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SUMMARY:Herding Cats: Turbulence in Spacetime - Predrag Cvitanović (Georg
 ia Institute of Technology)
DTSTART:20220329T133000Z
DTEND:20220329T140000Z
UID:TALK171167@talks.cam.ac.uk
DESCRIPTION:Suppose you find yourself face-to-face with Navier-Stokes or Y
 oung-Mills 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? O
 ur goal is to answer this question pedagogically\, as a sequence of pencil
  and paper calculations. First I will explain what is 'deterministic chaos
 ' by walking you through its simplest example\, the coin toss or Bernoulli
  map\, but reformulated as problem enumerating admissible global solutions
  on an integer-time lattice. Then I will do the same with the 'kicked roto
 r'\, the simplest mechanical system that is chaotic. Finally\, I will take
  an infinity of `rotors' coupled together on a spatial lattice 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 f
 amiliar continuum versions of a harmonic oscillator\, the Helmholtz and Po
 isson equations\, but instead of being "springy"\, this metamaterial has a
 n unstable rotor at every lattice site\, that gives\, rather than pushes b
 ack\, with the theory formulated in terms of Hill determinants and zeta fu
 nctions. We call this simplest of all chaotic field theories the `spatiote
 mporal cat'.In the spatiotemporal formulation of turbulence there is no ev
 olution in time\, there are only a repertoires of admissible spatiotempora
 l patterns\, or `periodic orbits'\, very much as the partition function of
  the Ising model is a weighted sum formed by enumerating its lattice state
 s. In other words: throw away your integrators\, and look for guidance in 
 clouds' repeating patterns. That's `turbulence'. And if you don't know\, n
 ow you know.No actual cats\, graduate or undergraduate\, have shown intere
 st in\, or were harmed during this research.
LOCATION:Seminar Room 1\, Newton Institute
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