Abstract

We present an analytical framework for evolving the dynamics of active rods under any periodic external potential, including confining channels and arrays of harmonic traps. As a proof of concept, we analyze the structure and dispersion of self-propelled rods under a soft, periodic one-dimensional (1D) confinement potential and under a two-dimensional (2D) periodic radial harmonic trap. While passive rods and polymers nematically order under 1D confinement, their diffusive transport along the director is limited by thermal diffusion. In contrast, self-propelled rods can generate large convective fluxes when combined with nematic ordering, producing a strong dispersion along the director. Combining theory and simulation, we demonstrate that nematic alignment and self-propulsion generates an exponential enhancement in active diffusivity along the director, in contrast to passive rods that experience at most a 2-fold increase.