The electrohydrodynamic instability in homeotropic nematic layers

Hertrich, A.; Decker, Werner; Pesch, Werner; Kramer, Lorenz

doi:10.1051/jp2:1992243

Cited by 58 publications

(47 citation statements)

References 11 publications

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“…Since boundary layers have to be resolved, one needs more (6 − 8) Galerkin modes than typically required in the standard planar case. These numerical calculations have achieved the same good agreement with the experiments in MBBA or Phase 5 [35,36], as previously in the case of the primary bifurcations (cases A and B). U c in Fig.…”

Section: Figuresupporting

confidence: 83%

Convective Patterns in Liquid Crystals Driven by Electric Field

Buka

Éber

Pesch

et al. 2006

NATO Science Series II: Mathematics, Physics and Chemistry

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A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. Particular emphasis is laid on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in five different wavenumber ranges, which depend on the anisotropies of the dielectric permittivity and of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). Experiments have revealed two additional pattern types which are not captured by the standard model of electroconvection and which still need a theoretical explanation.

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Section: Figuresupporting

confidence: 83%

Convective Patterns in Liquid Crystals Driven by Electric Field

Buka

Éber

Pesch

et al. 2006

NATO Science Series II: Mathematics, Physics and Chemistry

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“…2V F . With no external field selecting a preferred direction for n, the recent theoretical prediction is a direct transition from a disordered director configuration to turbulence in EC patterns observed as a function of the two control pa-rameters´ ͑V 2 2 V 2 c ͒͞V 2 c and n [12]. Indeed, in contrast to observations presented here, previously reported patterns at EC onset in the homeotropic geometry are irregular and nonstationary [13,14].…”

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confidence: 92%

Wavelength Doubling Cascade to Möbius Defect Turbulence in a 3D Anisotropic Liquid

Fradin

Finn²,

Brand

et al. 1998

Phys. Rev. Lett.

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The following wavelength doubling cascade from a uniform state to a turbulent pattern is observed in a 3D anisotropic liquid: First oscillating convective rolls followed by a stationary stripe pattern, then Möbius defect creation stabilizing an unusual curved roll pattern that eventually becomes turbulent. Once created, Möbius defects are topologically trapped and the initial uniform state is not recovered. The system experimentally investigated is electroconvection above a highly nonlinear base state.[S0031-9007(98)07240-8] PACS numbers: 47.54. + r, 05.70.Ln, 61.30.Gd One of the many reasons for the growing interest [1][2][3] in patterns formed and the onset of turbulence in 3D anisotropic liquids is that they reveal by controlled experiments the intricate interplay between spatial and temporal order. In particular, in the 3D anisotropic liquids, liquid crystals [4], and superfluid 3 He [5], the interplay between flow fields and the orientational ordering field generates qualitative and quantitative information relevant to deep insights in natural laws derived from nonlinear field theories [6].The subharmonic (wavelength doubling) cascade, described here for the first time ( Fig. 1) and not predicted by any theory, shows a new route to spatiotemporal disorder in an orientationally ordered liquid. The orientational order has complete rotational freedom in planes perpendicular to the driving force. Two remarkable consequences of this freedom are traveling rolls built on a highly nonlinear base state and orientational order that consistently evades containment in vortex flow shear planes Ќ to the roll axes, R. A line of roll disclinations with the same topological charge spontaneously forms to finally lock the orientational order ЌR. The result is an unusual curved roll pattern that we call the Zvinger pattern, in analogy to a cage for wild animals, as the orientational order rotates 2p in a Zvinger wavelength, l Z . When the external driving force is removed from Zvingers, a state with a length scale emerges that coarsens extremely slowly to the uniform state by defect motion (Fig. 2).This novel cascade is observed in a nematic liquid crystal [7]. In many organic materials, a nematic phase intervenes between the isotropic liquid and other more ordered thermodynamic phases. It is characterized by long range orientational order in a preferred direction,n. Asn is not polar, its only line defect is a 6p rotation ofn around a singular line. As a 6p rotation is used to create the "endless" surface of a Möbius band, Frank has called them Möbius disclinations [8].Möbius disclinations, Möbions, have a topological charge S 61͞2 because in a circuit around the defect line, n rotates 6p S 3 2p. Viewed along its line between crossed polarizers, S 61͞2 disclinations are characterized by two black "brushes" whenn is parallel to either the polarizer or the analyzer. For a Möbion, this occurs twice in one circuit (e.g., Fig. 2). Because the elastic energy diverges at the singular line, Möbions are usually not observed. Rather, ...

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“…52,53 This has been confirmed in experiments. 54 The resulting complex spatiotemporal attractor could be characterized near threshold by a novel Swift-Hohenberg equation, where the field is coupled to the Goldstone mode.…”

Section: B Convection Pattern In Liquid Crystalsmentioning

confidence: 62%

Complex spatiotemporal convection patterns

Pesch

1996

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper reviews recent efforts to describe complex patterns in isotropic fluids (Rayleigh-Benard convection) as well as in anisotropic liquid crystals (electro-hydrodynamic convection) when driven away from equilibrium. A numerical scheme for solving the full hydrodynamic equations is presented that allows surprisingly well for a detailed comparison with experiments. The approach can also be useful for a systematic construction of models (order parameter equations). (c) 1996 American Institute of Physics.

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The electrohydrodynamic instability in homeotropic nematic layers

Cited by 58 publications

References 11 publications

Convective Patterns in Liquid Crystals Driven by Electric Field

Convective Patterns in Liquid Crystals Driven by Electric Field

Wavelength Doubling Cascade to Möbius Defect Turbulence in a 3D Anisotropic Liquid

Complex spatiotemporal convection patterns

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