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Showing 1 to 4 of 4 for “"Periodic orbit theory"”.
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Coherent structures in incompressible fluid flows
… descriptions of turbulence is predicted by periodic orbit theory (POT) which expects to describe turbulence exactly, as opposed to approximately. The search for relative periodic orbits and traveling waves in pipe---the constituents solutions to periodic orbit theory---are discussed. The …
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Dynamical systems approach to one-dimensional spatiotemporal chaos -- A cyclist's view
… turbulence(spatiotemporal chaos) based on the periodic orbit theory, emphasizing the role of recurrent patterns and coherent structures. After a brief review of the periodic orbit theory and its application to low-dimensional dynamics, we discuss its possible extension to study dynamics of …
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Periodic orbit analysis of the Helmholtz equation in two-dimensional enclosures
This thesis examines how periodic orbits may be used in acoustics to understand solutions of the Helmholtz equation. A review of the links between ray and wave mechanics is given including WKBJ (Wentzel, Kramers, Brillouin and Jeffreys) and EBK (Einstein, Brillouin, Keller) methods. It is also …
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Exact coherent structures in spatiotemporal chaos: From qualitative description to quantitative predictions
… shaped by the invariant sets such as equilibria, periodic orbits, and invariant tori. State space of partial differential equations is infinite dimensional, nevertheless, recent computational advancements allow us to find their invariant solutions (exact coherent structures) numerically. In this …