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P Cvitanović
A field theory of turbulence
overheads (Oct 11, 2024 celebrating David K. Campbell's 37th - 30 min)
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Spatiotemporal chaotic field theory for solid state physicists, Fermi-Pasta-Ulam-Tsingou's imaginary time sister.
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P Cvitanović
Turbulence in spacetime
overheads (Apr 13, 2023 Working across scales in complex systems - Emory - 15 min)
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If there is one idea you should take from everything presented on this webpage, it is this: stop integrating unstable, turbulent, chaotic systems forward in time. Describe instead the repertoire of admissible spatiotemporal patterns, starting with the smallest, and working your way up to larger spatiotemporal domains.
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P Cvitanović
Recurrent solutions and dynamics of turbulent flows, as seen in experiments
overheads (Sep 24, 2022 Georgia Tech Math Colloquium - 44 min)
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In the world of moderate, everyday turbulence of fluids flowing across planes and down pipes, a quiet revolution is taking place. Today we routinely compute 'exact coherent structures', numerically precise 3D, fully nonlinear Navier-Stokes solutions: unstable equilibria, traveling waves, and (relative) periodic orbits. Experiments carried out at Georgia Tech (starts at min 24:15 of the video) measure 'exact coherent structures' and trace out their unstable manifolds. What emerges is a dynamical systems theory of low-Reynolds turbulence as a walk among sets of weakly unstable invariant solutions. |
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P Cvitanović
Are we there yet?
overheads (Jul 24, 2024 Mathematical Methods in Computational Neuroscience 2024 - Eresfjord - 35 min)
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A proposal for an intrinsic, invariant measurement of distance between spatiotemporal states. Used in computational neuroscience and ML as minimization of Kullback-Leibler divergence (Video do be added.) |
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P Cvitanović
Field theory of spatiotemporal chaos
overheads (Jan 26, 2023 Georgia Tech Math Physics Seminar - XX min)
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Gutzwiller semi-classics, Ruelle zeta functions, stat mech partition functions, and QFT path integrals are here developed in a common field-theoretic description of both (low-dimension) chaotic dynamical systems, and (infinite-dimension) spatiotemporally turbulent flows, in a lattice discretized field-theoretic framework. |
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P Cvitanović
A chaotic field theory
overheads (December 19, 2023 125th Statistical Mechanics Conference,
Rutgers University - slides only, 20 min talk)
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Emphasis on the exact spatiotemporal zeta function over infinite-dimensional spacetime, in a lattice discretized field-theoretic framework.
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P Cvitanović
Herding cats: turbulence in spacetime
(Mar 29, 2022 talk in the Newton Institute TURW04
"Wall-bounded turbulence: beyond current boundaries" workshop - 25 min)
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An introduction into the spatiotemporal deterministic field theory of chaos. In particular, we explain that the probability of a given spatiotemporal solution is given by the inverse of its Hill determinant. |
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P Cvitanović
Hearding cats : chaotic field theory
overheads (December 6, 2021 QM3 Quantum Matter meets Maths,
Lisbon - 1 h talk)
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Emphasis on the quantum physics motivation. |
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P Cvitanović
Are clouds supercomputers in the sky?
overheads (March 4, 2021 Mathematics Colloquium,
The Simons Center for Geometry and Physics, Stony Brook, NY - 55 min talk)
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P Cvitanović
Spatiotemporal cat : a chaotic field theory
overheads (December 16, 2020 Mathematical Physics Webinar,
Rutgers University - 55 min talk)
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P Cvitanović
Herding cats : a chaotic field theory
overheads (September 25, 2020 ITS Symposium on Chaos and Quantum Field Theory - 1 hour talk)
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P Cvitanović and H Liang
Herding cats : a chaotic field theory
overheads (July 2020) | video (similar to 2020 APS below, but 1h long)
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P Cvitanović, H Liang and M N Gudorf
Is space time? a spatiotemporal tiling of turbulence
overheads (March 2, 2020 APS March Meeting - 30 min talk)
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Revolution will not be twitterized!.
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P Cvitanović and M Gudorf
A spatiotemporal theory of turbulence - computational challenges
overheads (October 12, 2020 Intern. Conf. Computer Simulation in Physics and beyond CSP2020, Moscow - 40 min plenary talk) |
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Matthew N. Gudorf
Spatiotemporal tiling of the Kuramoto-Sivashinsky system
thesis (November 20, 2020 - 1 hour talk)
Georgia Tech thesis repository link
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P Cvitanović:
Dynamical systems are a fraud!
ChaosBook.org/course1
(5:40 min manifesto Jan 11, 2022)
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Act locally, think globally, tighten the rubber band: elaborated a bit in the next two videos.
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P Cvitanović:
What do we talk about when we talk about chaos I
(9:41 min, July 29, 2020)
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When we talk, we talk about evolving in time, derive the forward-in-time Jacobian.
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P Cvitanović:
What do we talk about when we talk about chaos II
(8:40 min July 30, 2020)
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When we walk the walk, we determine the global orbit and
its global stability, derive its orbit Jacobian.
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Spatiotemporal blog
(Nov 6, 2022)
OrbitHunter
(Oct 01, 2021)
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Working notes -very rough, read at your own risk, but with lots of literature pointers- on how to recast finding invariant solutions of the 1D Kuramoto-Sivashinsky PDE into the problem of finding spatio-temporal fixed point solutions.
We have give up on finding compact solutions by forward integration in time - instead, we develop variational methods to multiply-periodic solutions in spacetime. In particular, it would be very nice if someone extends OrbitHunter to a general spatiotemporal Navier-Stokes solver that runs on a higly parallelized machines. |
