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: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/427302 |
| Acceso en línea: | https://hdl.handle.net/2117/427302 https://dx.doi.org/10.1007/s10208-025-09699-6 |
| Access Level: | acceso abierto |
| Palabra clave: | Euler equations Beltrami fields Turing machines Computational complexity Turing completeness Universality Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
| 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 R^3 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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