Seminario Q-Math

Universal computation and hydrodynamics

Ponente:  Daniel Peralta (ICMAT)
Fecha:  martes 31 de mayo de 2022 - 13:00
Lugar:  Room 2.2.D08, Universidad Carlos III de Madrid
Online: (The online session will be active only on demand. Please contact the organisers if you want to attend online)


Is hydrodynamics capable of performing computations? or in other words, does there exist a fluid flow that can simulate any computer algorithm? This intriguing question was first formulated by C. Moore in 1991, and has been open for decades. In this talk I will show how to construct stationary and time-dependent solutions of the Euler equations that are Turing complete, i.e., they can simulate any Turing machine. A striking consequence of this is the existence of undecidable fluid particle paths, in the sense that there is no general algorithm to decide whether the trajectories of the flow starting at certain points will reach a certain open set. This is a manifestation of complexity in hydrodynamics very different from the theory of chaos. This is based on joint works with R. Cardona, E. Miranda and F. Presas.