Title:
Spatiotemporal Tiling of the Kuramoto-Sivashinsky equation
Spatiotemporal Tiling of the Kuramoto-Sivashinsky equation
Author(s)
Gudorf, Matthew
Advisor(s)
Cvitanović, Predrag
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Abstract
Motivated by space-time translational invariance and
exponentially unstable dynamics,
`spatiotemporally chaotic' or `turbulent' flows are recast
as a (D+1)-dimensional spatiotemporal theory
which treats space and time equally.
Time evolution is replaced by a repertoire of
spatiotemporal patterns taking the form of (D+1)
dimensional invariant tori (periodic orbits).
Our claim is that the entirety of space-time can be described as the
shadowing of a finite collection of `fundamental orbits'.
We demonstrate that not only can fundamental orbits be extracted
from larger orbits, they can also be used as the `building blocks' of turbulence.
In the future we aim to explain all of these results by constructing a
(D+1)-dimensional symbolic dynamics whose alphabet is the set of fundamental orbits,
however, in order to do so we must first find all fundamental orbits.
These ideas are investigated in the context of
the 1+1 dimensional space-time of the Kuramoto-Sivashinsky equation
using the independently developed Python package 'orbithunter'.
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Date Issued
2020-12-06
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Resource Type
Text
Resource Subtype
Dissertation