  Our recent work identifies material surfaces in incompressible flows that
extremize the transport of an arbitrary, weakly diffusive scalar field relative
to neighboring surfaces. Such barriers and enhancers of transport can be
located directly from the deterministic component of the velocity field without
diffusive or stochastic simulations. Here we extend these results to
compressible flows and to diffusive concentration fields affected by sources or
sinks, as well as by spontaneous decay. We construct diffusive transport
extremizers with and without constraining them on a specific initial
concentration distribution. For two-dimensional flows, we obtain explicit
differential equations and a diagnostic scalar field that identify the most
observable extremizers with pointwise uniform transport density. We illustrate
our results by uncovering diffusion barriers and enhancers in analytic,
numerical, and observational velocity fields.
