The Swift-Hohenberg equation has growth rate for the control parameter .

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems

Many Parts, One Behaviour, Ch Pattern formation: instabilities that choose a wavelength

Problem

The Swift-Hohenberg equation has growth rate σ(q)=r−(1−q2)2\sigma(q) = r - (1-q^2)^2 for the control parameter r=0.05r = 0.05. ((a)) Find the edges of the unstable band of wavenumbers qq. ((b)) State the fastest-growing wavenumber and its growth rate.

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