Ordered defect chains in the 2D anisotropic complex Ginzburg-Landau equation

Chaos, solitons and fractals

Volumn 10, Issue 4, 1999, Pages 745-752

  Faller, Roland ^a   Kramer, Lorenz ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; CHEMICAL BONDS; CHEMICAL REACTIONS; COMPUTER SIMULATION; CRYSTAL DEFECTS; DIFFERENTIAL EQUATIONS; HYDRODYNAMICS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; TWO DIMENSIONAL; WAVE EQUATIONS;

BELOUSOV-ZHABOTINSKY REACTION; COMPLEX GINZBURG-LANDAU EQUATION; HOPF BIFURCATION; ORDERED DEFECT CHAINS; SURFACE REACTION;

SOLITONS;

EID: 0033114842     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00024-1     Document Type: Note

References (25)

1. 1. W. Schöpf, W. Zimmermann. Convection in binary fluids: codimension-2-bifurcation and thermal fluctuations, Phys. Rev. E47, 1739-1764 (1993).
2. 2. M. Treiber, N. Éber, Á. Buka, L. Kramer. Travelling Waves in Electroconvection of the Nematic Phase 5: A Test of the Weak Electrolyte model, J. de Physique II 7, 649-661 (1997).
3. 3. P. Coullet, L. Gil, P. Rocca. Optical vortices, Optics Comm. 73, 403-408 (1989).
4. 4. F. Hynne, P. Graae Sorenson, T. Moller. Complete optimization of models of the Belousov-Zhabotinsky reaction at a Hopf bifurcation, J. Chem. Phys. 98, 219-230 (1993).
5. 5. M. Baer, M. Hildebrand, M. Eiswirth, M. Falcke, H. Engel, M. Neufeld. Chemical turbulence and standing waves in a surface reaction model: The influence of global coupling and wave instabilities, Chaos 4, 499-508 (1994).
6. 6. M.C. Cross, P.C. Hohenberg. Pattern formation outside of equilibrium, Rev. Mod. Phys. 65, 851-1112 (1993).
7. 7. W.v. Saarlos, P.C. Hohenberg. Fronts, pulses, sources and sinks in generalized complex Ginzburg-Eandau equations, Physica D56, 303-367 (1992).
8. 8. S.Popp, O.stiller, I.s.aranson und L.kramer. Hole solutions in the 1d complex Ginzburg-Landau Equations, Physica D87, 398-423 (1995).
9. 9. H. Chaté, P. Manneville. Phase Diagram of the Two-Dimensional complex Ginzburg-Landau equation, Physica A224, 348-368 (1996).
10. 10. I. Aranson, A. Bishop. Stretching of vortex lines and generation of vorticity in the three-dimensional complex Ginzburg-Landau equation, Phys. Rev. Lett. 79, 4179 (1997). further details? http://xxx.lanl.gov/abs/patt- sol/9705009.
11. 11. T. M. Haeusser, S. Leibovich. Amplitude and mean drift equations for the oceanic Ekman layer, Phys. Rev. Letters 79, 329-332 (1997).
12. 12. L. Kramer and W. Pesch, in Pattern formation in liquid crystals, A. Buka and L. Kramer, eds. (Springer, New York, 1996) p. 221.
13. 13. A. Weber, E.Bodenschatz, L. Kramer. Defects in continuous Media, Advanced Materials 3, 191-197 (1991).
14. 14. I. Aranson, L. Aranson, L. Kramer, A. Weber. Stability of spirals and travelling waves in nonequilibrium media, Phys. Rev. A46, 2992(1992); A. Weber, L. Kramer, I. S. Aranson und L. B. Aranson. Stability Limits of Traveling Waves and the Transition to Spatiotemporal Chaos in the Complex Ginzburg-Landau Equation, Physica D61, 279-283 (1992).
15. 14. I. Aranson, L. Aranson, L. Kramer, A. Weber. Stability of spirals and travelling waves in nonequilibrium media, Phys. Rev. A46, 2992(1992); A. Weber, L. Kramer, I. S. Aranson und L. B. Aranson. Stability Limits of Traveling Waves and the Transition to Spatiotemporal Chaos in the Complex Ginzburg-Landau Equation, Physica D61, 279-283 (1992).
16. 15. I. Aranson, L. Kramer, A. Weber. The core instability and spatio-temporal intermittency of spiral waves in oscillatory media, Phys. Rev. Lett. 72, 2316-2319 (1994).
17. 16. D. Barkley. Euclidean symmetry and the dynamics of rotating spiral waves, Phys. Rev. Lett. 72, 164-167 (1994).
18. 17. I. S. Aranson, L. Kramer, A. Weber. The theory of Interaction and Bound States of Spiral Waves in Oscillatory Media, Phys. Rev. E47, 3231 (1993).
19. 18. I. Aranson, L. Kramer, A. Weber. The Formation of Asymmetric States of Spiral Waves in Oscillatory Media, Phys. Rev. E48, R9-R12 (1993).
20. 19. G. Huber, P. Alstrom, T. Bohr. Nucleation and Transients at the Onset of Vortex Turbulence, Phys. Rev. Lett. 69, 2380-2383 (1992).
21. 20. T. Bohr, G. Huber, E.Ott. The structure of spiral-domain patterns and shocks in the 2D complex Ginzburg-Landau equation, Physica D106, 95-112 (1997).
22. 21. A. G Roßberg, L. Kramer. Pattern formation from Defect Chaos - A Theory of Chevrons, Physica D, in press.Further details?
23. 22. A. Weber. Private communication. What year?
24. 23. G. Huber. Vortex Solids and Vortex Liquids in a Complex Ginzburg-Landau System in Spatio-Temporal Patterns in Nonequilibrium Complex Systems, P. E. Cladis and P. Palffy-Muhoray, eds., SFI Studies in the Sciences Of Complexity, Addison-Wesley, Reading MA 1995.
25. 24. P. Manneville and H. Chaté Physica D96, 30-46 (1996).