  We consider the trajectories of particles diffusing between two infinite
baths of fixed concentrations connected by a channel, e.g. a protein channel of
a biological membrane. The steady state influx and efflux of Langevin
trajectories at the boundaries of a finite volume containing the channel and
parts of the two baths is replicated by termination of outgoing trajectories
and injection according to a residual phase space density. We present a
simulation scheme that maintains averaged fixed concentrations without creating
spurious boundary layers, consistent with the assumed physics.
