Anomalous diffusion and Lévy distribution of particle velocity in soft-mode turbulence in electroconvection

Tamura, Koyo; Hidaka, Yoshiki; Yusuf, Yusril; Kai, Shoichi

doi:10.1016/s0378-4371(02)00494-6

Cited by 26 publications

(20 citation statements)

References 18 publications

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“…Recently, Tamura et al 14), 15) tracked the trajectory of a particle injected into a two-dimensional thin layer of nematic liquid crystal exhibiting soft-mode turbulence. 16) They observed that diffusive motion occurs in two dimensions, and the MSD displays crossover between anomalous superdiffusion and normal diffusion.…”

Section: §1 Introductionmentioning

confidence: 99%

Crossover between Anomalous Superdiffusion and Normal Diffusion in Oscillating Convection Flows

Ito

Miyazaki

2003

Progress of Theoretical Physics

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Section: §1 Introductionmentioning

confidence: 99%

Crossover between Anomalous Superdiffusion and Normal Diffusion in Oscillating Convection Flows

Ito

Miyazaki

2003

Progress of Theoretical Physics

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“…We experimentally found the dual structure of the modal autocorrelation in SMT and have theoretically revealed the mechanisms of the dual structure [29]. It has been reported that the spatiotemporal disorder in SMT generates non-thermal fluctuations [12,30] by which a nonMarkovian (i.e., memory) effect is expected to play a significant role in the relaxation dynamics.…”

Section: Introductionmentioning

confidence: 76%

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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“…The random motion driven by nonthermal fluctuations or chaotic flows [1][2][3][4][5][6] has been investigated in the context of nonlinear physics and statistical mechanics far from equilibrium. Among these phenomena, motion dynamics driven by soft-mode turbulence (SMT) in the electroconvection of a nematic liquid crystal is interesting because of the existence of hierarchical structures such as locally aligned convective rolls and a globally disordered structure [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Among these phenomena, motion dynamics driven by soft-mode turbulence (SMT) in the electroconvection of a nematic liquid crystal is interesting because of the existence of hierarchical structures such as locally aligned convective rolls and a globally disordered structure [7,8]. Previous studies discussed the statistical-mechanical properties of the Brownianlike motion in SMT, such as anomalous behavior in the short time regime [4], the non-Gaussian distribution of velocity [5], and the application of the fluctuation theorem (FT) [6]. In these articles, although the asymptotic behavior of the finite-time diffusion coefficient was qualitatively associated with the local structure of SMT, the quantitative relation is still ambiguous.…”

Section: Introductionmentioning

confidence: 99%

Duality of diffusion dynamics in particle motion in soft-mode turbulence

et al. 2013

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Nonthermal Brownian motion is investigated experimentally by injecting a particle into soft-mode turbulence (SMT), in the electroconvection of a nematic liquid crystal. It is clarified that the particle motion can be classified into two phases: fast motion, where particles move with the local convective flow, and slow motion, where they are carried by global slow pattern dynamics. We propose a simplified model to clarify the mechanism of the short-time and asymptotic behavior of diffusion. In our model, the correlation time is estimated as a function of a control parameter ɛ. The scaling of the SMT pattern correlation time, τ(d)∼ɛ(-1), is estimated from the particle dynamics, which is consistent with a previous report observed from the Eulerian viewpoint. The origin of the non-Gaussian distribution of the displacement in the short-time regime is also discussed and an analytical curve is introduced that quantitatively agrees with the experimental data. Our results clearly illustrate the characteristics of diffusive motion in SMT, which are considerably different from the conventional Brownian motion.

show abstract

Anomalous diffusion and Lévy distribution of particle velocity in soft-mode turbulence in electroconvection

Cited by 26 publications

References 18 publications

Crossover between Anomalous Superdiffusion and Normal Diffusion in Oscillating Convection Flows

Crossover between Anomalous Superdiffusion and Normal Diffusion in Oscillating Convection Flows

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

Duality of diffusion dynamics in particle motion in soft-mode turbulence

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