dorsal/arxiv
View SchemaTemporal Forcing of Small-Amplitude Waves in Anisotropic Systems
| Authors | Hermann Riecke, Mary Silber, Lorenz Kramer |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9310003 |
| URL | https://arxiv.org/abs/patt-sol/9310003 |
| DOI | 10.1103/PhysRevE.49.4100 |
| Journal | Phys. Rev. E 49 (1994) 4100 |
Abstract
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.
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"abstract": "We investigate the effect of resonant temporal forcing on an anisotropic\nsystem that exhibits a Hopf bifurcation to obliquely traveling waves in the\nabsence of this forcing. We find that the forcing can excite various\nphase-locked standing-wave structures: rolls, rectangles and cross rolls. At\nonset, at most one of the two - rolls or rectangles - is stable. The cross\nrolls can arise in a secondary bifurcation and can be stable. Experimentally,\nthey would appear as a periodic switching between a structure in which the\n`zig\u0027-component dominates and one with dominating `zag\u0027-structure. Since there\nare two symmetry-related states of this kind one may expect disordered\nstructures to arise due to the break-up of the pattern into domains. The\nresults are consistent with recent experiments on electro-convection in nematic\nliquid crystals by de la Torre and Rehberg. We also apply the general analysis\nto a model of the behavior near a Lifshitz point, where the angle of\nobliqueness vanishes. This analysis indicates that phase-locked standing\nrectangles are always unstable in this parameter regime.",
"arxiv_id": "patt-sol/9310003",
"authors": [
"Hermann Riecke",
"Mary Silber",
"Lorenz Kramer"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.49.4100",
"journal_ref": "Phys. Rev. E 49 (1994) 4100",
"title": "Temporal Forcing of Small-Amplitude Waves in Anisotropic Systems",
"url": "https://arxiv.org/abs/patt-sol/9310003"
},
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