External Noise Effect on the Onset of Williams Domain in Nematic Liquid Crystals

Kawakubo, Tatsuyuki; Yanagita, Akihiro; Kabashima, Shigeharu

doi:10.1143/jpsj.50.1451

Cited by 86 publications

(59 citation statements)

References 9 publications

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“…in the case of containers with a moderate aspect ratio, the surface deformation is described by a single standing wave mode oscillating at half the driving frequency. For fluids of small viscosity, the amplitude of this mode is governed by an equation analogous to the one derived for the parametric oscillator (9). The main difference between the two systems is that the Faraday experiment also involve many stable modes that may play a role in the presence of noise.…”

Section: Parametric Amplification Of Surface Wavesmentioning

confidence: 99%

“…Previous studies involve electronic oscillators [6], spin waves in ferrites and antiferromagnets [7,8] and electroconvection in nematic liquid crystals [9,10], but only the effect of noise on supercritical bifurcations has been considered so far. Only recently, experiments on the effect of noise on parametrically driven surface waves have been performed in the case of a subcritical bifurcation.…”

Section: Introductionmentioning

confidence: 99%

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Effect of multiplicative noise on parametric instabilities

Berthet¹,

Petrossian

Residori

et al. 2003

Physica D: Nonlinear Phenomena

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We report a study on the effect of external multiplicative noise on parametric instabilities using two different experimental systems: an electronic RLC circuit, parametrically pumped with a voltage-variable capacitor, and surface waves generated by vertically vibrating a layer of fluid (the Faraday instability). Both systems are forced by the superposition of a sinusoidal and a noisy component. We study the statistical properties of the response of both systems to noisy parametric forcing and compare them with theoretical predictions. When the detuning from parametric resonance is such that the bifurcation in the absence of noise is supercritical, both systems behave in the same way under the influence of noise. We find that the effect of noise is twofold: on one hand, it triggers the instability before its deterministic onset under the form of oscillatory bursts; on the other hand, it inhibits the nonlinearly saturated oscillatory response above the deterministic onset. When the detuning is such that the bifurcation is subcritical, we find that the two systems behave differently. In the case of the electronic oscillator, noise mostly triggers random transitions between the two states of the bistable region that exists in the absence of noise, whereas in the surface wave experiment new states are created by noise and the bistable region is strongly enlarged.

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Section: Parametric Amplification Of Surface Wavesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of multiplicative noise on parametric instabilities

Berthet¹,

Petrossian

Residori

et al. 2003

Physica D: Nonlinear Phenomena

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“…It is well known that a linear oscillator submitted to parametric noise can be unstable even if damping is taken into account [10,15]. This noise-induced energetic instability has been observed in diverse experimental contexts such as electronic oscillators [16,17], nematic liquid crystals [18] and surface waves (Faraday instability) [19]. In engineering fields this instability plays a crucial role in the study of the dynamic response of flexible structures to random environmental loading such as the wave-induced motion of off-shore structures or the vibration of tall buildings in a turbulent wind [20].…”

Section: Introductionmentioning

confidence: 99%

Anomalous diffusion in nonlinear oscillators with multiplicative noise

Mallick

Marcq

2002

Phys. Rev. E

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The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest, such as the oscillator's mechanical energy, root-mean-square position and velocity, grow algebraically with time. The scaling exponents and associated generalized diffusion constants are calculated when the oscillator's potential energy grows as a power of its position: U(x) ∼ x 2n for |x| → ∞. Correlated noise yields anomalous diffusion exponents equal to half the value found for white noise.

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“…Stochastic resonance [3], multiplicative stochastic processes [4], and noise-induced pattern formations [2] are well-known nontrivial noise phenomena. In this study, we address noise-induced threshold shifts and pattern change in ac-driven electrohydrodynamic convections (EHC) in nematic liquid crystals (NLCs) [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…(or correlation time TN) [4][5][6][7][8][9]. By considering an expanded CH mechanism in external multiplicative noise [5,7,8] stabilization effects due to the noise-driven random oscillation against the periodic ac-based CH instability. Recently, we noticed that if fc becomes lower than the critical value fc ., the noise plays a role in destabilization, which facilitates the CH instability.…”

Section: Introductionmentioning

confidence: 99%