Memory function of turbulent fluctuations in soft-mode turbulence

Narumi, Takayuki; Yoshitani, Junichi; Suzuki, Masaru; Hidaka, Yoshiki; Nugroho, Fahrudin; Nagaya, Takashi; Kai, Shoichi

doi:10.1103/physreve.87.012505

Cited by 10 publications

(17 citation statements)

References 36 publications

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“…Furthermore, we have proved that the memory effect due to the turbulent fluctuations originates from the patch structure [29].…”

Section: Introductionmentioning

confidence: 95%

“…Mori and Okamura have numerically and analytically discovered a dual structure in the KS equation [28]; the relaxation dynamics is dominated by the deterministic and stochastic orbits in the short-time and long-time region, respectively. 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: 96%

“…The numerically-obtained memory function Γ ′ k (τ ) has a sharp peak at τ = 0, implying that the nonthermal fluctuations in SMT can be divided into Markov and non-Markov parts [29], i.e.,…”

Section: B Memory Functionmentioning

confidence: 99%

“…We have proposed an approach by the memory function derived in the projection-operator formalism [29]. The evolution equation for the modal autocorrelation function is represented as…”

Section: B Memory Functionmentioning

confidence: 99%

“…II, the net and modal autocorrelation functions are defined and the memory function is reviewed according to Ref. [29]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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“…Furthermore, we have proved that the memory effect due to the turbulent fluctuations originates from the patch structure [29].…”

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 96%

Section: B Memory Functionmentioning

confidence: 99%

“…We have proposed an approach by the memory function derived in the projection-operator formalism [29]. The evolution equation for the modal autocorrelation function is represented as…”

Section: B Memory Functionmentioning

confidence: 99%

“…II, the net and modal autocorrelation functions are defined and the memory function is reviewed according to Ref. [29]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Transient power dynamics in nematic electroconvection

Peel,

Daum,

Cerbus

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We have observed the transient dynamics in nematic electroconvection during a sudden change in the driving voltage. The steady state dynamics of nematic electroconvection during a constant driving voltage are well characterized examples of spatiotemporal chaos, and thus are useful for the study of chaotic transients. For a set of starting conditions, we were able to show that the system can enter a long-lived transient state with a larger power dissipation rate. This transient state decays through the skew varicose instabilities into steady state defect turbulence. We observed the onset of both Eckhaus and skew varicose instabilities, interpret this transition in the framework of dynamical crisis, and quantify the transition through the evolution of the information entropy in the images as well as the power dissipated by the sample. We identify this long-lived but transient state as originating from the structure of the convective rolls in the initial state and hypothesize that the exploitation of transient states such as these may occur in natural systems and could be leveraged for industrial processing.

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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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Memory function of turbulent fluctuations in soft-mode turbulence

Cited by 10 publications

References 36 publications

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

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

Transient power dynamics in nematic electroconvection

Glassy dynamics in relaxation of soft-mode turbulence

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