Topics in the mathematical design of materials

We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phase-transforming and shape-morphing materials, (ii) epitaxy as an approach of central importance in the design of advanced semiconductor materials, (iii) selected design problems in soft matter, (iv) mathematical problems in magnetic materials, (v) some open problems in liquid crystals and soft materials and (vi) mathematical problems on liquid crystal colloids. The presentation combines topics from soft and hard condensed matter, with specific focus on those design themes where mathematical approaches could possibly lead to exciting progress. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Automated summary

The article discusses various research directions in the mathematical design of new materials, including phase-transforming materials, semiconductor materials, soft matter, magnetic materials, liquid crystals, and liquid crystal colloids. It emphasizes the potential for exciting progress that mathematical approaches could bring to these design themes in both soft and hard condensed matter.