The Swift-Hohenberg equation has growth rate for a 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 a control parameter rr. Take r=0.16r = 0.16. ((a)) State the critical wavenumber qcq_{\rm c}. ((b)) Find the two edges of the unstable band of qq.

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