Nonlinear Science Seminar & Webinar
February 26, 2020 - 1:15pm to 2:15pm
Howey - School of Physics
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.