Description of Medium-Range Order in Amorphous Structures by Persistent Homology
Takenobu Nakamura, Yasuaki Hiraoka, Akihiko Hirata, Emerson G. Escolar, Kaname Matsue, Yasumasa Nishiura · arXiv (Cornell University) · 2015
The description of amorphous structures has been a long-standing problem, and conventional methods are insufficient for revealing intrinsic structures. In this Letter, we propose a computational homological approach that provides indicators of amorphous structures. We found curves in the persistence diagram (PD), which describes shapes and scales of medium-range order (MRO). The presence of such curves explicitly indicates geometric constraints on amorphous structures, which have not been observed using conventional methods. Furthermore, the PD reproduces the wavelength of the first sharp diffraction peak (FSDP) observed in the structure factor and clarifies the real space origin of FSDP. These curves are preserved under strain, indicating that PDs also contain information on elastic response.