Nonlinear Science Seminar & Webinar

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, than 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.