Persistent global power fluctuations near a dynamic transition in electroconvection

Relaxation with long-period oscillation in defect turbulence of planar nematic liquid crystals

Through experiments, we studied defect turbulence, a type of spatiotemporal chaos in planar systems of nematic liquid crystals, to clarify the chaotic advection of weak turbulence. In planar systems of large aspect ratio, structural relaxation, which is characterized by the dynamic structure factor, exhibits a long-period oscillation that is described well by a combination of a simple exponential relaxation and underdamped oscillation. The simple relaxation arises as a result of the roll modulation while the damped oscillation is manifest in the repetitive gliding of defect pairs in a local area. Each relaxation is derived analytically by the projection operator method that separates turbulent transport into a macroscopic contribution and fluctuations. The analysis proposes that the two relaxations are not correlated. The nonthermal fluctuations of defect turbulence are consequently separated into two independent Markov processes. Our approach sheds light on diversity and universality from a unified viewpoint for weak turbulence.

Event-driven power-law relaxation in weak turbulence

We characterize the spectral properties of weak turbulence in a liquid crystal sample driven by an external electric field, as a function of the applied voltage, and we find a 1/f noise spectrum S(f) proportional, variant1/f;{eta} within the whole range 0<eta<2. We theoretically explore the hypothesis that the system complexity is driven by non-Poisson events resetting the system through creation and annihilation of coherent structures, retaining no memory of previous history (crucial events). We study the time asymptotic regime by means of the density psi(tau) of the time distances between two crucial events, yielding eta=3-micro, where micro is defined through the long-time form psi(tau) proportional, variant1/tau;{micro}, with 1<micro<3. The system regression to equilibrium after an abrupt voltage change experimentally confirms the theory, proving violations of the ordinary linear response theory for both eta>1 and eta<1.

Test of steady-state fluctuation theorem in turbulent Rayleigh-Bénard convection

The local entropy production rate sigma (r,t) in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in an aspect-ratio-one cell filled with water. The statistical properties of the time-averaged sigma (r,t) are analyzed and the results are compared with the predictions of the steady-state fluctuation theorem (SSFT) of Gallavotti and Cohen. The experiment reveals that the SSFT can indeed be extended to the local variables, but further development is needed in order to incorporate the common dynamic complexities of far-from-equilibrium systems into the theory.

Conductive and dielectric defects, and anisotropic and isotropic turbulence in liquid crystals: Electric power fluctuation measurements

Fluctuations of the injected electric power during electroconvection (EHC) of liquid crystals are reported in both the conductive and the dielectric regime of convection. The amplitude and the frequency of the fluctuations, as well as the probability density functions have been compared in these two regimes and substantial differences have been found both in defect turbulence of EHC and at the DSM1-->DSM2 transition.

Distribution of injected power fluctuations in electroconvection

We report on the distribution spectra of the fluctations in the amount of power injected into a liquid crystal undergoing electroconvective flow. The probability distribution functions (PDFs) of the fluc-tuations as well as the magnitude of the fluctuations have been determined in a wide range of imposed stress both for unconfined and confined flow geometries. These spectra are compared to those found in other systems held far from equilibrium, and find that in certain conditions we obtain the universal PDF form reported by Phys. Rev. Lett. 84, 3744 (2000)]. Moreover, the PDF approaches this universal form via an interesting mechanism whereby the distribution's negative tail evolves towards form in a different manner than the positive tail.