Via Hexagons to Squares in Ferrofluids: Experiments on Hysteretic Surface Transformations under Variation of the Normal Magnetic Field

Details Via Hexagons to Squares in Ferrofluids: Experiments on Hysteretic Surface Transformations under Variation of the Normal Magnetic Field Via Hexagons to Squares in Ferrofluids: Experiments on Hysteretic Surface Transformations under Variation of the Normal Magnetic Field

2006-07-26

arxiv.org/abs/nlin/0607059v2

J. Phys. Condens. Matter 18 (2006) S2643-S2656

Nonlinear Sciences

Pattern Formation and Solitons

17 pages, 14 figures

Scientific paper

10.1088/0953-8984/18/38/S08

We report on different surface patterns on magnetic liquids following the Rosensweig instability. We compare the bifurcation from the flat surface to a hexagonal array of spikes with the transition to squares at higher fields. From a radioscopic mapping of the surface topography we extract amplitudes and wavelengths. For the hexagon--square transition, which is complex because of coexisting domains, we tailor a set of order parameters like peak--to--peak distance, circularity, angular correlation function and pattern specific amplitudes from Fourier space. These measures enable us to quantify the smooth hysteretic transition. Voronoi diagrams indicate a pinning of the domains. Thus the smoothness of the transition is roughness on a small scale.

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