  The jamming transition characterizes athermal systems of particles
interacting via finite range repulsive potentials, and occurs on increasing the
density when particles cannot avoid making contacts with those of their first
coordination shell. We have recently shown [M. Pica Ciamarra and P. Sollich,
arXiv:1209.3334] that the same systems are also characterized by a series of
jamming crossovers. These occur at higher volume fractions as particles are
forced to make contact with those of subsequent coordination shells. At finite
temperature, the crossovers give rise to dynamic and thermodynamic density
anomalies, including a diffusivity anomaly and a negative thermal expansion
coefficient. Density anomalies may therefore be related to structural changes
occurring at the jamming crossovers. Here we elucidate these structural
changes, investigating the evolution of the structure and of the mechanical
properties of a jammed system as its volume fraction varies from the jamming
transition to and beyond the first jamming crossover. We show that the first
jamming crossover occurs at a well defined volume fraction, and that it induces
a rearrangement of the force network causing a softening of the system. It also
causes qualitative changes in the normal mode density of states and the spatial
properties of the normal mode vectors.
