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Swim pressure on walls with curves and corners

The concept of swim pressure quantifies the average force exerted by microswimmers on confining walls in non-equilibrium. Here we explore how the swim pressure depends on the wall curvature and on the presence of sharp corners in the wall. For active Brownian particles at high dilution, we present a coherent framework which describes the force and torque on passive particles of arbitrary shape, in the limit of large particles compared to the persistence length of the swimmer trajectories. The resulting forces can be used to derive, for example, the activity-induced depletion interaction between two disks, as well as to optimize the shape of a tracer particle for high swimming velocity. Our predictions are verifiable in experiments on passive obstacles exposed to a bath of bacteria or artificial microswimmers.