D37.00002. Is space time? A spatiotemporal tiling of turbulence

Presented by: Predrag Cvitanovic


(35:10) We address the long standing problem of how to describe, by means of discrete symbolic dynamics, the spatiotemporal chaos (or turbulence) in spatially extended, strongly nonlinear field theories. One way to capture the essential features of turbulent motions is offered by coupled map lattice models, in which the spacetime is discretized, with the dynamics of small-scale spatial structures modeled by maps attached to lattice sites. The discretization that we study, the "spatiotemporal cat," has a remarkable feature that its every solution is uniquely encoded by a linear transformation from the corresponding finite alphabet symbol lattice. A spatiotemporal window into system dynamics is provided by a finite block of symbols, and the central question is to determine the likelihood of a given block's occurrence. As spatiotemporal states that share the same sub-blocks shadow each other exponentially well within the corresponding spatiotemporal windows, the dynamical zeta functions are now sums over spacetime tori, rather than time-periodic orbits. In the spatiotemporal formulation of turbulence there is no evolution in time, there are only a repertoires of admissible spatiotemporal patterns. In other words: throw away your integrators, and look for guidance in clouds' repeating patterns.


  • Predrag Cvitanovic
  • Matthew N Gudorf
  • Han Liang


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