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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Herding Cats: Turbulence in Spacetime - Predrag Cv
itanoviÄ‡ (Georgia Institute of Technology)
DTSTART;TZID=Europe/London:20220329T143000
DTEND;TZID=Europe/London:20220329T150000
UID:TALK171167AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/171167
DESCRIPTION:Suppose you find yourself face-to-face with Navier
-Stokes or Young-Mills or a nonlinear PDE or a fun
ky metamaterial or a cloudy day. And you ask yours
elf\, is this thing "turbulent"? What does that ev
en mean? Our goal is to answer this question pedag
ogically\, as a sequence of pencil and paper calcu
lations. First I will explain what is 'determinist
ic chaos' by walking you through its simplest exam
ple\, the coin toss or Bernoulli map\, but reformu
lated as problem enumerating admissible global sol
utions on an integer-time lattice. Then I will do
the same with the 'kicked rotor'\, the simplest me
chanical system that is chaotic. Finally\, I will
take an infinity of `rotors' coupled together on a
spatial lattice to explain what `chaos' or `turbu
lence' looks like in the spacetime. What emerges i
s a spacetime which is very much like a big spring
mattress that obeys the familiar continuum versio
ns of a harmonic oscillator\, the Helmholtz and Po
isson equations\, but instead of being "springy"\,
this metamaterial has an unstable rotor at every
lattice site\, that gives\, rather than pushes bac
k\, with the theory formulated in terms of Hill de
terminants and zeta functions. We call this simple
st of all chaotic field theories the `spatiotempor
al cat'.In the spatiotemporal formulation of turbu
lence there is no evolution in time\, there are on
ly a repertoires of admissible spatiotemporal patt
erns\, or `periodic orbits'\, very much as the par
tition function of the Ising model is a weighted s
um formed by enumerating its lattice states. In ot
her words: throw away your integrators\, and look
for guidance in clouds' repeating patterns. That's
`turbulence'. And if you don't know\, now you kno
w.No actual cats\, graduate or undergraduate\, hav
e shown interest in\, or were harmed during this r
esearch.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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