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Curious if anyone has any other potential applications they can share? The authors listed only a few, but the possibilities seem quite vast.
What possible applications?
Meaning, what other possible real-world uses can be conceived of?
Yeah I'm really trying to think. It's tough to think of something where a computer can't just process and then have some output that changes physical matter after or even during the process. So it would need to be something that requires the object that is doing the calculation to change while calculating?

I'm trying to view it in a good way.

If they make their fluid inert (what is a relative characteristic), there are probably several application in chemistry.
Radiation-resistant computation comes to mind.
If the methodology works with arbitrary fluid droplets (not just water) there could be interesting work done from blood analysis to drug synthesis.
Maybe I missed it, but it doesn't work with water. They're using ferrofluid.
Reminds me of the water integrator, a water based computer built in the Soviet Union in the 20s: http://en.wikipedia.org/wiki/Water_integrator

And also of MONIAC, a computer from the late 40s that modeled the UK's economy using water: http://en.wikipedia.org/wiki/MONIAC_Computer

MONIAC was the first i thought about as well.

Note that it was created by the same guy that gave economics the Phillips curve. And frankly the hydraulic computer was his better work.

Why it has gotten ignored is perhaps because it is inherently non-equilibrium and packed with feedback loops, both elements that are anathema to (neo-)classical economics.

If someone wants to have a look at a modern replacement, i would recommend Minsky.

http://www.debtdeflation.com/blogs/minsky/

And no one has, yet, mentioned Glooper from Making Money.