Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
1993-10-15
Phys. Rev. E 49 (1994) 4100
Nonlinear Sciences
Pattern Formation and Solitons
36 pages (Revtex 3), 12 figures (postscript)
Scientific paper
10.1103/PhysRevE.49.4100
We investigate the effect of resonant temporal forcing on an anisotropic system that exhibits a Hopf bifurcation to obliquely traveling waves in the absence of this forcing. We find that the forcing can excite various phase-locked standing-wave structures: rolls, rectangles and cross rolls. At onset, at most one of the two - rolls or rectangles - is stable. The cross rolls can arise in a secondary bifurcation and can be stable. Experimentally, they would appear as a periodic switching between a structure in which the `zig'-component dominates and one with dominating `zag'-structure. Since there are two symmetry-related states of this kind one may expect disordered structures to arise due to the break-up of the pattern into domains. The results are consistent with recent experiments on electro-convection in nematic liquid crystals by de la Torre and Rehberg. We also apply the general analysis to a model of the behavior near a Lifshitz point, where the angle of obliqueness vanishes. This analysis indicates that phase-locked standing rectangles are always unstable in this parameter regime.
Kramer Lorenz
Riecke Hermann
Silber Mary
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