Pattern Formation
In this area, I am interested in;
- Patterns in convection, Faraday wave and Taylor-Couette experiments
- Secondary instabilities of patterns
- Mode interactions
- Hidden symmetries
- Quasipatterns and the small divisor problem
More details of PhD topics
Example of an approximate quasipattern in a periodically forced PDE
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Example of an approximate quasipattern in a periodically forced PDE.
Spatial Fourier transforms of quasipatterns observed in Faraday wave
experiments suggest that the patterns are well represented by the sum of 8, 10
or 12 Fourier modes with wavevectors equally spaced around a circle.
However, nonlinear interactions between these wavevectors generate
new modes that come arbitrarily close to the original 8, 10 or 12 wavevectors,
which leads to complications in the theory for these patterns.
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