A layer described by the Swift-Hohenberg equation is held at 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

A layer described by the Swift-Hohenberg equation ∂tu=ru−(1+∂x2)2u−u3\partial_t u = ru - (1+\partial_x^2)^2u - u^3 is held at control parameter r=0.04r = 0.04. ((a)) State the critical wavenumber qcq_{\rm c} at which the instability first appears as rr is raised through zero. ((b)) Find the two edges of the unstable band of wavenumbers at r=0.04r = 0.04. ((c)) State the wavenumber of the fastest-growing mode and its growth rate.

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