Thread by @anderssandberg

#FridayPhysicsFun - Is water stable or potentially explosive? The answer may depend on whether one can construct a computer out of fluid.

Fluid motion is described by the Navier-Stokes equations. They are non-linear and really tricky to solve.
quantamagazine.org/what-makes-the…

One problem mathematicians would like to solve is whether an initial state of finite fluid velocities will remain finite, or whether it could evolve into something with a singularity.

This is typical mathematics: are there always well-defined solutions for these equations? Actual liquids of course flow like they do, but there may be worthwhile insights in seeing where our models break down.

Terence Tao had a clever approach to the problem: he showed that for liquids *almost* like the NS-equations one could make a flow pattern that makes a smaller and faster copy of itself, and so on: this will blow up in finite time.
terrytao.wordpress.com/2014/02/04/fin…

He pointed out that the pattern was very much like a Turing machine implementing self-replication. So if you can show you can get Turing-machines in a fluid you can make it (theoretically) blow up for some initial conditions.

Since Turing-machines can produce undecidable behaviour (no general recipe for predicting it given the program) it would also mean fluids could be undecidable. Not just unpredictable or chaotic, but undecidable (and explosive).

Recently there was a paper showing that for Eulerian fluids (i.e. without viscosity) in compact space one can get Turing-completeness. arxiv.org/abs/2012.12828 That is interesting, since superfluid helium is Eulerian.

There has been plenty of liquid computers. arxiv.org/abs/1811.09989 Some were analog computers using water to represent amounts. MONIAC modelled the national economic processes of the United Kingdom. en.wikipedia.org/wiki/MONIAC

Another approach is fluidic logic. Ones and zeros can be represented by the presence or absence of flow, and jets made to interact to make logic gates, amplifiers and other components. en.wikipedia.org/wiki/Fluidics

One can also use droplets as billiard balls to perform collision-based computing. arxiv.org/abs/1708.04807

All of these computers have used solid parts to direct the fluid. Could one actually do it without any solid parts? It does not seem impossible that the right vortex tube configuration could make Turing-universal gates. Error-correction is another matter. vimeo.com/284767041

Another kind of water singularity is found when concentric waves are combined in a wave tank.

One can get similar but smaller jets by shaking cylindrical containers. nature.com/articles/35000… researchgate.net/profile/Emil-H…

The non-linearity of the Navier-Stokes equations allows for a lot of fun effects. But deep down they are just Newton's F=ma force-equals-mass-times-acceleration law written for a vector field. (image from Quanta article at top)