Some Specific Examples of Mathematics–Materials Science Collaboration at AIMR

Abstract

In today’s modern research environment, the emphasis is placed on the direct interaction of mathematics with other scientific fields and industry groups to solve complex problems jointly faced by various disciplines. The demand for the participation of mathematicians in materials science is growing. One reason for this growth is to provide new mathematical tools to understand the relationship between microscopic geometric structures and macroscopic properties and functions. Although much technology for observations at the atom/molecule level has largely been developed, we need mathematical tools to analyze and interpret the experimental data in a deeper and more sophisticated way and to create a conceptual understanding of the essence of microscopic structures. Another reason is to establish a basis for the prediction and smart design of novel functional materials by using accumulated data and high performance computatsion. Of course, these two factors are related. At AIMR, we set up a place where world-leading materials scientists (both experimentalists and theorists) and mathematicians meet daily and discuss materials science problems to establish new science. Here we present some of the results that have emerged.