Patterns in the Bulk and at the Interface of Liquid Crystals

Buka, Ágnes; Börzsönyi, Tamás; Éber, Nándor; Tóth-Katona, Tibor

doi:10.1007/3-540-44698-2_19

Cited by 5 publications

(3 citation statements)

References 76 publications

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“…The formation of these patterns is governed by experimentally easily controllable parameters, the amplitude and the frequency of the applied voltage and the magnitude of magnetic field. The advantage of liquid crystals over other fluids in these experiments besides its transparency and its phase transition temperatures being close to the room temperature, which makes detection of patterns easier, [3], is the fact that their molecules are locally oriented along desired direction. In [28], it is reported that the described system has a tendency to form chevron structures after a transition to defect chaos and that chevron patterns are generally observed when the isotropy of the system is spontaneously broken, this effect is achieved either by increasing the voltage or by applying a weak magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Global behavior of solutions to chevron pattern equations

Kalantarova

Kalantarov

Vantzos³

2020

Journal of Mathematical Physics

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Considering a system of equations modeling the chevron pattern dynamics, we show that the corresponding initial boundary value problem has a unique weak solution that continuously depends on initial data, and the semigroup generated by this problem in the phase space X 0 ∶= L 2 (Ω) × L 2 (Ω) has a global attractor. We also provide some insight into the behavior of the system, by reducing it under special assumptions to systems of ordinary differential equations, which can, in turn, be studied as dynamical systems.

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Section: Introductionmentioning

confidence: 99%

Global behavior of solutions to chevron pattern equations

Kalantarova

Kalantarov

Vantzos³

2020

Journal of Mathematical Physics

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“…As such this deformation could be explained by the anisotropy of the linear dispersion relation of the convective mode, which can be removed by a simple rescaling of the x axis. But in some cases the defects stretch considerably and are then more naturally characterized as "phase jump lines" [21,22,23]. These structures seem to be related to weakly unstable saddles corresponding to the stable PJL reported here.…”

Section: Introductionmentioning

confidence: 68%

Observation of stable phase jump lines in convection of a twisted nematic liquid crystal

2006

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We report observations of stable, localized, linelike structures in the spatially periodic pattern formed by nematic electroconvection, along which the phase of the pattern jumps by pi. With increasing electric voltage, these lines form a gridlike structure that goes over into a structure indistinguishable from the well-known grid pattern. We present theoretical arguments that suggest that the twisted cell geometry we are using is indirectly stabilizing the phase jump lines, and that the phase jump lines lattice is caused by an interaction of phase jump lines and a zig-zag instability of the surrounding pattern.

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“…nematic liquid crystals), driven out of equilibrium, offer a rich palette of pattern forming phenomena [1,2]. Electroconvection (EC) is a classical example of such instabilities [3].…”

Section: Introductionmentioning

confidence: 99%

Electroconvection in homeotropic nematic liquid crystals

Éber

Buka

2005

Phase Transitions

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Electroconvection is a classical example of pattern-forming phenomena in liquid crystals, typically observed in nematics with negative dielectric and positive conductivity anisotropies. This article focuses on how electroconvection in the homeotropic geometry differs from that in planar alignment. The influence of an additional magnetic field on the pattern characteristics and on secondary instabilities (the normal roll-abnormal roll transition) is discussed. The homeotropic alignment offers unique possibilities also for studying defect motion. Basic characteristics of some patterns of large wavelength are presented and compared with those of the classical Carr-Helfrich structures. Finally, electroconvection in substances with negative conductivity anisotropy is addressed.

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Patterns in the Bulk and at the Interface of Liquid Crystals

Cited by 5 publications

References 76 publications

Global behavior of solutions to chevron pattern equations

Global behavior of solutions to chevron pattern equations

Observation of stable phase jump lines in convection of a twisted nematic liquid crystal

Electroconvection in homeotropic nematic liquid crystals

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