Instabilities of Hexagons with Rotation1
To explore the possible instabilities
and ensuing dynamics of hexagonal patterns in the presence of
rotation we investigate a modified Swift-Hohenberg Equation:
The instabilities can be long-wave or
short-wave instabilities, steady or oscillatory. Of particular
interest is the situation in which hexagons become unstable at all
wavelengths as shown in the stability diagram below. In this case there are no
stable steady hexagon solutions above R=0.09.
In this regime regular hexagon patterns
decay into a persistently changing disordered pattern that has a mixed
cellular and stripe-like appearance.
This is shown in the
movie (800k).
For a smaller version look at
movie (200k).
Another view of the same data are shown in this
movie (400k).
Footnotes:
1
work performed with F. Sain
Research supported by NASA and DOE.
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