title: Materials inspired by mathematics.
abstract: Our world is transforming into an interacting system of the physical world and the digital world. What will be the materials science in the new era? With the rising expectations of the rapid development of computers, information science and mathematical science including statistics and probability theory, 'data-driven materials design' has become a common term. There is knowledge and experience gained in the physical world in the form of know-how and recipes for the creation of material. An important key is how we establish vocabulary and grammar to translate them into the language of the digital world. In this article, we outline how materials science develops when it encounters mathematics, showing some emerging directions.
authors.affiliation: WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai, Japan; Mathematical Institute, Graduate School of Science, Tohoku University, Sendai, Japan.
authors.forename: Motoko
authors.initials: M
authors.lastname: Kotani
authors.affiliation: WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University , Sendai , Japan.
authors.forename: Susumu
authors.initials: S
authors.lastname: Ikeda
keywords: 400 Modeling/Simulations; 402 Multi-scale modeling; 404 Materials informatics/genomics; 60 New topics/Others; Multiscale hierarchical materials; carbon networks; data-driven materials design; disordered systems; non equilibrium materials; topological data analysis