Control Parameter Dependence of Spatial Domain Structures in Soft-Mode Turbulence

Tamura, Koyo; Anugraha, Rinto; Matsuo, Ryohei; Hidaka, Yoshiki; Kai, Shoichi

doi:10.1143/jpsj.75.063801

Cited by 12 publications

(6 citation statements)

References 26 publications

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“…It is consequently noteworthy that the non-thermal fluctuation caused by the patch structure leads to non-exponential relaxation. This argument is supported by the fact that the average patch size increases with decreasing ε [22], which is consistent with the results shown in Fig. 2.…”

supporting

confidence: 91%

“…Several works have already pointed out similarity between chaotic and glassy dynamics qualitatively [16][17][18][19][20]; our study experimentally provides quantitative evidences for the similarity. SMT consists of randomly oriented roll domains and shows patch structures [21,22] which may be strongly related to GFL properties such as the dynamical heterogeneity. In this Letter, we discuss our results from these viewpoints.…”

mentioning

confidence: 99%

“…Does the cooperative effect exist in SMT? It has been also reported that, in SMT, there exist patch domains in which the roll direction q(r)/|q(r)| is unique [21,22]. Since each patch domain is regarded as being stable, the domain should keep its size, and then the rolls in a patch should move cooperatively.…”

mentioning

confidence: 99%

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Glassy dynamics in relaxation of soft-mode turbulence

Nugroho¹,

Narumi²,

Hidaka³

et al. 2012

Phys. Rev. E

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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.

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confidence: 91%

mentioning

confidence: 99%

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Glassy dynamics in relaxation of soft-mode turbulence

Nugroho¹,

Narumi²,

Hidaka³

et al. 2012

Phys. Rev. E

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“…The interaction between the convective and Goldstone modes are different between oblique and normal rolls [45,46]; the convective wave vector in SMT tend to become parallel to the C-director in the normal roll and oblique in the oblique roll. The patch structure is observed only in the oblique rolls [13,14].…”

Section: Soft-mode Turbulencementioning

confidence: 95%

Compressed exponential relaxation as superposition of dual structure in pattern dynamics of nematic liquid crystals

Narumi

Nugroho

Yoshitani

et al. 2013

AIP Conference Proceedings

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Soft-mode turbulence (SMT) is the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals, where non-thermal fluctuations are induced by nonlinear coupling between the NambuGoldstone and convective modes. The net and modal relaxations of the disorder pattern dynamics in SMT have been studied to construct the statistical physics of nonlinear nonequilibrium systems. The net relaxation dynamics is well-described by a compressed exponential function and the modal one satisfies a dual structure, dynamic crossover accompanied by a breaking of time-reversal invariance. Because the net relaxation is described by a weighted mean of the modal ones with respect to the wave number, the compressed-exponential behavior emerges as a superposition of the dual structure. Here, we present experimental results of the power spectra to discuss the compressed-exponential behavior and the dual structure from a viewpoint of the harmonic analysis. We also derive a relationship of the power spectra from the evolution equation of the modal autocorrelation function. The formula will be helpful to study non-thermal fluctuations in experiments such as the scattering methods.

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“…A characteristic length for these cooperative regions increases as the glass transition point is approached. In SMT, on the other hand, patch domains exist in which convective rolls align in a unique orientation [17][18][19]. The characteristic size ξ of a patch domain is several times longer than the typical size of convective rolls and decreases with the distance from SMT onset; ξ ∼ ε −1/2 with control parameter ε.…”

Section: Introductionmentioning

confidence: 99%

Memory function of turbulent fluctuations in soft-mode turbulence

et al. 2013

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Modal relaxation dynamics has been observed experimentally to clarify statistical-physical properties of softmode 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 non-thermal fluctuations has been defined by a projection-operator method and obtained numerically using experimental results. The results of the memory function suggest that the non-thermal 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 the 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.

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Control Parameter Dependence of Spatial Domain Structures in Soft-Mode Turbulence

Cited by 12 publications

References 26 publications

Glassy dynamics in relaxation of soft-mode turbulence

Glassy dynamics in relaxation of soft-mode turbulence

Compressed exponential relaxation as superposition of dual structure in pattern dynamics of nematic liquid crystals

Memory function of turbulent fluctuations in soft-mode turbulence

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