New Scenario for Transition to Turbulence?

Tribelsky, Michael I.; Tsuboi, Kazuhiro

doi:10.1103/physrevlett.76.1631

Cited by 81 publications

(99 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The Lifshitz equation, that reduces to the generalized Swift-Hohenberg equation for η = d = c = 0, has already been used to describe the transition from smectic to helicoidal phase in liquid crystals [32] and the pulse dynamics in reaction diffusion systems [33]. When one neglects the cubic and the nonlinear diffusion terms (d = 0), it reduces to the Nikolaevskii equation that describes longitudinal seismic waves [34].…”

Section: Theoretical Descriptionmentioning

confidence: 99%

Bouncing localized structures in a liquid-crystal light-valve experiment

Clerc

Petrossian²,

Residori³

2005

Phys. Rev. E

View full text Add to dashboard Cite

Experimental evidence of bouncing localized structures in a nonlinear optical system is reported. Oscillations in the position of the localized states are described by a consistent amplitude equation, which we call the Lifshitz normal form equation, in analogy with phase transitions. Localized structures are shown to arise close to the Lifshtiz point, where non-variational terms drive the dynamics into complex and oscillatory behaviors. [11,12,13] and cavity solitons in lasers [14]. Localized states are patterns which extend only over a small portion of a spatially extended and homogeneous system [15]. Different mechanisms leading to stable localization have been proposed [16]. Among these, two main classes of localized structures have to be distinguished, namely those localized structures arising as solutions of a quintic Swift-Hohenberg like equation [16] and those that are stabilized by nonvariational terms in the subcritical Ginzburg-Landau equation [17]. The main difference between the two cases is that the first-type localized structures have a characteristic size which is fixed by the pinning mechanism over the underlying pattern or by spatial damped oscillations between homogenous states [16,18], whereas the second-type ones have no intrinsic spatial length, their size being selected by non-variational effects and going to infinity when dissipation goes to zero. In both cases, non-variational effects may lead to dynamical behaviors of localized structures [19]. Variational models based on a generalized Swift-Hohenberg equation have been proposed to describe the appearance of localized structures in nonlinear optics [20]. However, a generalization including non-variational terms is generically expected to apply even in optics, as happens, for instance, in semiconductor laser instabilities [21], giving rise to dynamical behaviors of localized structures, such as propagation and oscillations of their positions [22]. PacsWe report here an experimental evidence of localized structures dynamics in a Liquid-Crystal-Light-Valve (LCLV) with optical feedback. It is already known that, in the simultaneous presence of bistability and pattern forming diffractive feedback, the LCLV system shows localized structures [12,23,24,25]. Recently, rotation of localized structures along concentric rings have been reported in the case of a rotation angle introduced in the feedback loop [26]. Here, we fix a zero rotation angle and we show a new dynamical behavior, the bouncing of two adjacent localized structures, that is not related to imposed boundary conditions but is instead a direct consequence of the non-variational character of the system under study. Theoretically, we show that the LCLV system has several branches of bistability connecting an homogeneous state to a patterned one and we derive an amplitude equation accounting for the appearance of localized structures. This is a one-dimensional model, that we call the Lifshitz normal form equation [22], characterizing the dynamics of localized structures close to each po...

show abstract

Section: Theoretical Descriptionmentioning

confidence: 99%

Bouncing localized structures in a liquid-crystal light-valve experiment

Clerc

Petrossian²,

Residori³

2005

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The directors n tilt in an arbitrary direction with respect to the z-axis above V F , accompanied by spontaneous violation of the rotational symmetry. The projection of the director onto the x-y plane, called C-director, can rotate on the x-y plane without requiring additional energy, i.e., C-director behaves as the Nambu-Goldstone mode [42][43][44]. With further increasing V , the electrohydrodynamic convection occurs at the electroconvective threshold voltage V c .…”

Section: Soft-mode Turbulencementioning

confidence: 99%

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

Narumi

Nugroho

Yoshitani

et al. 2013

AIP Conference Proceedings

View full text Add to dashboard Cite

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.

show abstract

“…The initial focus within the equation was on the formation and stability of patterns such as stationary rolls, which emerge from an instability in a spatially uniform state [6]- [9]. Further attention was given to more complex dynamics, especially chaos [3,10]. Generally, the Nikolaevskiy equation includes two groups of terms-the dispersion terms and dissipation/excitation terms, with the latter group being responsible for the growth or decay of the patterns.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stability in seismic waves

Ali

Strunin

2018

ANZIAMJ

View full text Add to dashboard Cite

We analyse a passive system featuring a neutrally stable shortwavelength mode. The system is modelled by the Nikolaevskiy equation relevant to elastic waves, reaction-diffusion systems and convection. After quickly falling onto a centre manifold, the system then exhibits slow decay. Using the centre manifold technique, we deduce that the decay law is the inverse square root of time. The result is confirmed by direct computations of the system.

show abstract

New Scenario for Transition to Turbulence?

Cited by 81 publications

References 8 publications

Bouncing localized structures in a liquid-crystal light-valve experiment

Bouncing localized structures in a liquid-crystal light-valve experiment

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

Nonlinear stability in seismic waves

Contact Info

Product

Resources

About