SIDEWALL FORCING OF HEXAGONAL TURING PATTERNS - RHOMBIC PATTERNS

Rhombic arrays were obtained by sidewall forcing during Turing pattern formation in numerical simulations. Locking between the frequency of forcing and the wave length between blobs was obtained in accordance w ith the Farey sequence. This locking appears as a perfect rhombic arra y oriented in the direction of the imposed forcing. For a constant for cing in duration and amplitude, the following scheme of bifurcation wa s observed: parallel stripes --> rhombic array --> domains of hexagons and rhombi separated by ''penta-hepta'' defects. Symmetry considerati ons based on a non-uniform stretching along the the x-axis were used t o describe these transitions. Unstable ''varicose-vein'' stripes were observed to evolve during the temporal evolution arrays.