Abstract
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'.
| Original language | English |
|---|---|
| Article number | 20200108 |
| Pages (from-to) | 20200108 |
| Number of pages | 1 |
| Journal | Philosophical transactions. Series A, Mathematical, physical, and engineering sciences |
| Volume | 379 |
| Issue number | 2201 |
| DOIs | |
| Publication status | Published - 12 Jul 2021 |
Bibliographical note
Funding Information:Data accessibility. This article has no additional data. Authors’ contributions. A.Z. coordinated and compiled the paper. All authors contributed to the writing and correcting of the manuscript. All authors read and approved the manuscript. The authors are listed in alphabetical order. Competing interests. We declare we have no competing interests. Funding. X.C. thanks the financial support by HK Research Grants Council of Hong Kong through the grant no. 16201019. M.R. acknowledges funding from the Slovenian Research Agency ARRS under contracts P1-0099, J1-2462 and J1-1697 and EU ERC Advanced grant LOGOS. I.F. was partially supported by the National Science Foundation (NSF) under grants no. DMS-1411646 and DMS-1906238. V.S. acknowledges support by
Funding Information:
Leverhulme grant no. RPG-2018-438. The work of A.Z. is supported by the Basque Government through the BERC 2018-2021 program, by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2017-0718 and through project MTM2017-82184-R funded by (AEI/FEDER, UE) and acronym ‘DESFLU’. Acknowledgements. The authors gratefully acknowledges the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme ‘The design of new materials’ when work on this paper was undertaken. This work was supported by: EPSRC grant nos. EP/K032208/1 and EP/R014604/1. X.C., M.R., V.S. and A.Z. gratefully acknowledge a Simons Fellowship during this programme. I.F. gratefully acknowledges a Kirk Distinguished Visiting Fellowship during this programme.
Publisher Copyright:
© 2021 The Author(s) Published by the Royal Society. All rights reserved.
Keywords
- alloys
- colloids
- epitaxy
- liquid crystals
- magnetic materials
- materials design
- soft matter