TDA on Amorphous Structures

The atomic structures of amorphous states such as glasses are difficult to characterize. Understanding the structure-functionality relationship in amorphous states is one of the important unsolved problem in physics, and it is expected to lead to new developments of high functional materials. We are collaborating with physicists and materials scientists to develop new descriptors for amorphous structural analysis using TDA.

literature

• Y. Hiraoka, T. Nakamura, A. Hirata, E. G. Escolar, K. Matsue, and Y. Nishiura. Hierarchical structures of amorphous solids characterized by persistent homology. Proceedings of the National Academy of Sciences of the United States of America 113 (2016), 7035-7040. doi: 10.1073/pnas.1520877113. http://www.pnas.org/content/early/2016/06/07/1520877113.abstract
• T. Nakamura, Y. Hiraoka, A. Hirata, E. G. Escolar, and Y. Nishiura. Persistent Homology and Many-Body Atomic Structure for Medium-Range Order in the Glass. Nanotechnology 26 (2015) 304001.
• M. Murakami, S. Kohara, N. Kitamura, J. Akola, H. Inoue, A. Hirata, Y. Hiraoka, Y. Onodera, I. Obayashi, J. Kalikka, N. Hirao, T. Musso, A. S. Foster, Y. Idemoto, O. Sakata, and Y. Ohishi. Ultrahigh-pressure form of SiO2 glass with dense pyrite-type crystalline homology. PHYSICAL REVIEW B 99, 045153 (2019).

Persistence Diagrams for SiO2 (left: crystal, middle: glass, right: liquid)