  We derive a mobility tensor for many cylindrical objects embedded in a
viscous sheet. This tensor guarantees a positive dissipation rate for any
configuration of particles and forces, analogously to the Rotne-Prager-Yamakawa
tensor for spherical particles in a three-dimensional viscous fluid. We test
our result for a ring of radially driven particles, demonstrating the
positive-definite property at all particle densities. The derived tensor can be
utilized in Brownian Dynamics simulations with hydrodynamic interactions for
such systems as proteins in biomembranes and inclusions in free-standing liquid
films.
