Towards a Fluid computer

Abstract

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.

11 pages, 3 figures

References in corpus (8)

• Undecidability of the Spectral Gap (short version)
• Constructing Turing complete Euler flows in dimension $3$
• Universality of Euler flows and flexibility of Reeb embeddings
• Computability and Beltrami fields in Euclidean space
• Turing universality of the incompressible Euler equations and a conjecture of Moore
• On the existence of critical compatible metrics on contact $3$-manifolds
• Coorbital homoclinic and chaotic dynamics in the Restricted 3-Body Problem
• An equivariant Reeb-Beltrami correspondence and the Kepler-Euler flow