  We consider the effect of geometric confinement on the steady-state
properties of a one-dimensional active suspension subject to thermal noise. The
random active force is modeled by an Ornstein-Uhlenbeck process and the system
is studied both numerically, by integrating the Langevin governing equations,
and analytically by solving the associated Fokker-Planck equation under
suitable approximations. The comparison between the two approaches displays a
fairly good agreement and in particular, we show that the Fokker-Planck
approach can predict the structure of the system both in the wall region and in
the bulk-like region where the surface forces are negligible. The simultaneous
presence of thermal noise and active forces determines the formation of a
layer, extending from the walls towards the bulk, where the system exhibits
polar order. We relate the presence of such ordering to the mechanical pressure
exerted on the container's walls and show how it depends on the separation of
the boundaries and determines a Casimir-like attractive force mediated by the
active suspension.
