ChaosBook.org overheads

turbulence in spacetime

Overheads

pdf B Gutkin, P Cvitanović, R Jafari, A K Saremi and L Han
Is space time? a spatio-temporal field theory
overheads (2018 working notes)
pdf P Cvitanović and M Gudorf
A spatiotemporal theory of turbulence - computational challenges
overheads (2018 working notes)

Chapter - Spatiotemporal cat map

pdf B Gutkin, P Cvitanović, R Jafari, A K Saremi and L Han
Linear encoding of the spatiotemporal cat map
Nonlinearity , (2018, in preparation)
2/3rds finished draft of the paper on our spacetime discretized model field theory.
Seminar Spatiotemporal cat map blog (dec 2017)
Working notes -very rough, read at your own risk, but with lots of literature pointers- on our elegant, analytically soluble baby model of a spatiotemporally discretized field theory, and the Ising model / Ihara zeta functions literature of potential relevance to the spatiotemporal reformulation of turbulent field theories. There is lots of theoretical directions to ponder here.

Chapter - Spatiotemporal theory of turbulence

Seminar Spatiotemporal blog (dec 2017)
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. The point is that we have give up on finding invariant solutions by forward integration in time from specified intial conditions - instead, we have to develop variational methods to multiply-periodic solutions in spacetime. In particular, it would be very nice if someone writes a working spatiotemporal solver and runs it on some higly parallelized machine.