A motile rod in an active nematic medium: caging, orientational trapping, and anomalous diffusion.

We study the dynamical and statistical properties of a motile polar rod embedded in a vibrated granular medium composed of fore-aft symmetric rods using particle-based numerical simulations. Our study reveals phase-dependent memory effects and transport behaviors of the polar rod governed by the structural phase of the medium. In the isotropic phase, the rod behaves as an active Brownian particle, experiencing a noisy environment with increasing medium concentration that leads to short-lived directional memory, resulting in enhanced rotational diffusion and reduced translational diffusivity. In the nematic phase-determined by the medium's concentration and the polar rod's intrinsic rotational noise-the rod exhibits two distinct states: a rotationally trapped state, in which its orientation is locked along the nematic director, and a rotationally free state, in which it explores all orientations despite a tendency to align with the director. At high concentrations, the medium forms periodic layers in which the rods are slightly tilted in opposite directions across adjacent layers relative to the nematic director, as reported by Sharma et al. [Soft Matter, 2024, 20, 6608-6617]. In this regime, the motile rod is effectively caged in the direction perpendicular to the nematic alignment. We further study the diffusive behavior of the polar rod in both states, demonstrating that the phase of the medium strongly influences its diffusion dynamics and the MSD exponent values, revealing a wide range of behavior from normal to superdiffusive dynamics.