Nonlinear Transport and Anomalous Brownian Motion in Soft-Mode Turbulence

Amplitude Equation of Higher-Dimensional Nikolaevskii Turbulence

“…9), 10) This equation has been applied to the study of spatio-temporal complexity observed experimentally in association with the instability of the homeotropic alignment of directors in electrohydrodynamic convection in nematic liquid crystals. 11) - 14) Furthermore, results suggesting the existence of a similar type of onset of irregular motion were recently obtained for a three-variable reaction diffusion system. 15) Very recently, we derived the equation of motion 16) φ(r, t) = −∇ 2 − ∇ 2 + k 2 0 2 φ + (∇φ) 2 ≡ L(−∇ 2 )φ + (∇φ) 2 , (1 .…”

Crossover between Anomalous Superdiffusion and Normal Diffusion in Oscillating Convection Flows

“…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.…”

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

“…4, the diffusion coefficient of mode F for each ε is well fitted using Eq. (4). The values of the fitting parameters a, , and α are summarized in Table I.…”

“…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].…”

“…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.…”