Jamming with Pins: How do different pin geometries affect jamming?

We simulate two-dimensional, zero temperature systems of soft disks with harmonic repulsive pair potentials. The pin lattices contain disks that employ the same potential, but are of negligible size. We study square, triangular, honeycomb, and random lattices. That is, it has been known for several years that the jamming threshold, φ_j, decreases with pin density, ρ. At low pin densities, all lattice geometries produce the same φ_j(ρ) which decreases linearly with ρ, but pin lattice geometry begins to matter as ρ increases further. At low densities, as expected, all lattices are equivalent with a linear dependence on ρ. At moderate densities, the square lattice supports jamming better than the random lattice; but interestingly, at higher densities the situation is reversed. We present data on φ_j parameterized by lattice constant and lattice density; and on structural features such as distributions of contacts and angular ordering of bonds between particles.