A coordinated theoretical and observational program to study the relation between hydrodynamic and particle acceleration processes in extended radio sources will be carried out. This program is a scientific and technical extension of past research which has contributed significantly to the empirical and physical understanding of compact and extended radio sources. A new class of numerical simulations will be carried out, in which results of microphysics calculations of particle acceleration in shocks and turbulence will be incorporated, for the first time, into state-of-the-art hydrodynamical simulations. The goals of the simulations include a better understanding of particle acceleration in astrophysical contexts as well as improved insight into the relationships between radio source surface brightness and the internal dynamics of the sources. The observational program will study the dependence of synchrotron emissivity on the inferred pressures in extended radio source shocks, and will let scientists search for and examine other features expected from the simulations. A unique view of the dynamics/emissivity relation will be produced through observations of the evolution of knots in the Cassiopeia A supernova remnant.
