Category theory based solution for the building block replacement problem in materials design
An important objective in materials design is to develop a systematic methodology for replacing unavailable or expensive material building blocks by simpler and abundant ones, while maintaining or improving the functionality of the material. The mathematical field of category theory provides a forma...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Wiley Blackwell
2013
|
| Online Access: | http://hdl.handle.net/1721.1/77560 https://orcid.org/0000-0002-4173-9659 https://orcid.org/0000-0002-6601-9199 |
| _version_ | 1811077184328040448 |
|---|---|
| author | Giesa, Tristan Spivak, David I. Buehler, Markus J. |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Giesa, Tristan Spivak, David I. Buehler, Markus J. |
| author_sort | Giesa, Tristan |
| collection | MIT |
| description | An important objective in materials design is to develop a systematic methodology for replacing unavailable or expensive material building blocks by simpler and abundant ones, while maintaining or improving the functionality of the material. The mathematical field of category theory provides a formal specification language which lies at the heart of such a methodology. In this paper, we apply material ologs, category-theoretic descriptions of hierarchical materials, to rigorously define a process by which material building blocks can be replaced by others while maintaining large-scale properties, to the extent possible. We demonstrate the implementation of this approach by using algebraic techniques to predict concrete conditions needed for building block replacement. As an example, we specify structure–function relationships in two systems: a laminated composite and a structure–function analogue, a fruit salad. In both systems we illustrate how ologs provide us with a mathematical tool that allows us to replace one building block with others to achieve approximately the same functionality, and how to use them to model and design seemingly distinct physical systems with a consistent mathematical framework. |
| first_indexed | 2024-09-23T10:39:08Z |
| format | Article |
| id | mit-1721.1/77560 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:39:08Z |
| publishDate | 2013 |
| publisher | Wiley Blackwell |
| record_format | dspace |
| spelling | mit-1721.1/775602022-09-27T13:58:17Z Category theory based solution for the building block replacement problem in materials design Giesa, Tristan Spivak, David I. Buehler, Markus J. Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Massachusetts Institute of Technology. Department of Mathematics Giesa, Tristan Spivak, David I. Buehler, Markus J. An important objective in materials design is to develop a systematic methodology for replacing unavailable or expensive material building blocks by simpler and abundant ones, while maintaining or improving the functionality of the material. The mathematical field of category theory provides a formal specification language which lies at the heart of such a methodology. In this paper, we apply material ologs, category-theoretic descriptions of hierarchical materials, to rigorously define a process by which material building blocks can be replaced by others while maintaining large-scale properties, to the extent possible. We demonstrate the implementation of this approach by using algebraic techniques to predict concrete conditions needed for building block replacement. As an example, we specify structure–function relationships in two systems: a laminated composite and a structure–function analogue, a fruit salad. In both systems we illustrate how ologs provide us with a mathematical tool that allows us to replace one building block with others to achieve approximately the same functionality, and how to use them to model and design seemingly distinct physical systems with a consistent mathematical framework. 2013-03-05T20:40:08Z 2013-03-05T20:40:08Z 2012-06 2012-05 Article http://purl.org/eprint/type/JournalArticle 1438-1656 1527-2648 http://hdl.handle.net/1721.1/77560 Giesa, Tristan, David I. Spivak, and Markus J. Buehler. “Category Theory Based Solution for the Building Block Replacement Problem in Materials Design.” Advanced Engineering Materials 14.9 (2012): 810–817. https://orcid.org/0000-0002-4173-9659 https://orcid.org/0000-0002-6601-9199 en_US http://dx.doi.org/10.1002/adem.201200109 Advanced Engineering Materials Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Wiley Blackwell MIT web domain |
| spellingShingle | Giesa, Tristan Spivak, David I. Buehler, Markus J. Category theory based solution for the building block replacement problem in materials design |
| title | Category theory based solution for the building block replacement problem in materials design |
| title_full | Category theory based solution for the building block replacement problem in materials design |
| title_fullStr | Category theory based solution for the building block replacement problem in materials design |
| title_full_unstemmed | Category theory based solution for the building block replacement problem in materials design |
| title_short | Category theory based solution for the building block replacement problem in materials design |
| title_sort | category theory based solution for the building block replacement problem in materials design |
| url | http://hdl.handle.net/1721.1/77560 https://orcid.org/0000-0002-4173-9659 https://orcid.org/0000-0002-6601-9199 |
| work_keys_str_mv | AT giesatristan categorytheorybasedsolutionforthebuildingblockreplacementprobleminmaterialsdesign AT spivakdavidi categorytheorybasedsolutionforthebuildingblockreplacementprobleminmaterialsdesign AT buehlermarkusj categorytheorybasedsolutionforthebuildingblockreplacementprobleminmaterialsdesign |