The mathematical design of new materials

Programme 3rd January 2019 to 28th June 2019 Organisers: Arghir Zarnescu BCAM - Basque Center for Applied Mathematics, Institute of Mathematics of the Romanian Academy Xian Chen Hong Kong University of Science and Technology Miha Ravnik University of Ljubljana, Jozef Stefan Institute Valeriy Slastikov University of Bristol

Above image: "Martensitic Material", an experiment of Tomonari Inamura's group.

Many recent and spectacular advances in the world of materials are related to complex materials having extraordinary and unique features, usually determined by their specific microstructure. Such materials are key to much technology appearing in our daily lives: they are in liquid crystal displays, in miniaturised phones, special steels in cars, plastics and composites in the construction of modern airplanes, in biological implants in human bodies, and so on.

However, despite the impressive technological applications of these materials, the theoretical understanding and modelling of them are still inadequate.The need for models and basic understanding is not just of theoretical interest, but indeed a key requirement for being able to access and further develop the true potential of these materials, to optimise them, to combine them into new materials, and to use them for creating new devices, with predefined abilities and behaviours.

The current programme aims to bring together mathematicians and scientists working in various areas of materials science and applied mathematics in order to initiate a systematic study of the optimal design of new complex materials, focusing on:

1. Topological metamaterials

2. Colloid composites

3. Composite alloys

4. Layered heterostructures

5. Woven or printed materials

6. Structural optimisation

as the distinct existing attempts from engineering, physics and chemistry. Building on the mathematical areas that are directly relevant to the scientific questions of interest, namely, optimisation and calculus of variations, geometry and topology, continuum mechanics and partial differential equations, the programme aims to identify and study the common principles and techniques of optimal material design that apply more broadly.