Prandtl–Batchelor Theory for Kolmogorov Flows

Kolmogorov inertial range for inhomogeneous turbulent flows.

Kolmogorov-Arnold-Moser (KAM) Theory

Dynamics of reversals and condensates in two-dimensional Kolmogorov flows.

We present numerical simulations of the different two-dimensional flow regimes generated by a constant spatially periodic forcing balanced by viscous dissipation and large-scale drag with a dimensionless damping rate 1/Rh. The linear response to the forcing is a 6×6 square array of counterrotating vortices, which is stable when the Reynolds number Re or Rh are small. After identifying the seque...

Kolmogorov Complexity: Sources, Theory and Applications

The theory of Kolmogorov complexity is based on the discovery, by Alan Turing in 1936, of the universal Turing machine. After proposing the Turing machine as an explanation of the notion of a computing machine, Turing found that there exists one Turing machine which can simulate any other Turing machine. Complexity, according to Kolmogorov, can be measured by the length of the shortest program ...

Time - Bounded Kolmogorov Complexity in Complexity Theory

This paper presents one method of using time-bounded Kol-mogorov complexity as a measure of the complexity of sets, and outlines a number of applications of this approach to diierent questions in complexity theory. Connections will be drawn among the following topics: NE predicates, ranking functions, pseudorandom generators, and hierarchy theorems in circuit complexity.