Materials inspired by mathematics
Source abstract
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.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: Topological and Geometric Data Analysis · Machine Learning in Materials Science · Quasicrystal Structures and Properties
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai, Japan
Mathematical Institute, Graduate School of Science, Tohoku University, Sendai, Japan
Funding
MEXT, Japan
References (33)
Show source-provided references
1. 10.1063/1.302251510.1063/1.3022515 ↗
2. 10.1073/pnas.080605110510.1073/pnas.0806051105 ↗
3. 10.1021/ma100959v10.1021/ma100959v ↗
4. 10.1103/PhysRevLett.106.12550410.1103/PhysRevLett.106.125504 ↗
5. Wang D · Phys. Lett · 2012 · 100 · 251905
6. Wigner EP · Comm. Pure Appl. Math · 190 · 1
7. Cromwell PR · 1997
8. 10.1090/conm/338/0607710.1090/conm/338/06077 ↗
9. 10.1090/S0002-9947-00-02632-510.1090/S0002-9947-00-02632-5 ↗
10. 10.1103/PhysRevLett.53.195110.1103/PhysRevLett.53.1951 ↗
11. Connes A · 1994
12. 10.1090/crmm/01310.1090/crmm/013 ↗
13. 10.1007/s00454-002-2885-210.1007/s00454-002-2885-2 ↗
14. 10.1126/science.123245010.1126/science.1232450 ↗
15. Nakamura T, Hiraoka Y, Hirata A, et al. Description of medium-range order in amorphous structures by persistent homology. arxiv:1501.03611.
16. 10.1088/0957-4484/26/30/30400110.1088/0957-4484/26/30/304001 ↗
17. 10.1103/PhysRevLett.95.22680110.1103/PhysRevLett.95.226801 ↗
18. 10.1063/1.53075810.1063/1.530758 ↗
19. 10.1007/s00220-013-1814-y10.1007/s00220-013-1814-y ↗
20. 10.1063/1.490237710.1063/1.4902377 ↗
21. 10.1007/s00220-013-1819-610.1007/s00220-013-1819-6 ↗
22. Kubota Y10.1007/s00220-016-2699-3 ↗
23. Sunada T · Amer Math Soc · 2008 · 55 · 208
24. 10.1103/PhysRevLett.102.05570310.1103/PhysRevLett.102.055703 ↗
25. 10.1016/j.carbon.2014.04.07710.1016/j.carbon.2014.04.077 ↗
26. 10.1103/PhysRevB.92.04510810.1103/PhysRevB.92.045108 ↗
27. Kotani M10.1016/j.cagd.2017.09.002 ↗
28. 10.1137/13091990810.1137/130919908 ↗
29. 10.1016/j.jallcom.2013.01.19310.1016/j.jallcom.2013.01.193 ↗
30. Odom W. Report of the senior assessment panel for the international assessment of the U.S. mathematicalsciences. National Science Foundation (NSF); 1998. Available from: http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf9895
31. Brown DL, Bell J, Estep D, et al. Applied mathematics at the U.S. department of energy: past, present and view to the future. U.S. Department of Energy (DOE); 2008. Available from: http://science.energy.gov/~/media/ascr/pdf/program-documents/docs/brown_report_may_08.pdf10.2172/944335 ↗
32. Global Science Forum. Report on mathematics in industry. Organisation for Economic Co-operation and Development (OECD). Available from: http://www.oecd.org/science/sci-tech/41019441.pdf 2008
33. 10.1007/978-4-431-55864-410.1007/978-4-431-55864-4 ↗