Herding Cats: A Chaotic Field Theory
Speaker: Predrag Cvitanović
(with M.N.S Gudorf and H. Liang)
Center for Nonlinear Science, School of Physics
Georgia Institute of Technology
Atlanta, GA USA
Abstract:
Suppose you find yourself face-to-face with Young-Mills or Navier-Stokes or a nonlinear PDE or a funky metamaterial or a cloudy day.
And you ask yourself, is this thing "turbulent"? What does that even mean?
If you were ever taught 'chaos', you must have learned about the coin toss (Bernoulli map).
I'll walk you through this basic example of deterministic chaos, then through the 'kicked rotor', a neat physical system that is chaotic,
and then put infinity of these together to explain what 'chaos' or 'turbulence' looks like in the spacetime.
What emerges is a spacetime which is very much like a big spring mattress
that obeys the familiar continuum versions of a harmonic oscillator, the Helmholtz and Poisson equations,
but instead of being "springy,” this metamaterial has an unstable rotor at every lattice site that gives, rather than pushes back.
We call this simplest of all chaotic field theories the 'spatiotemporal cat'.
That's 'turbulence'.
And if you don't know, now you know.
No actual cats, graduate or undergraduate, have shown interest in, or were harmed during this research.