Towards a Fluid Computer
In 1991, Moore (Nonlinearity 4:199–230, 1991) raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao (J Am Math Soc 29(3):601–674, 2016) asked whether a mechanical system, including a fluid flow, can simulate a universal Turing machine. In this e...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/484461 |
| Acceso en línea: | http://hdl.handle.net/2072/484461 |
| Access Level: | acceso abierto |
| Palabra clave: | Beltrami fields Computational complexity Euler equations Turing completeness Turing machines Universality 51 |
| Sumario: | In 1991, Moore (Nonlinearity 4:199–230, 1991) raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao (J Am Math Soc 29(3):601–674, 2016) asked whether a mechanical system, including a fluid flow, can simulate a universal Turing machine. In this expository article, we review the construction in Cardona et al. (Proc Natl Acad Sci 118(19):e2026818118, 2021) 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 (Chern and Hamilton in On Riemannian metrics adapted to three-dimensional contact manifolds, Springer, Berlin, 1985). We also sketch the completely different construction for the Euclidean metric in R3 as given in Cardona et al. (J Math Pures Appl 169:50–81, 2023). These results reveal the existence of undecidable fluid particle paths. We conclude the article with a list of open problems. |
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