Dynamics and bifurcations in the weak electrolyte model for electroconvection of nematic liquid crystals: a Ginzburg-Landau approach

European Journal of Mechanics, B/Fluids

Volumn 27, Issue 6, 2008, Pages 726-749

  Oprea, Iuliana ^a   Dangelmayr, Gerhard ^a  

^a Veterinary Dentistry and Oral Surgery   (United States)

Author keywords

Amplitude equations; Eckhaus stability; Hopf bifurcation; Nematic electroconvection; Spatiotemporal chaos; Weak electrolyte model

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; CHAOTIC SYSTEMS; CHLORINE COMPOUNDS; CRYSTALLOGRAPHY; DYNAMICS; ELECTROLYSIS; ELECTROLYTES; HOPF BIFURCATION; LIGHT SOURCES; LINEAR STABILITY ANALYSIS; LIQUID CRYSTALS; NONLINEAR ANALYSIS; NONLINEAR EQUATIONS; OPTICAL BISTABILITY; SYSTEM STABILITY; TWO DIMENSIONAL;

AMPLITUDE EQUATIONS; ANISOTROPIC SYSTEMS; CHAOTIC ATTRACTORS; COMPLEX GINZBURG-LANDAU EQUATIONS; ECKHAUS STABILITY; ELECTROCONVECTION; GINZBURG-LANDAU; LINEAR STABILITY; MEASURED VALUES; NEMATIC ELECTROCONVECTION; NORMAL FORM; PERIOD DOUBLING; PERIOD DOUBLING CASCADE; PHYSICAL MECHANISMS; REFLECTIONAL SYMMETRY; SPATIAL VARIATIONS; SPATIO-TEMPORAL DYNAMICS; SPATIOTEMPORAL CHAOS; STABILITY BOUNDARIES; TRAVELLING WAVES; WEAK ELECTROLYTE MODEL;

NEMATIC LIQUID CRYSTALS;

EID: 50849122642     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechflu.2007.12.004     Document Type: Article

References (30)

1. Kramer L., and Pesch W. Convection instabilities in nematic liquid crystals. In: Hoffmann H., Schwoerer M., and Vogtmann T. (Eds). Macromolecular Systems: Microscopic Interactions and Macroscopic Properties (2000), Wiley 250-294
2. Pesch W., and Behn U. Electrohydrodynamic convection in nematic. In: Busse F.H., and Müller S. (Eds). Evolution of Spontaneous Structures in Dissipative Continuous Systems (1998), Springer-Verlag, Berlin 335-383
3. Buka A., Éber N., and Pesch W. Convective patterns in liquid crystals driven by electric field. Liquid Crystal Commun. (2005) 1-21. http://www.e-lc.org/docs/2005_07_12_04_29_54 (electronic)
4. Chandrasekhar S. Liquid Crystals (1977), University Press, Cambridge
5. Dennin M., Ahlers G., and Cannell D.S. Spatiotemporal chaos in electroconvection. Science 272 (1996) 388
6. Dennin M., Ahlers G., and Cannell D.S. Chaotic localized states near the onset of electroconvection. Phys. Rev. Lett. 77 (1996) 2475
7. Gleeson J.T. Sustained spatiotemporal chaotic flow at onset of electroconvection in nematic liquid crystals. Physica A 239 (1997) 211
8. G. Dangelmayr, J. Gleeson, G. Acharya, I. Oprea, J. Ladd, Diagnosis of spatiotemporal chaos in wave-envelopes of an electroconvection pattern, in preparation, 2008
9. Carr E.F. Influence of electric fields on the molecular alignment in the liquid crystal p-(anisalamino)-phenil acetate. Mol. Cryst. Liqu. Cryst. 7 (1969) 253-269
10. Helfrich W. Conduction-induced alignment of nematic liquid crystals: basic model and stability considerations. J. Chem. Phys. 51 (1969) 4092-4105
11. Zimmermann W., and Kramer L. Oblique-roll electrodynamic in nematics. Phys. Rev. Lett. 55 (1985) 402
12. M. Dennin, A study in pattern formation: Electroconvection in nematic liquid crystals, PhD Thesis, Department of Physics, University of California, Santa Barbara, 1995
13. Treiber M., and Kramer L. Bipolar electrodiffusion model for electroconvection in nematics. Mol. Cryst. Liqu. Cryst. 261 (1995) 311
14. Dennin M., Treiber M., Kramer L., Ahlers G., and Cannell D.S. Origin of traveling rolls in electroconvection of nematic liquid crystals. Phys. Rev. Lett. 76 (1996) 319
15. M. Treiber, On the theory of the electrohydrodynamic instability in nematic liquid crystals near onset, PhD Thesis, University of Bayreuth, 1996
16. Treiber M., and Kramer L. Coupled complex Ginzburg-Landau equations for the weak electrolyte model of electroconvection. Phys. Rev. E 58 (1998) 1973
17. Dangelmayr G., and Wegelin M. Hopf bifurcations in anisotropic systems. In: Golubitsky M., Luss D., and Strogatz S. (Eds). Pattern Formation in Continuous and Coupled Systems. IMA Vol. Math. Appl. vol. 115 (1999) 33-42
18. Dangelmayr G., Fiedler B., Kirchgässner K., and Mielke A. Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability (1996), Addison-Wesley Longman Ltd.
19. Dangelmayr G., and Kramer L. Mathematical tools for pattern formation. In: Busse F.H., and Müller S. (Eds). Evolution of Spontaneous Structures in Dissipative Continuous Systems (1998), Springer-Verlag, Berlin 1-85
20. Oprea I., Triandaf I., Dangelmayr G., and Schwartz I.B. Quantitative and qualitative characterization of zigzag spatiotemporal chaos in a system of amplitude equations for nematic electroconvection. Chaos 17 (2007) 023101
21. Werner B. Numerical computation of degenerate Hopf bifurcation points. ZAMM 78 (1998) 807-821
22. Allgower E., Georg K., Oprea I., and Dangelmayr G. Matrix-free numerical computation of instabilities of periodic patterns. In: Dangelmayr G., and Oprea I. (Eds). Dynamics and Bifurcation of Patterns in Dissipative Systems. World Scientific Series on Nonlinear Sciences, Series B (2004), World Scientific Publisher 20-38
23. Silber M., Riecke H., and Kramer L. Symmetry breaking Hopf bifurcation in anisotropic systems. Physica D 61 (1992) 260
24. M. Wegelin, Nichtlineare Dynamik raumzeitlicher Muster in hierarchischen Systemen, PhD Dissertation, Department of Physics, Tubingen, 1993
25. Dangelmayr G., and Oprea I. Modulational stability of travelling waves in 2D anisotropic systems. J. Nonlinear Sci. 18 1 (2008) 1-56
26. Dangelmayr G., and Oprea I. A bifurcation study of wave patterns for electroconvection in nematic liquid crystals. Mol. Cryst. Liqu. Cryst. 413 (2004) 2441
27. Swift J.H. Hopf bifurcation with the symmetry of the square. Nonlinearity 1 (1988) 333-377
28. Lega J. Phase diffusion and weak turbulence. In: Dangelmayr G., and Oprea I. (Eds). Dynamics and Bifurcation of Patterns in Dissipative Systems. World Scientific Series on Nonlinear Sciences, Series B (2004), World Scientific Publisher 157-183
29. Daniels K.E., Brausch O., Pesch W., and Bodenschatz E. Competition and bistability of ordered undulations and undulation chaos in inclined layer convection. J. Fluid. Mech. 57 (2008) 261-282
30. Schneider G., and Uecker H. The amplitude equations for the first instability of electroconvection in nematic liquid crystals in case of two unbounded space directions. Nonlinearity 20 (2007) 1361-1386