Lattice-based random jammed configurations for hard particles

Jammed packings that arise from particle removals from the close-packed triangular lattice (disks), and from the face-centered and body-centered cubic lattices (spheres), were examined. Three categories of jammed packings were distinguished: locally jammed, collectively jammed, and strictly jammed. Upper limits on the vacancy concentrations for each category were identified, as well as some of those vacancy-cluster configurations that would violate the jamming classification. Using the notion of particle-environment attrition factors, approximate local jamming enumeration functions of vacancy concentration for the three lattices were derived, and in each case a single enumeration (entropy) maximum appeared as a function of that vacancy concentration.