ABSTRACT
The responses of soft-mode turbulence, a kind of spatiotemporal chaos seen in electroconvection of a nematic liquid crystal, to alternating-current magnetic fields is investigated to uncover the dynamical properties of spatiotemporal chaos. The dynamical responses can be measured by an order parameter, M(p)(t), which indicates ordering in the convective roll pattern induced by the magnetic field. Determined by properties of the liquid crystal in a magnetic field, M(p)(t) oscillates in accordance with the square of the magnetic field. The relaxation time of the system was obtained by fitting the frequency dependence of the complex susceptibility for the pattern obtained from the oscillation of M(p)(t) to the Debye-type relaxation spectra. However, for the high-frequency regime, the susceptibility deviates from the spectra because slow and large fluctuations of M(p)(t) contribute to the oscillation. The properties of this type of fluctuation were investigated by introducing a dynamic ordering parameter defined as the period average of M(p)(t).
ABSTRACT
Modal relaxation dynamics has been observed experimentally to clarify statistical-physical properties of soft-mode turbulence, the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals. We found a dual structure, dynamical crossover associated with violation of time-reversal invariance, the corresponding time scales satisfying a dynamical scaling law. To specify the origin of the dual structure, the memory function due to nonthermal fluctuations has been defined by a projection-operator method and obtained numerically using experimental results. The results of the memory function suggest that the nonthermal fluctuations can be divided into Markov and non-Markov contributions; the latter is called the turbulent fluctuation (TF). Consequently, the relaxation dynamics is separated into three characteristic stages: bare-friction, early, and late stages. If the dissipation due to TFs dominates over that of the Markov contribution, the bare-friction stage contracts; the early and late stages then configure the dual structure. The memory effect due to TFs results in a time-reversible relaxation at the early stage, and the disappearance of the memory by turbulent mixing leads to a simple exponential relaxation at the late stage. Furthermore, the memory effect due to TFs is shown to originate from characteristic spatial coherency called the patch structure.
Subject(s)
Information Storage and Retrieval/methods , Liquid Crystals/chemistry , Models, Chemical , Models, Molecular , Models, Statistical , Computer SimulationABSTRACT
The autocorrelation function of pattern fluctuation is used to study soft-mode turbulence (SMT), a spatiotemporal chaos observed in homeotropic nematics. We show that relaxation near the electroconvection threshold deviates from the exponential. To describe this relaxation, we propose a compressed exponential appearing in dynamics of glass-forming liquids. Our findings suggest that coherent motion contributes to SMT dynamics. We also confirmed that characteristic time is inversely proportional to electroconvection's control parameter.
Subject(s)
Glass/chemistry , Liquid Crystals/chemistry , Models, Chemical , Models, Molecular , Phase Transition , Computer Simulation , Nonlinear DynamicsABSTRACT
Chaotic patterns in electroconvection of homeotropic nematics, soft-mode turbulence (SMT), and the related spatiotemporal chaos (STC) are discussed, and the quantitative definition of the patterns is considered. The order parameter S, obtained directly from the 2D spectra of the patterns, is introduced. The contribution of the Nambu-Goldstone mode and the increase in pattern regularity under the influence of an external magnetic field H are evaluated. We propose a schematic phase diagram of STC patterns based on the value of S.
ABSTRACT
We have found an unusual and unexpected link between micro- (nematic director) and macro- (velocity) fields in nematodynamics, which exhibits itself in extended defects of a new type. In particular, we have shown that black lines (BLs) observed in electroconvection of a homeotropically aligned nematic layer are simultaneously Bloch's domain walls for the director field and lines of zero velocity intersecting a roll pattern for the convection. A detailed experimental study revealing the fine structure of BLs and their point defects is presented.
