Imperfect wave-number selection by ramps in a model for Taylor vortex flow

In pattern-forming systems the wave-number bands accessible to the system are drastically reduced if the control parameters are varied slowly in space from supercritical to subcritical. Using a recently derived matching condition, these wave-number bands are calculated in a simple model for Taylor vortex flow. They show qualitatively the same behavior as observed in the experiments on this system: (1) starting from a minimal bandwidth, the band grows both for decreasing as well as increasing control parameter; and (2) the dependence of the selected wave number on the system length shows a phase shift of half a wavelength during the crossover from small- to large- behavior. These results are in quantitative agreement with a numerical simulation of the model.