Towards a Fluid computer
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911128446042112 |
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| author | Cardona, Robert Miranda, Eva Peralta-Salas, Daniel |
| author_facet | Cardona, Robert Miranda, Eva Peralta-Salas, Daniel |
| contents | 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 $\mathbb R^3$ as given in [7]. These results reveal the existence of undecidable fluid particle paths. We conclude the article with a list of open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20999 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a Fluid computer Cardona, Robert Miranda, Eva Peralta-Salas, Daniel Dynamical Systems Computation and Language Analysis of PDEs Symplectic Geometry 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 $\mathbb R^3$ as given in [7]. These results reveal the existence of undecidable fluid particle paths. We conclude the article with a list of open problems. |
| title | Towards a Fluid computer |
| topic | Dynamical Systems Computation and Language Analysis of PDEs Symplectic Geometry |
| url | https://arxiv.org/abs/2405.20999 |