  The role of fixed degrees of freedom in soft/granular matter systems has
broad applicability and theoretical interest. Here we address questions of the
geometrical role that a scaffolding of fixed particles plays in tuning the
threshold volume fraction and force network in the vicinity of jamming. Our 2d
simulated system consists of soft particles and fixed "pins", both of which
harmonically repel overlaps. On one hand, we find that many of the critical
scalings associated with jamming in the absence of pins continue to hold in the
presence of even dense pin latices. On the other hand, the presence of pins
lowers the jamming threshold, in a universal way at low pin densities and a
geometry-dependent manner at high pin densities, producing packings with lower
densities and fewer contacts between particles. The onset of strong lattice
dependence coincides with the development of bond-orientational order.
Furthermore, the presence of pins dramatically modifies the network of forces,
with both unusually weak and unusually strong forces becoming more abundant.
The spatial organization of this force network depends on pin geometry and is
described in detail. Using persistent homology we demonstrate that pins modify
the topology of the network. Finally, we observe clear signatures of this
developing bond-orientational order and broad force distribution in the elastic
moduli which characterize the linear response of these packings to strain.
