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We use numerical minimization of a model free energy functional to study theeffects of columnar pinning centers on the structure and thermodynamics of asystem of pancake vortices in the mixed phase of highly anisotropic layeredsuperconductors. The magnetic field and the columnar pins are assumed to beperpendicular to the layers. Our methods allow us to study in detail thedensity distribution of vortices in real space. We present results for thedependence of the average number of vortices trapped at a pinning center ontemperature and pinning strength, and for the effective interaction betweennearby pinned vortices arising from short-range correlations in the vortexliquid. For a commensurate, periodic array of pinning centers, we find a lineof first order vortex lattice melting transitions in the temperature $T$ vs.pin concentration $c$ plane, which terminates at an experimentally accessiblecritical point as $c$ is increased. Beyond this point, the transition isreplaced by a crossover. Our results should also apply, with little change, tothin-film superconductors with strong point pinning.Comment: 15 pages including 17 Figures. Higher resolution gray scale plots  available from author

Vortices in layered superconductors with columnar pins: A density-functional study