online videos, presentations

turbulence in spacetime

Online talks

YouTube P Cvitanović
Turbulence in spacetime
overheads (Apr 13, 2023 Working across scales in complex systems - Emory - 15 min)
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.
YouTube P Cvitanović
Recurrent solutions and dynamics of turbulent flows, as seen in experiments
overheads (Sep 24, 2022 Georgia Tech Math Colloquium - 44 min)
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.
YouTube P Cvitanović
Field theory of spatiotemporal chaos
overheads (Jan 26, 2023 Georgia Tech Math Physics Seminar - XX min)
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.
pdf P Cvitanović
A chaotic field theory
overheads (December 19, 2023 125th Statistical Mechanics Conference, Rutgers University - slides only, 20 min talk)
Emphasis on the exact spatiotemporal zeta function over infinite-dimensional spacetime, in a lattice discretized field-theoretic framework.
YouTube 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)
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.
YouTube P Cvitanović
Hearding cats : chaotic field theory
overheads (December 6, 2021 QM3 Quantum Matter meets Maths, Lisbon - 1 h talk)
Emphasis on the quantum physics motivation.
pdf 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)
pdf P Cvitanović
Spatiotemporal cat : a chaotic field theory
overheads (December 16, 2020 Mathematical Physics Webinar, Rutgers University - 55 min talk)
pdf P Cvitanović
Herding cats : a chaotic field theory
overheads (September 25, 2020 ITS Symposium on Chaos and Quantum Field Theory - 1 hour talk) | abstract | video (1 hour 10 min)
pdf P Cvitanović and H Liang
Herding cats : a chaotic field theory
overheads (July 2020) | video (similar to 2020 APS below, but 1h long)
pdf 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)
Revolution will not be twitterized!.

Chaotic lattice field theory

pdf Han Liang and Predrag Cvitanović
A chaotic lattice field theory in one dimension (April 2022, includes explanatory videos)
J. Phys. A 55, 304002 (2022)
[ arXiv:2201.11325 | DOI ]
Our approach to time-reversal invaraince, with an unexpected zeta function.
pdf Predrag Cvitanović and Han Liang
Chaotic field theory slides (November 2022)
links to corresponding video clips are included in the above paper
[why? | Bernoulli | deterministic field theory | spacetime tilings | cat | spatiotemporal cat | time reversal | Hill's formula | time is dead ]
pdf Predrag Cvitanović and Han Liang
A chaotic lattice field theory in two dimensions
rough draft , (April 2023)
Our discretized spacetime model field theory, 3rd millennium formulation.
pdf S. V. Williams, M. N. Gudorf, X. Wang, H. Liang and P. Cvitanović
Nonlinear chaotic lattice field theory
rough draft , (April 2022)
Our discretized spacetime nonlinear field theory.
pdf B Gutkin, P Cvitanović, R Jafari, A K Saremi and L Han
Linear encoding of the spatiotemporal cat map
Nonlinearity 34, 2800--2836 (2021)
[ arXiv:1912.02940 | DOI ]
Our spacetime discretized model field theory, pre-1969 Soviet style approach.
Seminar Spatiotemporal cat map blog (feb 2022) Working notes -very rough, read at your own risk, with many literature pointers- on our elegant, analytically soluble baby model of a spatiotemporally discretized chaotic field theory, on the Ising model / Ihara zeta functions literature of potential relevance to the spatiotemporal reformulation of turbulent field theories. There are many promising directions to ponder here.

Spatiotemporal theory of turbulence

YouTube 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)
pdf Matthew N. Gudorf
Spatiotemporal tiling of the Kuramoto-Sivashinsky system
thesis (November 20, 2020 - 1 hour talk) Georgia Tech thesis repository link
Video P Cvitanović:
Dynamical systems are a fraud!
(5:40 min manifesto Jan 11, 2022)
Act locally, think globally, tighten the rubber band: elaborated a bit in the next two videos.
Video P Cvitanović: What do we talk about when we talk about chaos I (9:41 min, July 29, 2020) When we talk, we talk about evolving in time, derive the forward-in-time Jacobian.
Video P Cvitanović: What do we talk about when we talk about chaos II (8:40 min July 30, 2020) When we walk the walk, we determine the global orbit and its global stability, derive its orbit Jacobian.
Seminar Spatiotemporal blog (Nov 6, 2022)
OrbitHunter (Oct 01, 2021)
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.

Chaotic Field Theory

Predrag Cvitanović
Chaotic Field Theory: a sketch,
Physica A 288 , 61 (2000) [ arXiv:nlin.CD/0001034 | DOI | NSF review panel critique ]