Anomalous diffusion and Lévy distribution of particle velocity in soft-mode turbulence in electroconvection

We study the complex behavior in soft-mode turbulence (SMT), a recently discovered type of spatiotemporal chaos observed in electrohydrodynamic instability (EHD) of a nematic liquid crystal with homeotropic alignment. A particle, small compared to the characteristic length of the macroscopic flow, injected in SMT travels with random velocity such as an active Brownian motion. Tracking the particle trajectory induces changes in the flow velocity as a function of space and time (the Lagrange picture). The mean amplitude of the velocity is linearly proportional to the control parameter , normalized voltage in EHD. The probability density distribution of the particle velocity changes from Lévy for small to Gaussian distribution for large through intermediate distributions. The different regimes of anomalous diffusions are also observed. The stochastic properties of SMT are discussed based on these results.