A Swift-Hohenberg pattern is started from numerical noise of typical amplitude at…

PHYSICS · Subjective · 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 Swift-Hohenberg pattern is started from numerical noise of typical amplitude A0≈10−3A_0 \approx 10^{-3} at control parameter r=0.02r = 0.02. Using the projected amplitude equation A˙=rA−34A3\dot A = rA - \tfrac34A^3, estimate, to the nearest order of magnitude, the (dimensionless) time needed for the amplitude to grow up to the neighbourhood of its saturated value A∗=(4r/3)1/2A^* = (4r/3)^{1/2}.

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