Following fluctuating signs: anomalous active superdiffusion of swimmers in anisotropic media

TL;DR

This paper uncovers anomalous superdiffusive behavior of active particles in anisotropic nematic media, showing ballistic motion along the director and superdiffusive transverse motion with a specific logarithmic scaling, supported by theory and simulations.

Contribution

It introduces a theoretical framework predicting superdiffusive transverse motion of active particles in nematic media, validated by numerical simulations and applicable to various self-propelled systems.

Findings

Translational motion parallel to the nematic director is ballistic.

Transverse motion exhibits superdiffusion with a t ln t scaling.

The behavior is universal for dilute active particles in nematic backgrounds.

Abstract

Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic, nematic background. Whilst the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is super-diffusive, with an anomalous scaling $\propto t \ln t$ of the mean squared displacement with time $t$. This behavior is predicted by an analytical theory that we present here, and is corroborated by numerical simulation of active particle diffusion in a simple lattice model for a nematic liquid crystal. It is universal for any collection of self-propelled elements (e.g., bacteria or active rods) moving in a nematic background, provided only that the swimmers are sufficiently dilute that their interactions with each other can be neglected, and that they do not perform "hairpin" turns.