title: Fractional Brownian motion run with a multi-scaling clock mimics diffusion of spherical colloids in microstructural fluids.
abstract: The collective molecular reorientations within a nematic liquid crystal fluid bathing a spherical colloid cause the colloid to diffuse anomalously on a short time scale (i.e., as a non-Brownian particle). The deformations and fluctuations of long-range orientational order in the liquid crystal profoundly influence the transient diffusive regimes. Here we show that an anisotropic fractional Brownian process run with a nonlinear multiscaling clock effectively mimics this collective and transient phenomenon. This novel process has memory, Gaussian increments, and a multiscale mean square displacement that can be chosen independently from the fractal dimension of a particle trajectory. The process is capable of modeling multiscale sub-, super-, or classical diffusion. The finite-size Lyapunov exponents for this multiscaling process are defined for future analysis of related mixing processes.
authors.affiliation: Department of Earth, Atmospheric and Planetary Sciences, Purdue University , 550 Stadium Mall Drive, West Lafayette, Indiana 47907, United States.
authors.forename: Moongyu
authors.initials: M
authors.lastname: Park
authors.forename: John Howard
authors.initials: JH
authors.lastname: Cushman
authors.forename: Dan
authors.initials: D
authors.lastname: O'Malley