Electroconvection In Nematic Liquid Crystals Research Articles

Observation of Electroconvection in Nematic Liquid Crystals by X-Ray Interferometric Method

Observation of Electroconvection in Nematic Liquid Crystals by X-Ray Interferometric Method

In–Out Intermittency with Nested Subspaces in a System of Globally Coupled, Complex Ginzburg–Landau Equations

Chaos and intermittency are studied for the system of globally coupled, complex Ginzburg–Landau equations governing the dynamics of extended, two-dimensional anisotropic systems near an oscillatory (Hopf) instability of a basic state with two pairs of counterpropagating, oblique traveling waves. Parameters are chosen such that the underlying normal form, which governs the dynamics of the spatially constant modes, has two symmetry-conjugated chaotic attractors. Two main states residing in nested invariant subspaces are identified, a state referred to as Spatial Intermittency ([Formula: see text]) and a state referred to as Spatial Persistence ([Formula: see text]). The [Formula: see text]-state consists of laminar phases where the dynamics is close to a normal form attractor, without spatial variation, and switching phases with spatiotemporal bursts during which the system switches from one normal form attractor to the conjugated normal form attractor. The [Formula: see text]-state also consists of two symmetry-conjugated states, with complex spatiotemporal dynamics, that reside in higher dimensional invariant subspaces whose intersection forms the 8D space of the spatially constant modes. We characterize the repeated appearance of these states as (generalized) in–out intermittency. The statistics of the lengths of the laminar phases is studied using an appropriate Poincaré map. Since the Ginzburg–Landau system studied in this paper can be derived from the governing equations for electroconvection in nematic liquid crystals, the occurrence of in–out intermittency may be of interest in understanding spatiotemporally complex dynamics in nematic electroconvection.

Prewavy instability-originated dielectric chevrons of electroconvection in nematic liquid crystals.

This paper reports the pattern formation and evolution in a high-frequency dielectric regime observed in the AC-driven electroconvection of nematic liquid crystals (NLCs). It is determined that prewavy (PW) instability is essential for the formation and evolution. Specifically, in a twisted-aligned NLC cell, we observe a unique pattern that is comparable to the dielectric chevrons (DCVs) typically observed in a conventional planarly aligned pattern. It is determined to be a combined PW pattern with dielectric normal rolls (DNRs). Moreover, the power indices (α_{PW}, α_{DNR},andα_{DCV}) are determined from the frequency-dependent thresholds (V_{th}∝f^{α}) of PW, DNR, and DCV. By taking into account the appearance of PW and the different power indices, the pattern evolution scenarios for DCV are proposed, which can well explain the previous experimental results. Specifically, the PW-originated DCV2 clearly differs from the defect-mediated DCV1, which is known as a typical pattern evolution.

Additional Deterministic and Stochastic Field-Induced Shifts of the Threshold and Wavenumber of AC-Driven Electroconvection in Nematic Liquid Crystals

We report shifts of the threshold and wavenumber of ac-driven electroconvection (EC) in nematic liquid crystals under additionally applied deterministic and stochastic amplitudes and phases. A robu...

Grid pattern emerging from complex dynamics of defects.

The formation process and growth dynamics of the grid pattern, a cellular convective pattern in the electroconvection of nematic liquid crystals, are investigated. The grid pattern appears via a disordered state called defect turbulence with the increasing of an applied voltage. The averaged defect density increases with the applied voltage and then the defects that have been in the continuous process of creation and annihilation are frozen as grid cells forming domain structures. The area fraction of the grid domains is adopted as the order parameter. The temporal growth of the area fraction for the step voltage was also measured. By applying the Kolmogorov-Avrami model to the results, it is suggested that the growth dynamics of the grid domain is not primarily governed by domain growth, but by the local transition of the rolls to the cellular flow via preliminary grid structures that transiently appear.

Formation of grid patterns in an ac-driven electroconvection system.

We report the formation mechanism of a unique pattern observed in ac-driven electroconvection of nematic liquid crystals (NLCs), in which many well-organized grid cells are very regularly aggregated in a two-dimensional plane, globally forming a nearly perfect grid pattern (GP). Intuitively, the formation of such a pattern is unpredictable; usually, the perfectly regular normal roll (NR) showing a preferred roll direction is observed in this system by imposing a fixed initial direction of an NLC. The GP was investigated by varying the ac voltage and frequency. To characterize the GP, the density ρ_{GP}, the width a and length b of the grids, and the oscillation period T_{GP} of an inner optical pattern of the grids were measured; moreover, the lengths L[over ¯]_{x} and L[over ¯]_{y} characterizing phase-jump lines (PJLs) in the GP were examined. By taking into account the process of evolution from a fluctuating NR with defects to the GP, the velocity and director fields of the GP are estimated. Furthermore, in comparison with the bimodal mechanism proposed in the earlier study, a possible mechanism for the GP formed by the PJLs is discussed; various routes to GPs depending on the ac frequency are proposed.

Traveling Waves in One-Dimensional Electroconvection of Nematic Liquid Crystals

We report ac-driven electroconvection (EC) of nematic liquid crystals (NLCs) in one-dimensional cells employing an in-plane switching mode. The dynamical features of traveling waves (TWs), such as ...

Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls

The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence.

A period doubling route to spatiotemporal chaos in a system of Ginzburg-Landau equations for nematic electroconvection

In this paper we investigate the transition from periodic solutions to spatiotemporal chaos in a system of four globally coupled Ginzburg Landau equations describing the dynamics of instabilities in the electroconvection of nematic liquid crystals, in the weakly nonlinear regime. If spatial variations are ignored, these equations reduce to the normal form for a Hopf bifurcation with \begin{document}$O(2) × O(2)$\end{document} symmetry. Both the amplitude system and the normal form are studied theoretically and numerically for values of the parameters including experimentally measured values of the nematic liquid crystal Merck I52. Coexistence of low dimensional and extensive spatiotemporal chaotic patterns, as well as a temporal period doubling route to spatiotemporal chaos, corresponding to a period doubling cascade towards a chaotic attractor in the normal form, and a kind of spatiotemporal intermittency that is characteristic for anisotropic systems are identified and characterized. A low-dimensional model for the intermittent dynamics is obtained by perturbing the eight-dimensional normal form by imperfection terms that break a continuous translation symmetry.

Coexistence of stable branched patterns in anisotropic inhomogeneous systems

A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class and a model equation, we show that branched stripe patterns emerge, which for a given parameter set are stable within a band of different wave numbers and different numbers of branching points (defects). Moreover, the branched patterns and unbranched ones (defect-free stripes) coexist over a finite parameter range. We propose two systems where this generic scenario can be found experimentally, surface wrinkling on elastic substrates and electroconvection in nematic liquid crystals, and relate them to the findings from the amplitude equation.

Lagrangian chaos and particle diffusion in electroconvection of planar nematic liquid crystals.

Two types of spatiotemporal chaos in the electroconvection of nematic liquid crystals, such as defect turbulence and spatiotemporal intermittency, have been statistically investigated according to the Lagrangian picture. Here fluctuations are traced using the motion of a single particle driven by chaotic convection. In the defect turbulence (fluctuating normal rolls), a particle is mainly trapped in a roll but sometimes jumps to a neighboring roll. Its activation energy is then obtained from the jumping (hopping) rate. This research clarifies that diffusion in the defect turbulence regime in electroconvection can be regarded as a kind of hopping process. The spatiotemporal intermittency appears as a coexistent state of ordered grid domains and turbulent domains. The motion of a single particle shows weak and strong diffusion, respectively, in the ordered and turbulent domains. The diffusion characteristics intermittently change from one to another with certain durations as the domains change. This research has found that the distribution function of the duration that a particle remains in an ordered area has a power-law decay for which the index is different from that obtained by the Eulerian measurement.

Chaos and Spatiotemporal Chaos in Convective Systems

Much of early research on chaos from the viewpoint of physics was performed using spatially confined convective systems. In spatially extended convective systems, on the other hand, spatiotemporal chaos occurs. However, there is no unified definition for the term spatiotemporal chaos as for chaos. To unify definition, a property common to the three kinds of spatiotemporal chaos observed in electroconvection of nematic liquid crystals is presented.

Asymmetry of the time dynamics of breathers in the electroconvection twist structure of a nematic

Dynamics of breather defects in the periodic structures of rolls arising at electroconvection in nematic liquid crystals twisted by π/2 has been studied experimentally and theoretically. The axial components of the velocity of a hydrodynamic flow in the twist structures of nematics are opposite in the neighboring rolls. Dynamics of the breather defect is the periodic creation and annihilation of a pair of classical dislocations with the topological indices “+1” and “-1.” The annihilation occurs faster than the creation. It has been shown that the asymmetric time dynamics of the breather defect is described well by the solution of the perturbed sine-Gordon equation in the form of an interacting soliton and antisoliton.

Faraday Waves under Time-Reversed Excitation

Do parametrically driven systems distinguish periodic excitations that are time mirrors of each other? Faraday waves in a Newtonian fluid are studied under excitation with superimposed harmonic wave forms. We demonstrate that the threshold parameters for the stability of the ground state are insensitive to a time inversion of the driving function. This is a peculiarity of some dynamic systems. The Faraday system shares this property with standard electroconvection in nematic liquid crystals [J. Heuer et al., Phys. Rev. E 78, 036218 (2008)]. In general, time inversion of the excitation affects the asymptotic stability of a parametrically driven system, even when it is described by linear ordinary differential equations. Obviously, the observed symmetry has to be attributed to the particular structure of the underlying differential equation system. The pattern selection of the Faraday waves above threshold, on the other hand, discriminates between time-mirrored excitation functions.

Breathers in the one-dimensional roll structure of twisted nematics

The dynamics of nonsingular defects has been studied experimentally and theoretically in the periodic roll structures arising at electroconvection in nematic liquid crystals twisted by π/2. The presence of an axial component of the velocity of the hydrodynamic flow with the opposite direction in the neighboring rolls is characteristic of roll structures in twisted nematics. The quantitative estimates of the critical frequency of the oscillations of structural defects have been obtained on the basis of the nonlinear equation of motion for the roll displacement. It has been found that the periodic creation and annihilation of a pair of edge dislocations with the topological indices +1 and −1 occur in the process of oscillations of a defect with a nonsingular nucleus. It has been demonstrated that oscillating defects with zero topological indices correspond to the solution of the sine-Gordon equation in the form of standing breathers.

The electroconvection in nematic liquid crystals with short range smectic C order and negative electroconductivity anisotropy

The electroconvective instability (ECI) in nematic liquid crystals (NLCs), appearing beyond smectic C at cooling known as N with short range smecic C order, presents an unique electrooptical phenomenon due to generation and frustration of the smectic layering, which manifests inside the N temperature range. We found that the response time in this material is about an order shorter than those in the classical nematics. For the first time in NLCs were detected harmonics higher than fourth order. A twist type instability is suggested for this material.

Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals

We investigate growing interfaces of topological-defect turbulence in the electroconvection of nematic liquid crystals. The interfaces exhibit self-affine roughening characterized by both spatial and temporal scaling laws of the Kardar-Parisi-Zhang theory in 1+1 dimensions. Moreover, we reveal that the distribution and the two-point correlation of the interface fluctuations are universal ones governed by the largest eigenvalue of random matrices. This provides quantitative experimental evidence of the universality prescribing detailed information of scale-invariant fluctuations.

Experimental realization of directed percolation criticality in turbulent liquid crystals

This is a comprehensive report on the phase transition between two turbulent states of electroconvection in nematic liquid crystals, which was recently found by the authors to be in the directed percolation (DP) universality class [K. A. Takeuchi, Phys. Rev. Lett. 99, 234503 (2007)]. We further investigate both static and dynamic critical behaviors of this phase transition, measuring a total of 12 critical exponents, 5 scaling functions, and 8 scaling relations, all in full agreement with those characterizing the DP class in 2+1 dimensions. Developing an experimental technique to create a seed of topological-defect turbulence by pulse laser, we confirm in particular the rapidity symmetry, which is a basic but nontrivial consequence of the field-theoretic approach to DP. This provides a clear experimental realization of this outstanding truly out-of-equilibrium universality class, dominating most phase transitions into an absorbing state.

Spatiotemporal synchronization of domain oscillations in the system of electroconvection in nematic liquid crystals

The dynamics of a nonstationary pseudo-hexagonal domain structure that appears during the electroconvection in nematic liquid crystals (NLCs) in a constant electric field has been studied using the optical diffraction techniques and the temporal Fourier analysis of the intensity of light transmitted through an NLC cell. The system evolution from an unperturbed state to a regime of developed domain oscillations is traced. It is established that, above the electrohydrodynamic instability threshold, the spatiotemporal synchronization of domain oscillations in a planar NLC layer takes place in the entire sample, which is manifested by the formation of a superlattice with the nodes at the sources of phase waves.

Noise Effects on Threshold of Electrohydrodynamic Convection in Nematic Liquid Crystals

New experimental aspects of multiplicative noise effects on the onset of ac-driven electroconvection in nematic liquid crystals are presented. In the superposition of a stochastic field with a deterministic one, the variation in the threshold voltage V c (of the deterministic one) was investigated as a function of the intensity ( V N ), cutoff frequency ( f c ), and correlation time (τ N ) of the stochastic noise. In particular, it is observed that the noise effects vanish for certain stochastic and deterministic conditions.