Towards a fluid computer
In 1991, Moore [20] raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao [25] asked whether a mechanical system, including a fluid flow, can simulate a universal Turing machine. In this expository article, we review the construction in [8] of a...
| Autores: | , , |
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| Formato: | informe técnico |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/414239 |
| Acesso em linha: | https://hdl.handle.net/2117/414239 https://dx.doi.org/10.48550/arXiv.2405.20999 |
| Access Level: | acceso abierto |
| Palavra-chave: | Classificació AMS::68 Computer science Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Resumo: | In 1991, Moore [20] raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao [25] asked whether a mechanical system, including a fluid flow, can simulate a universal Turing machine. In this expository article, we review the construction in [8] of a "Fluid computer" in dimension 3 that combines techniques in symbolic dynamics with the connection between steady Euler flows and contact geometry unveiled by Etnyre and Ghrist. In addition, we argue that the metric that renders the vector field Beltrami cannot be critical in the Chern-Hamilton sense [9]. We also sketch the completely different construction for the Euclidean metric in R3 as given in [7]. These results reveal the existence of undecidable fluid particle paths. We conclude the article with a list of open problems. |
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