, we proposed a high-speed calculation method for the curved graphene structure.
An example is shown in which there is a strong correlation between the curvature of a curved surface and its physical properties.

Free Research Field

数学・材料科学

Academic Significance and Societal Importance of the Research Achievements

従来とは異なる離散幾何解析的なアプローチによって材料物性を解析できる可能性を示した. 従来の材料科学では経験的な手法によって望ましい物性を探索することが多く, また近年のデータ駆動型アプローチでも, 多くの既存のデータを用いることが多い. 一方, 我々が行なった離散幾何解析的アプローチは, 材料の幾何学的性質を考察することにより,
望ましい物性・新奇な物性をもつ材料を探索する可能性を開拓した.