Swift-Hohenberg Equation

g1 zero: Stripes g1 nonzero: Hexagons

The parameter g1 is the coefficient of the quadratic non-linear term in the equation of motion:

These applets demonstrate the important and general principle that if the dynamical equations are not symmetric under change of sign of the field then a hexagonal pattern is typically expected near onset (small eps). On the other hand if the equations have this symmetry then stripes are often seen (although squares or rectangles are other possibilities).

The Swift-Hohenberg equation is symmetric under a change of sign of the field if g1=0. A nonzero g1 eliminates this symmetry.

You can also look at the Fourier transform of the field by changing PlotFFT to Yes (the absolute value is plotted).


Last modified Tuesday, June 22, 1999
Michael Cross