Weakly active particles near boundaries: towards solving the boundary value problem for active particles.

Boundaries play an important role in shaping the behavior of a system of active particles. By considering the limit of noninteracting weakly-active Ornstein-Uhlenbeck particles, for which passive Brownian diffusion cannot be neglected and activity can be treated perturbatively, we develop a relatively simple expansion for the density of active particles in powers of the Peclet number and in terms of Hermite polynomials. This approach allows us to cleanly formulate boundary conditions and study how active particles behave near boundaries in several different geometries: confinement by a single wall or between two walls in 1D, confinement in a circular or wedge-shaped region in 2D, motion near a corrugated or rough boundary, and absorption onto a sphere. In this talk, we focus particularly on weakly active particles confined on a line and in a wedge-shaped region, and absorbing onto a sphere. We discuss how quantites such as the pressure and flow of active particles changes as we gradually increase the activity away from a passive system.