Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls

Abstract

The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence.

On the Fractional Diffusion-Advection Equation for Fluids and Plasmas

“…A fundamental goal of fluid and plasma physics is to understand transport properties, given that transport governs, for example, the dispersion of pollutants in the atmosphere and the oceans, the confinement of plasmas in laboratory devices, and the acceleration and propagation of energetic particles in astrophysics [1][2][3]. Non-diffusive anomalous transport, that is, different from standard Brownian diffusion, is observed in a large variety of physical systems [4][5][6], including both laboratory and astrophysical plasmas [1,3,[7][8][9][10][11][12][13].…”

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems

“…From (d), during the short time regime, the RMSD exponents of free and a s = 3.5 are very close to 1.25, meaning that in this regime, the system dynamics is super-diffusive but not ballistic, a signature of LC behavior. 63,64 However, in systems with a s = 1.5, 2.0 and 2.5, the RMSD exponents are close to 1, meaning that systems are diffusive in radial directions within the short time regime. But, still the substrate-induced pinned hexatic ( a s = 1.5) and 2D-solid ( a s = 2.0) states are dynamically different as XMSD exponent is <1 and YMSD exponent is >1.…”

Editorial for Special Issue “Multiscale Turbulent Transport”

“…Yamanaka et al (2018) [1] focused on weak defect turbulence in the electroconvection of nematic liquid crystals, from the experimental point of view. Increasing the coarse-graining time, the authors showed that the type of diffusion changes from superdiffusion first to subdiffusion and then to the standard diffusive behaviour, a result reflecting the coexistence of local order and global disorder in the analysis of convective rolls.…”