Reorientation of a hexagonal pattern under broken symmetry: the hexagon flip.

ABSTRACT

An unexpected pattern transition has been found experimentally in the transformation from hexagons to stripes caused by an applied anisotropy effect. The particular system studied is the surface instability of a horizontal layer of magnetic liquid in a tilted magnetic field. Two orthogonal Helmholtz pairs of coils provide a vertical and a tangential magnetic field. Whereas the vertical component destabilizes the flat layer, the tangential one preserves its stability. The ensuing surface patterns comprise regular hexagons, anisotropic hexagons, and stripelike ridges. The phase diagram for the tilted field instability is measured using a radioscopic technique. The investigation reveals an interesting effect the flip from one hexagonal pattern to another under an increasing tangential field component, which is explained in terms of amplitude equations as a saddle-node bifurcation.